Transformer (deep learning architecture)

6833: 5058: 6817: 6809: 5132:, and each layer in a transformer model has multiple attention heads. While each attention head attends to the tokens that are relevant to each token, multiple attention heads allow the model to do this for different definitions of "relevance". In addition, the influence field representing relevance can become progressively dilated in successive layers. Many transformer attention heads encode relevance relations that are meaningful to humans. For example, some attention heads can attend mostly to the next word, while others mainly attend from verbs to their direct objects. The computations for each attention head can be performed in 3492: 3159: 3151: 3484: 5050: 3195: 6797: 6825: 960: 6575: 6164: 6440: 8146: 16425: 15501: 2156: 16405: 6178: 7763: 6082: 11420: 15511: 8935: 6435:{\displaystyle {\begin{aligned}{\text{given input vectors }}&h_{0},h_{1},\dots \\{\text{combine them into a matrix }}H&={\begin{bmatrix}h_{0}\\h_{1}\\\vdots \end{bmatrix}}\\{\text{EncoderLayer}}(H)&={\begin{bmatrix}{\text{FFN}}({\text{MultiheadedAttention}}(H,H,H)_{0})\\{\text{FFN}}({\text{MultiheadedAttention}}(H,H,H)_{1})\\\vdots \end{bmatrix}}\\\end{aligned}}} 5892: 11112: 8141:{\displaystyle {\text{RoPE}}{\big (}x_{m}^{(1)},x_{m}^{(2)},m{\big )}={\begin{pmatrix}\cos m\theta &-\sin m\theta \\\sin m\theta &\cos m\theta \end{pmatrix}}{\begin{pmatrix}x_{m}^{(1)}\\x_{m}^{(2)}\\\end{pmatrix}}={\begin{pmatrix}x_{m}^{(1)}\cos m\theta -x_{m}^{(2)}\sin m\theta \\x_{m}^{(2)}\cos m\theta +x_{m}^{(1)}\sin m\theta \\\end{pmatrix}}} 1196:(Luong et al, 2015) compared the relative performance of global (that of (Bahdanau et al, 2014)) and local (sliding window) attention model architectures for machine translation, and found that a mixed attention architecture had higher quality than global attention, while the use of a local attention architecture reduced translation time. 6750: 8752: 1128:. LSTM became the standard architecture for long sequence modelling until the 2017 publication of Transformers. However, LSTM still used sequential processing, like most other RNNs. Specifically, RNNs operate one token at a time from first to last; they cannot operate in parallel over all tokens in a sequence. 11107: 14258:

Chowdhery, Aakanksha; Narang, Sharan; Devlin, Jacob; Bosma, Maarten; Mishra, Gaurav; Roberts, Adam; Barham, Paul; Chung, Hyung Won; Sutton, Charles; Gehrmann, Sebastian; Schuh, Parker; Shi, Kensen; Tsvyashchenko, Sasha; Maynez, Joshua; Rao, Abhishek (2022-04-01). "PaLM: Scaling Language Modeling with

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ALiBi allows pretraining on short context windows, then finetuning on longer context windows. Since it is directly plugged into the attention mechanism, it can be combined with any positional encoder that is plugged into the "bottom" of the entire network (which is where the sinusoidal encoder on the

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A "decoder-only" Transformer is not literally decoder-only, since without an encoder, the cross-attention mechanism has nothing to attend to. Thus, the decoder layers in a decoder-only Transformer is composed of just two sublayers: the causally masked self-attention, and the feedforward network. This

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Transformer layers, which carry out repeated transformations on the vector representations, extracting more and more linguistic information. These consist of alternating attention and feedforward layers. There are two major types of transformer layers: encoder layers and decoder layers, with further

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controller (1992) learns to compute a weight matrix for further processing depending on the input. One of its two networks has "fast weights" or "dynamic links" (1981). A slow neural network learns by gradient descent to generate keys and values for computing the weight changes of the fast neural

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Transformers are used in large language models for autoregressive sequence generation: generating a stream of text, one token at a time. However, in most settings, decoding from language models is memory-bound, meaning that we have spare compute power available. Speculative decoding uses this spare

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As the Transformer architecture natively processes numerical data, not text, there must be a translation between text and tokens. A token is an integer that represents a character, or a short segment of characters. On the input side, the input text is parsed into a token sequence. Similarly, on the

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In a prefixLM task, the sequence is divided into two parts. The first part is presented as context, and the model predicts the first token of the second part. Then that would be revealed, and the model predicts the second token, and so on. The loss function for the task is still typically the same.

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The plain transformer architecture had difficulty converging. In the original paper the authors recommended using learning rate warmup. That is, the learning rate should linearly scale up from 0 to maximal value for the first part of the training (usually recommended to be 2% of the total number of

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Wolf, Thomas; Debut, Lysandre; Sanh, Victor; Chaumond, Julien; Delangue, Clement; Moi, Anthony; Cistac, Pierric; Rault, Tim; Louf, Remi; Funtowicz, Morgan; Davison, Joe; Shleifer, Sam; von Platen, Patrick; Ma, Clara; Jernite, Yacine; Plu, Julien; Xu, Canwen; Le Scao, Teven; Gugger, Sylvain; Drame,

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to an image. Parti is an encoder-decoder Transformer, where the encoder processes a text prompt, and the decoder generates a token representation of an image. Muse is an encoder-only Transformer that is trained to predict masked image tokens from unmasked image tokens. During generation, all input

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The original Transformer paper reported using a learned positional encoding, but finding it not superior to the sinusoidal one. Later, found that causal masking itself provides enough signal to a Transformer decoder that it can learn to implicitly perform absolute positional encoding without the

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Like the first encoder, the first decoder takes positional information and embeddings of the output sequence as its input, rather than encodings. The transformer must not use the current or future output to predict an output, so the output sequence must be partially masked to prevent this reverse

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The purpose of each encoder layer is to create contextualized representations of the tokens, where each representation corresponds to a token that "mixes" information from other input tokens via self-attention mechanism. Each decoder layer contains two attention sublayers: (1) cross-attention for

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where the first columns correspond to the "prefix", and the subsequent columns correspond to the autoregressively generated text based on the prefix. They resemble encoder-decoder models, but has less "sparsity". Such models are rarely used, though they are cited as theoretical possibilities and

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Key advancements in FlashAttention-2 include the reduction of non-matmul FLOPs, improved parallelism over the sequence length dimension, better work partitioning between GPU warps, and added support for head dimensions up to 256 and multi-query attention (MQA) and grouped-query attention (GQA).

1182:-size output vector, which was then processed by another recurrent network into an output. If the input is long, then the output vector would not be able to contain all relevant information, and the output quality degrades. As evidence, reversing the input sentence improved seq2seq translation. 6585:

Each decoder consists of three major components: a causally masked self-attention mechanism, a cross-attention mechanism, and a feed-forward neural network. The decoder functions in a similar fashion to the encoder, but an additional attention mechanism is inserted which instead draws relevant

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Each encoder layer consists of two major components: a self-attention mechanism and a feed-forward layer. It takes an input as a sequence of input vectors, applies the self-attention mechanism, to produce an intermediate sequence of vectors, then applies the feed-forward layer for each vector

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Dosovitskiy, Alexey; Beyer, Lucas; Kolesnikov, Alexander; Weissenborn, Dirk; Zhai, Xiaohua; Unterthiner, Thomas; Dehghani, Mostafa; Minderer, Matthias; Heigold, Georg; Gelly, Sylvain; Uszkoreit, Jakob (2021-06-03). "An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale".

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tokens are masked, and the highest-confidence predictions are included for the next iteration, until all tokens are predicted. Phenaki is a text-to-video model. It is a bidirectional masked transformer conditioned on pre-computed text tokens. The generated tokens are then decoded to a video.

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The original 2017 Transformer used the post-LN convention. It was difficult to train and required careful hyperparameter tuning and a "warm-up" in learning rate, where it starts small and gradually increases. The pre-LN convention was developed in 2020, which was found to be easier to train,

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The encoder layers are stacked. The first encoder layer takes the sequence of input vectors from the embedding layer, producing a sequence of vectors. This sequence of vectors is processed by the second encoder, and so on. The output from the final encoder layer is then used by the decoder.

11659: 8703: 9530: 9146: 6077:{\displaystyle M_{\text{causal}}={\begin{bmatrix}0&-\infty &-\infty &\dots &-\infty \\0&0&-\infty &\dots &-\infty \\0&0&0&\dots &-\infty \\\vdots &\vdots &\vdots &\ddots &\vdots \\0&0&0&\dots &0\end{bmatrix}}} 6782:

The last decoder is followed by a final un-embedding layer. to produce the output probabilities over the vocabulary. Then, one of the tokens is sampled according to the probability, and the decoder can be run again to produce the next token, etc, autoregressively generating output text.

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Choromanski, Krzysztof; Likhosherstov, Valerii; Dohan, David; Song, Xingyou; Gane, Andreea; Sarlos, Tamas; Hawkins, Peter; Davis, Jared; Belanger, David; Colwell, Lucy; Weller, Adrian (2020-09-30). "Masked Language Modeling for Proteins via Linearly Scalable Long-Context Transformers".

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In an autoregressive task, the entire sequence is masked at first, and the model produces a probability distribution for the first token. Then the first token is revealed and the model predicts the second token, and so on. The loss function for the task is still typically the same. The

1211:. The new model was a seq2seq model where the encoder and the decoder were both 8 layers of bidirectional LSTM. It took nine months to develop, and it achieved a higher level of performance than the statistical approach, which took ten years to develop. In the same year, self-attention 11415:{\displaystyle {\text{Attention}}(q,K,V)={\text{softmax}}\left({\frac {qK^{\mathrm {T} }}{\sqrt {d_{k}}}}\right)V\approx {\frac {\varphi (q)^{T}\sum _{i}e^{\|k_{i}\|^{2}/2\sigma ^{2}}\varphi (k_{i})v_{i}^{T}}{\varphi (q)^{T}\sum _{i}e^{\|k_{i}\|^{2}/2\sigma ^{2}}\varphi (k_{i})}}} 11773:

Multimodal models can either be trained from scratch, or by finetuning. A 2022 study found that Transformers pretrained only on natural language can be finetuned on only 0.03% of parameters and become competitive with LSTMs on a variety of logical and visual tasks, demonstrating

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Jaegle, Andrew; Borgeaud, Sebastian; Alayrac, Jean-Baptiste; Doersch, Carl; Ionescu, Catalin; Ding, David; Koppula, Skanda; Zoran, Daniel; Brock, Andrew; Shelhamer, Evan; Hénaff, Olivier (2021-08-02). "Perceiver IO: A General Architecture for Structured Inputs & Outputs".

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There are also mixed seq2seq models. For example, in 2020, Google Translate replaced the previous RNN-encoder–RNN-decoder model by a Transformer-encoder–RNN-decoder model, on the argument that an RNN-decoder runs much faster than Transformer-decoder when run autoregressively.

4930: 1585: 6608: 11816:(2021), Parti (2022), Phenaki (2023), and Muse (2023). Unlike later models, DALL-E is not a diffusion model. Instead, it uses a decoder-only Transformer that autoregressively generates a text, followed by the token representation of an image, which is then converted by a 3128:. This allows the transformer to take any encoded position and find a linear sum of the encoded locations of its neighbors. This sum of encoded positions, when fed into the attention mechanism, would create attention weights on its neighbors, much like what happens in a 7479: 6856:(LayerNorm, or LN), which while conceptually unnecessary, are necessary for numerical stability and convergence. Similarly to how the feedforward network modules are applied individually to each vector, the LayerNorm is also applied individually to each vector. 1286:

Already in spring 2017, even before the "Attention is all your need" preprint was published, one of the co-authors applied the "decoder-only" variation of the architecture to generate fictitious Knowledge articles. Transformer architecture is now used in many

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If a transformer is used with a baked-in prompt, such as , then the key and value vectors can be computed for the prompt, and saved on disk. The saving in compute is significant when the model is used for many short interactions, such as in online chatbots.

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architecture. The encoder consists of encoding layers that process all the input tokens together one layer after another, while the decoder consists of decoding layers that iteratively process the encoder's output and the decoder's output tokens so far.

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word of the source text was processed. Although in theory such a vector retains the information about the whole original sentence, in practice the information is poorly preserved, since the input is processed sequentially by one recurrent network into a

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An improved version, FlashAttention-2, was developed to cater to the rising demand for language models capable of handling longer context lengths. It offers enhancements in work partitioning and parallelism, enabling it to achieve up to 230 TFLOPs/s on

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In general, there are 3 classes of language modelling tasks: "masked", "autoregressive", and "prefixLM". These classes are independent of a specific modeling architecture such as Transformer, but they are often discussed in the context of Transformer.

1278:, by removing its recurrence to process all tokens in parallel, but preserving its dot-product attention mechanism to keep its text processing performance. Its parallelizability was an important factor to its widespread use in large neural networks. 10811: 10400:

Ordinary transformers require a memory size that is quadratic in the size of the context window. Attention-free transformers reduce this to a linear dependence while still retaining the advantages of a transformer by linking the key to the value.

8930:{\displaystyle B={\begin{pmatrix}0&1&2&3&\cdots \\-1&0&1&2&\cdots \\-2&-1&0&1&\cdots \\-3&-2&-1&0&\cdots \\\vdots &\vdots &\vdots &\vdots &\ddots \\\end{pmatrix}}} 8400: 9890:

In speculative decoding, a smaller model or some other simple heuristic is used to generate a few speculative tokens that are subsequently verified by the larger model. For example, suppose a small model generated four speculative tokens:

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The idea of encoder-decoder sequence transduction had been developed in the early 2010s (see for previous papers). The papers most commonly cited as the originators that produced seq2seq are two concurrently published papers from 2014.

1318:(2018), an encoder-only Transformer model. In 2019 October, Google started using BERT to process search queries. In 2020, Google Translate replaced the previous RNN-encoder–RNN-decoder model by a Transformer-encoder–RNN-decoder model. 6535: 11525: 8594: 9367: 9040: 12270:

Parisotto, Emilio; Song, Francis; Rae, Jack; Pascanu, Razvan; Gulcehre, Caglar; Jayakumar, Siddhant; Jaderberg, Max; Kaufman, Raphaël Lopez; Clark, Aidan; Noury, Seb; Botvinick, Matthew; Heess, Nicolas; Hadsell, Raia (2020-11-21).

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Gulati, Anmol; Qin, James; Chiu, Chung-Cheng; Parmar, Niki; Zhang, Yu; Yu, Jiahui; Han, Wei; Wang, Shibo; Zhang, Zhengdong; Wu, Yonghui; Pang, Ruoming (2020). "Conformer: Convolution-augmented Transformer for Speech Recognition".

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incorporating the output of encoder (contextualized input token representations), and (2) self-attention for "mixing" information among the input tokens to the decoder (i.e. the tokens generated so far during inference time).

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For non-greedy decoding, similar ideas apply, except the speculative tokens are accepted or rejected stochastically, in a way that guarantees the final output distribution is the same as if speculative decoding was not used.

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Specifically, consider a transformer model like GPT-3 with a context window size of 512. To generate an entire context window autoregressively with greedy decoding, it must be run for 512 times, each time generating a token

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Raffel, Colin; Shazeer, Noam; Roberts, Adam; Lee, Katherine; Narang, Sharan; Matena, Michael; Zhou, Yanqi; Li, Wei; Liu, Peter J. (2019). "Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer".

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Chang, Huiwen; Zhang, Han; Barber, Jarred; Maschinot, A. J.; Lezama, Jose; Jiang, Lu; Yang, Ming-Hsuan; Murphy, Kevin; Freeman, William T. (2023-01-02). "Muse: Text-To-Image Generation via Masked Generative Transformers".

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judging the pragmatic acceptability of natural language. For example, the following sentence might be judged "not acceptable", because even though it is syntactically well-formed, it is improbable in ordinary human usage:

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In contrast, the cross-attention mechanism attends to the output vectors of the encoder, which is computed before the decoder starts decoding. Consequently, there is no need for masking in the cross-attention mechanism.

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Seq2seq models with attention (including self-attention) still suffered from the same issue with recurrent networks, which is that they are hard to parallelize, which prevented them to be accelerated on GPUs. In 2016,

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Tay, Yi; Dehghani, Mostafa; Abnar, Samira; Shen, Yikang; Bahri, Dara; Pham, Philip; Rao, Jinfeng; Yang, Liu; Ruder, Sebastian; Metzler, Donald (2020-11-08). "Long Range Arena: A Benchmark for Efficient Transformers".

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An "encoder-decoder" Transformer is generally the same as the original Transformer, with 2 sublayers per encoder layer and 3 sublayers per decoder layer, etc. They might have minor architectural improvements, such as

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Each encoder layer contains 2 sublayers: the self-attention and the feedforward network. Each decoder layer contains 3 sublayers: the causally masked self-attention, the cross-attention, and the feedforward network.

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Benchmarks revealed FlashAttention-2 to be up to 2x faster than FlashAttention and up to 9x faster than a standard attention implementation in PyTorch. Future developments include optimization for new hardware like

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Note that while each of these tasks is trivial or obvious for human native speakers of the language (or languages), they have typically proved challenging for previous generations of machine learning architecture.

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An un-embedding layer is almost the reverse of an embedding layer. Whereas an embedding layer converts a token into a vector, an un-embedding layer converts a vector into a probability distribution over tokens.

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Ainslie, Joshua; Lee-Thorp, James; de Jong, Michiel; Zemlyanskiy, Yury; Lebrón, Federico; Sanghai, Sumit (2023-12-23). "GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints".

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A standard Transformer architecture, showing on the left an encoder, and on the right a decoder. Note: it uses the pre-LN convention, which is different from the post-LN convention used in the original 2017

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Xiong, Ruibin; Yang, Yunchang; He, Di; Zheng, Kai; Zheng, Shuxin; Xing, Chen; Zhang, Huishuai; Lan, Yanyan; Wang, Liwei; Liu, Tie-Yan (2020-06-29). "On Layer Normalization in the Transformer Architecture".

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Nguyen, Toan Q.; Salazar, Julian (2019-11-02). Niehues, Jan; Cattoni, Rolando; Stüker, Sebastian; Negri, Matteo; Turchi, Marco; Ha, Thanh-Le; Salesky, Elizabeth; Sanabria, Ramon; Barrault, Loic (eds.).

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When an autoregressive transformer is used for inference, such as generating text, the query vector is different at each step, but the already-computed key and value vectors are always the same. The

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text generation. For decoding, all-to-all attention is inappropriate, because a token cannot attend to tokens not yet generated. Thus, the self-attention module in the decoder is causally masked.

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is the distance one wishes to shift. This allows the transformer to take any encoded position, and find the encoding of the position n-steps-ahead or n-steps-behind, by a matrix multiplication.

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for additional processing of their outputs and contain residual connections and layer normalization steps. These feed-forward layers contain most of the parameters in a Transformer model.

6745:{\displaystyle {\begin{aligned}H'&={\text{MaskedMultiheadedAttention}}(H,H,H)\\{\text{DecoderLayer}}(H)&={\text{FFN}}({\text{MultiheadedAttention}}(H',H^{E},H^{E}))\end{aligned}}} 9232: 3615: 11520: 6129: 2943: 9838: 3894: 3808: 1508:

In a masked task, one or more of the tokens is masked out, and the model would produce a probability distribution predicting what the masked-out tokens are based on the context. The

1110:(1995), a RNN which used various innovations to overcome the vanishing gradient problem, allowing efficient learning of long-sequence modelling. One key innovation was the use of an 12353:

Ruoss, Anian; Delétang, Grégoire; Medapati, Sourabh; Grau-Moya, Jordi; Wenliang, Li; Catt, Elliot; Reid, John; Genewein, Tim (2024-02-07). "Grandmaster-Level Chess Without Search".

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Villegas, Ruben; Babaeizadeh, Mohammad; Kindermans, Pieter-Jan; Moraldo, Hernan; Zhang, Han; Saffar, Mohammad Taghi; Castro, Santiago; Kunze, Julius; Erhan, Dumitru (2022-09-29).

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adapt the transformer to computer vision by breaking down input images as a series of patches, turning them into vectors, and treating them like tokens in a standard transformer.

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is encoder-only. They are less often used currently, as they were found to be not significantly better than training an encoder-decoder Transformer, then taking just the encoder.

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By convention, we write all vectors as row vectors. This, for example, means that pushing a vector through a linear layer means multiplying it by a weight matrix on the right, as

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An "encoder-only" Transformer applies the encoder to map an input text into a sequence of vectors that represent the input text. This is usually used for text embedding and

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A positional encoding is a fixed-size vector representation of the relative positions of tokens within a sequence: it provides the transformer model with information about

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A "prefixLM" (prefix language model) is a decoder-only architecture, but with prefix masking, which is different from causal masking. Specifically, it has mask of the form

6557: 6464: 3421:(BERT). It is typically larger than the embedding size. For example, in both GPT-2 series and BERT series, the intermediate size of a model is 4 times its embedding size: 9570: 8980: 16299: 9771:

in CPUs, future tokens are computed concurrently, by speculating on the value of previous tokens, and are later discarded if it turns out the speculation was incorrect.

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Jaegle, Andrew; Gimeno, Felix; Brock, Andrew; Zisserman, Andrew; Vinyals, Oriol; Carreira, Joao (2021-06-22). "Perceiver: General Perception with Iterative Attention".

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Devlin, Jacob; Chang, Ming-Wei; Lee, Kenton; Toutanova, Kristina (11 October 2018). "BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding".

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Choromanski, Krzysztof; Likhosherstov, Valerii; Dohan, David; Song, Xingyou; Gane, Andreea; Sarlos, Tamas; Hawkins, Peter; Davis, Jared; Mohiuddin, Afroz (2022-11-19),

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Devlin, Jacob; Chang, Ming-Wei; Lee, Kenton; Toutanova, Kristina (11 October 2018). "BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding".

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In words, it means that each token can pay attention to itself, and every token before it, but not any after it. As an example of an uncommon use of mask matrix, the

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Modern Transformers overcome this problem, but unlike RNNs, they require computation time that is quadratic in the size of the context window. The linearly scaling

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Radford, Alec; Kim, Jong Wook; Xu, Tao; Brockman, Greg; McLeavey, Christine; Sutskever, Ilya (2022). "Robust Speech Recognition via Large-Scale Weak Supervision".

11102:{\displaystyle e^{\langle x,y\rangle /\sigma ^{2}}=\mathbb {E} \approx \langle e^{\|x\|^{2}/2\sigma ^{2}}\varphi (x),e^{\|y\|^{2}/2\sigma ^{2}}\varphi (y)\rangle } 10395: 6566:

As the encoder processes the entire input all at once, every token can attend to every other token (all-to-all attention), so there is no need for causal masking.

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Radford, Alec; Jong Wook Kim; Xu, Tao; Brockman, Greg; McLeavey, Christine; Sutskever, Ilya (2022). "Robust Speech Recognition via Large-Scale Weak Supervision".

5710: 9840:. However, if we had some educated guess for the values of these tokens, we could verify all of them in parallel, in one run of the model, by checking that each 8328: 1672: 15052:

Ferrando, Javier; Sarti, Gabriele; Bisazza, Arianna; Costa-jussà, Marta R. (2024-05-01). "A Primer on the Inner Workings of Transformer-based Language Models".

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Zhai, Shuangfei; Talbott, Walter; Srivastava, Nitish; Huang, Chen; Goh, Hanlin; Zhang, Ruixiang; Susskind, Josh (2021-09-21). "An Attention Free Transformer".

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Contribution), Woosuk Kwon*, Zhuohan Li*, Siyuan Zhuang, Ying Sheng, Lianmin Zheng, Cody Yu, Joey Gonzalez, Hao Zhang, and Ion Stoica (* Equal (2023-06-20).

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demonstrate the ability of transformers to perform a wide variety of NLP-related subtasks and their related real-world or practical applications, including:

8548:{\displaystyle {\text{RoPE}}{\big (}x,m{\big )}^{T}{\text{RoPE}}{\big (}y,n{\big )}={\text{RoPE}}{\big (}x,m+k{\big )}^{T}{\text{RoPE}}{\big (}y,n+k{\big )}} 8229: 14043:

Su, Jianlin; Lu, Yu; Pan, Shengfeng; Murtadha, Ahmed; Wen, Bo; Liu, Yunfeng (2021-04-01). "RoFormer: Enhanced Transformer with Rotary Position Embedding".

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Chung, Junyoung; Gulcehre, Caglar; Cho, KyungHyun; Bengio, Yoshua (2014). "Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling".

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Chen, Lili; Lu, Kevin; Rajeswaran, Aravind; Lee, Kimin; Grover, Aditya; Laskin, Michael; Abbeel, Pieter; Srinivas, Aravind; Mordatch, Igor (2021-06-24),

11803:, which is then treated like an image, i.e. broken down into a series of patches, turned into vectors and treated like tokens in a standard transformer. 10176:

Training transformer-based architectures can be expensive, especially for long inputs. Many methods have been developed to attempt to address the issue.

9894: 858: 12422: 5879:{\displaystyle {\begin{aligned}{\text{MaskedAttention}}(Q,K,V)={\text{softmax}}\left(M+{\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}\right)V\end{aligned}}} 15547: 14745: 14131: 13331:

Esser, Patrick; Kulal, Sumith; Blattmann, Andreas; Entezari, Rahim; Müller, Jonas; Saini, Harry; Levi, Yam; Lorenz, Dominik; Sauer, Axel (2024-03-05),

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Array of probability distributions, with shape (decoder vocabulary size x length(decoder output sequence)) /* encoder */ z_e ← encoder.tokenizer(t_e)

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Kariampuzha, William; Alyea, Gioconda; Qu, Sue; Sanjak, Jaleal; Mathé, Ewy; Sid, Eric; Chatelaine, Haley; Yadaw, Arjun; Xu, Yanji; Zhu, Qian (2023).

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Peng, Bo; Alcaide, Eric; Anthony, Quentin; Albalak, Alon; Arcadinho, Samuel; Biderman, Stella; Cao, Huanqi; Cheng, Xin; Chung, Michael (2023-12-10),

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represents no attention paid, the linear bias matrix increases attention paid in one direction and decreases attention paid in the other direction.

7018: 6870: 2829: 2011: 16141: 14508: 14374: 12973:

Parikh, Ankur P.; Täckström, Oscar; Das, Dipanjan; Uszkoreit, Jakob (2016-09-25). "A Decomposable Attention Model for Natural Language Inference".

11654:{\displaystyle {\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}\right)V\approx Q(K^{T}V/{\sqrt {d_{k}}})} 8698:{\displaystyle {\begin{aligned}{\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}+sB\right)V\end{aligned}}} 699: 14064:

Press, Ofir; Smith, Noah A.; Lewis, Mike (2021-08-01). "Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation".

13504:

Tay, Yi; Dehghani, Mostafa; Tran, Vinh Q.; Garcia, Xavier; Wei, Jason; Wang, Xuezhi; Chung, Hyung Won; Shakeri, Siamak; Bahri, Dara (2023-02-28),

9525:{\displaystyle {\text{MultiheadedAttention}}(Q,K,V)={\text{Concat}}_{i\in }\left({\text{Attention}}(XW_{i}^{Q},XW_{i}^{K},XW_{i}^{V})\right)W^{O}} 9141:{\displaystyle {\begin{aligned}{\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}+B\right)V\end{aligned}}} 2222: 1263:

you need". That hypothesis was against conventional wisdom of the time, and even his father, a well-known computational linguist, was skeptical.

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Raffel, Colin; Shazeer, Noam; Roberts, Adam; Lee, Katherine; Narang, Sharan; Matena, Michael; Zhou, Yanqi; Li, Wei; Liu, Peter J. (2020-01-01).

12566: 12222:

Luong, Minh-Thang; Pham, Hieu; Manning, Christopher D. (August 17, 2015). "Effective Approaches to Attention-based Neural Machine Translation".

4706:{\displaystyle {\begin{aligned}{\text{Attention}}(Q,K,V)={\text{softmax}}\left({\frac {QK^{\mathrm {T} }}{\sqrt {d_{k}}}}\right)V\end{aligned}}} 13804: 906: 14943:

Yu, Jiahui; Xu, Yuanzhong; Koh, Jing Yu; Luong, Thang; Baid, Gunjan; Wang, Zirui; Vasudevan, Vijay; Ku, Alexander; Yang, Yinfei (2022-06-21),

14280:

Kwon, Woosuk; Li, Zhuohan; Zhuang, Siyuan; Sheng, Ying; Zheng, Lianmin; Yu, Cody Hao; Gonzalez, Joseph; Zhang, Hao; Stoica, Ion (2023-10-23).

11770:

Transformers can also be used/adapted for modalities (input or output) beyond just text, usually by finding a way to "tokenize" the modality.

12887:

Wu, Yonghui; et al. (2016-09-01). "Google's Neural Machine Translation System: Bridging the Gap between Human and Machine Translation".

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Cho, Kyunghyun; van Merriënboer, Bart; Gulcehre, Caglar; Bahdanau, Dzmitry; Bougares, Fethi; Schwenk, Holger; Bengio, Yoshua (October 2014).

6832: 1955:

The token embedding vectors are added to their respective positional encoding vectors (see below), producing the sequence of input vectors.

1132: 13060: 10416: 11850: 10694: 863: 714: 13755:

Raffel, Colin; Shazeer, Noam; Roberts, Adam; Lee, Katherine; Narang, Sharan; Matena, Michael; Zhou, Yanqi; Li, Wei; Liu, Peter J. (2020).

13165: 4991: 9725:{\displaystyle {\text{MultiQueryAttention}}(Q,K,V)={\text{Concat}}_{i\in }\left({\text{Attention}}(XW_{i}^{Q},XW^{K},XW^{V})\right)W^{O}} 445: 4449:, which is useful for training due to computational matrix operation optimizations that quickly compute matrix operations. The matrices 13315: 12201:

Bahdanau; Cho, Kyunghyun; Bengio, Yoshua (September 1, 2014). "Neural Machine Translation by Jointly Learning to Align and Translate".

5666:

It may be necessary to cut out attention links between some word-pairs. For example, the decoder, when decoding for the token position

5320:{\displaystyle {\text{MultiheadedAttention}}(Q,K,V)={\text{Concat}}_{i\in }({\text{Attention}}(XW_{i}^{Q},XW_{i}^{K},XW_{i}^{V}))W^{O}} 946: 749: 4938: 4925:{\displaystyle \ell _{\text{seq, key}}=\ell _{\text{seq, value}},\;d_{\text{query}}=d_{\text{key}},\;d_{\text{value}}=d_{\text{head}}} 14636:

Peng, Hao; Pappas, Nikolaos; Yogatama, Dani; Schwartz, Roy; Smith, Noah A.; Kong, Lingpeng (2021-03-19). "Random Feature Attention".

12866:

Luong, Minh-Thang; Pham, Hieu; Manning, Christopher D. (2015). "Effective Approaches to Attention-based Neural Machine Translation".

5601: 3590:

The module takes three sequences, a query sequence, a key sequence, and a value sequence. The query sequence is a sequence of length

2208:

the words are in the input sequence. Without positional encoding, the model would be unable to process input sequence as more than a

15026: 14919:

Ramesh, Aditya; Pavlov, Mikhail; Goh, Gabriel; Gray, Scott; Voss, Chelsea; Radford, Alec; Chen, Mark; Sutskever, Ilya (2021-02-26),

1580:{\displaystyle {\text{Loss}}=-\sum _{t\in {\text{masked tokens}}}\ln({\text{probability of }}t{\text{ conditional on its context}})} 1166:

is another LSTM that converts the vector into a sequence of tokens. Similarly, (Cho et al, 2014) was 130M-parameter model that used

10410: 1644:

The following description follows exactly the Transformer as described in the original paper. There are variants, described in the

15657: 13597: 825: 14530: 13868: 13694: 12834: 12779:

Gruber, N.; Jockisch, A. (2020), "Are GRU cells more specific and LSTM cells more sensitive in motive classification of text?",

1185:(Bahdanau et al, 2014) introduced an attention mechanism to seq2seq for machine translation to solve the bottleneck problem (of 15540: 13197: 7474:{\displaystyle M_{\text{prefixLM}}={\begin{bmatrix}\mathbf {0} &-\infty \\\mathbf {0} &M_{\text{causal}}\end{bmatrix}}} 6800:(a) One encoder layer and one decoder layer. (b) Two encoder layers and two decoder layers. The sublayers are labelled as well. 1693:

output side, the output tokens are parsed back to text. The module doing the conversion between token sequences and texts is a

374: 16464: 14311: 12606:

Christoph von der Malsburg: The correlation theory of brain function. Internal Report 81-2, MPI Biophysical Chemistry, 1981.

12496: 12177: 3770: 12998: 12083: 9746:

method saves the computed key and value vectors at each attention block, so that they are not recomputed at each new token.

3955: 2104: 16330: 14213:"Introducing Together AI Chief Scientist Tri Dao, as he releases FlashAttention-2 to speed up model training and inference" 9326:

of a GPU, and by careful management of the blocks it minimizes data copying between GPU caches (as data movement is slow).

1864: 997: 883: 646: 181: 12619:

Jerome A. Feldman, "Dynamic connections in neural networks," Biological Cybernetics, vol. 46, no. 1, pp. 27-39, Dec. 1982.

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Chen, Charlie; Borgeaud, Sebastian; Irving, Geoffrey; Lespiau, Jean-Baptiste; Sifre, Laurent; Jumper, John (2023-02-02),

11792: 1388:(instead of after) multiheaded attention and feedforward layers stabilizes training, not requiring learning rate warmup. 1136:

network which computes answers to queries. This was later shown to be equivalent to the unnormalized linear Transformer.

901: 13672: 8591:

positional encoder that is directly plugged into the attention mechanism. Specifically, the ALiBi attention mechanism is

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leaves the model's state at the end of a long sentence without precise, extractable information about preceding tokens.

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Un-embedding layer, which converts the final vector representations back to a probability distribution over the tokens.

1596: 1322: 1288: 1099:(1990). In theory, the information from one token can propagate arbitrarily far down the sequence, but in practice the 1065: 734: 709: 658: 5495:

As an example, in the smallest GPT-2 model, there are only self-attention mechanisms. It has the following dimensions:

989: 16243: 15870: 15677: 15533: 13116: 9318:

FlashAttention is an algorithm that implements the transformer attention mechanism efficiently on a GPU. It performs

8333: 8151: 3712: 1255:

with an order of magnitude less parameters than LSTMs. One of its authors, Jakob Uszkoreit, suspected that attention

1204: 782: 777: 430: 12737:

Sutskever, Ilya; Vinyals, Oriol; Le, Quoc Viet (14 Dec 2014). "Sequence to sequence learning with neural networks".

5068: 3424: 3135:. In the author's words, "we hypothesized it would allow the model to easily learn to attend by relative position." 1010:

Transformers have the advantage of having no recurrent units, and therefore require less training time than earlier

16198: 13554: 9282:. This is contrasted with the original sinusoidal positional encoding, which is an "absolute positional encoding". 5350: 1233: 440: 78: 12485:

Parallel Distributed Processing, Volume 1: Explorations in the Microstructure of Cognition: Foundations, Chapter 2

6582:

A decoder consists of an embedding layer, followed by multiple decoder layers, followed by an un-embedding layer.

5886:

A non-masked attention module can be thought of as a masked attention module where the mask has all entries zero.

3094:{\displaystyle \sum _{j}c_{j}f(t+\Delta t_{j})=\left(\sum _{j}c_{j}\,\mathrm {diag} (f(\Delta t_{j}))\right)f(t)} 1730:. When faced with tokens outside the vocabulary, typically a special token is used, written as "" for "unknown". 1208: 14085:

Shaw, Peter; Uszkoreit, Jakob; Vaswani, Ashish (2018). "Self-Attention with Relative Position Representations".

12378:

Mariama; Lhoest, Quentin; Rush, Alexander (2020). "Transformers: State-of-the-Art Natural Language Processing".

10164:

is completely discarded. The process then repeats (starting from the 4th token) until all tokens are generated.

2826:

The main reason for using this positional encoding function is that using it, shifts are linear transformations:

16385: 16325: 15923: 3593: 1428: 939: 835: 599: 420: 14586: 12653: 11474: 7391: 7363: 7343:

The Transformer architecture, being modular, allows variations. Several common variations are described here.

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For example, the following matrix is commonly used in decoder self-attention modules, called "causal masking":

3138:

In typical implementations, all operations are done over the real numbers, not the complex numbers, but since

2917: 1189:

output vector), allowing the model to process long-distance dependencies more easily. They called their model

15918: 15607: 12380:

Proceedings of the 2020 Conference on Empirical Methods in Natural Language Processing: System Demonstrations

9778: 3856: 2474:{\displaystyle (f(t)_{2k},f(t)_{2k+1})=(\sin(\theta ),\cos(\theta ))\quad \forall k\in \{0,1,\ldots ,d/2-1\}} 810: 512: 288: 12414: 6963: 1170:(GRU) instead of LSTM. Later research showed that GRUs are neither better nor worse than LSTMs for seq2seq. 16360: 15757: 15714: 15667: 15662: 11930: 9291: 3813: 3620: 3503: 3129: 1706: 1349: 1081: 1004: 981: 767: 704: 614: 592: 435: 425: 20: 13446: 12925: 5136:, which allows for fast processing. The outputs for the attention layer are concatenated to pass into the 5057: 3650: 16411: 15707: 15633: 15403: 11893: 11830: 11425: 10180:(2020) is a standard benchmark for comparing the behavior of transformer architectures over long inputs. 7387: 7371: 7359: 6841: 3403: 1404: 1326: 1173:

These early seq2seq models had no attention mechanism, and the state vector is accessible only after the

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Liu, Zhuang; Mao, Hanzi; Wu, Chao-Yuan; Feichtenhofer, Christoph; Darrell, Trevor; Xie, Saining (2022).

11522:

first, then multiply it with the query. In essence, we have managed to obtain a more precise version of

8397:

The benefit of RoPE is that the dot-product between two vectors depends on their relative location only:

16035: 15970: 15571: 14500: 11716: 10649: 10322: 9175: 5137: 5041:. It is theoretically possible for all three to be different, but that is rarely the case in practice. 3902: 3257: 3183: 1407:

on a small task-specific dataset. The pretrain dataset is typically an unlabeled large corpus, such as

1361: 1244: 1100: 878: 805: 555: 450: 238: 171: 131: 12444: 11778:. The LLaVA was a vision-language model composed of a language model (Vicuna-13B) and a vision model ( 10131: 10095: 10032: 9996: 4784: 4724: 4335: 4255: 1499: 16436: 16294: 15933: 15764: 15587: 15514: 15460: 13693:

Yang, Zhilin; Dai, Zihang; Yang, Yiming; Carbonell, Jaime; Salakhutdinov, Russ R; Le, Quoc V (2019).

11916:

Beyond traditional NLP, the transformer architecture has had success in other applications, such as:

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RoPE (rotary positional embedding), is best explained by considering a list of 2-dimensional vectors

6816: 6808: 5569: 5468: 4814: 4126: 1267: 985: 932: 538: 306: 176: 14880: 13796: 13649:

Proceedings of the 2019 ACL Workshop BlackboxNLP: Analyzing and Interpreting Neural Networks for NLP

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z_d ← layer.layer_norm(z_d) z_d ← layer.masked_multiheaded_attention(z_d, z_d, z_d)

4754: 4445:

The attention calculation for all tokens can be expressed as one large matrix calculation using the

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Kitaev, Nikita; Kaiser, Łukasz; Levskaya, Anselm (2020). "Reformer: The Efficient Transformer".

7117:

The following is the pseudocode for a standard pre-LN encoder-decoder Transformer, adapted from

6586:

information from the encodings generated by the encoders. This mechanism can also be called the

16340: 16100: 15819: 15814: 15335: 15190: 12697:"Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation" 10286: 9237: 7523: 7507: 2785: 1633:

Embedding layer, which converts tokens and positions of the tokens into vector representations.

1155: 1107: 1053: 1015: 1007:

allowing the signal for key tokens to be amplified and less important tokens to be diminished.

687: 663: 565: 326: 301: 261: 73: 14000:

Gehring, Jonas; Auli, Michael; Grangier, David; Yarats, Denis; Dauphin, Yann N. (2017-07-17).

12701:

Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP)

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This has a neutral effect on model quality and training speed, but increases inference speed.

9005: 7283:

z_d ← layer.layer_norm(z_d) z_d ← layer.multiheaded_attention(z_d, z_e, z_e)

5735: 16370: 16355: 16320: 16008: 15908: 15776: 15391: 15202: 14867: 12610:

See Reprint in Models of Neural Networks II, chapter 2, pages 95-119. Springer, Berlin, 1994.

12021: 11989: 11858: 9768: 7743: 7351: 3473: 2594: 1588: 1315: 1069: 641: 463: 415: 271: 186: 58: 16238: 13619: 12562: 12112: 4395: 4123:. The attention weights are divided by the square root of the dimension of the key vectors, 3998: 3506:

units. For each unit, the transformer model learns three weight matrices: the query weights

3158: 16390: 16345: 15791: 15736: 15582: 15577: 15256: 14021:

Transformer Language Models without Positional Encodings Still Learn Positional Information

11983: 11904: 11834: 10068: 9843: 6755: 6595: 6530:{\displaystyle {\text{EncoderLayer}}(H)={\text{FFN}}({\text{MultiheadedAttention}}(H,H,H))} 5438: 4586: 4559: 4532: 4188: 4161: 4099: 4072: 3685: 3563: 3536: 3509: 3385: 3104: 1334: 1167: 1019: 1001: 570: 520: 10371: 7518:

The normalization used in the Transformer can be different from LayerNorm. One example is

2948:

By taking a linear sum, any convolution can also be implemented as linear transformations:

1266:

In 2017, the original (100M-sized) encoder-decoder transformer model was proposed in the "

8: 15965: 15943: 15692: 15687: 15645: 15597: 15466: 15023: 14680: 12672: 12283: 12001: 11952: 11940: 11877: 10365: 7503: 7395: 7247:

layer ← decoder.layers /* first sublayer */ z_d_copy ← copy(z_d)

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z_d ← z_d + z_d_copy /* second sublayer */ z_d_copy ← copy(z_d)

5465:

It is theoretically possible for each attention head to have a different head dimension

3194: 1654: 16350: 15928: 15075: 15053: 15038: 14995: 14968: 14948: 14924: 14899: 14811: 14789: 14768: 14721:"Vicuna: An Open-Source Chatbot Impressing GPT-4 with 90%* ChatGPT Quality | LMSYS Org" 14659: 14637: 14616: 14567: 14542: 14480: 14458: 14435: 14396: 14289: 14260: 14238: 14143: 14111: 14086: 14065: 14044: 14024: 13982: 13954: 13913: 13880: 13847: 13826: 13768: 13731: 13706: 13652: 13534: 13509: 13423: 13393: 13360: 13336: 13295: 13270: 13245: 13096: 13040: 12974: 12888: 12867: 12846: 12816: 12803: 12759: 12738: 12704: 12589: 12391: 12354: 12291: 12272: 12251: 12223: 12202: 12148: 11977: 11796: 11785: 11779: 10227: 9870: 9151: 8985: 8728: 8708: 8558: 7295:

z_d ← z_d + z_d_copy /* third sublayer */ z_d_copy ← copy(z_d)

6152: 6134: 5758: 5715: 5669: 5418: 5330: 5146: 5133: 5049: 4512: 4492: 4472: 4452: 4425: 4375: 4315: 4295: 4235: 4215: 4048: 4028: 3995:

Attention weights are calculated using the query and key vectors: the attention weight

3483: 2574: 2554: 2291: 2209: 1782: 1762: 1734: 1433: 1423: 1408: 1341: 1307: 1252: 1049: 651: 575: 361: 156: 14288:. SOSP '23. New York, NY, USA: Association for Computing Machinery. pp. 611–626. 14187: 13643:

Clark, Kevin; Khandelwal, Urvashi; Levy, Omer; Manning, Christopher D. (August 2019).

12952:

Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing

12483: 12460: 7549: 1802: 1193:, as it "emulates searching through a source sentence during decoding a translation". 1154:(Sutskever et al, 2014) was a 380M-parameter model for machine translation using two 16416: 16404: 16208: 15860: 15731: 15724: 15155: 15000: 14702: 14368: 14307: 13986: 13974: 13778: 13589: 13403: 13381: 13068: 13006: 12917: 12820: 12808: 12541: 12533: 12492: 12464: 12395: 12387: 12332: 12140: 12132: 11948: 11920: 11775: 10188:

The standard attention graph is either all-to-all or causal, both of which scales as

9362:

Multi-Query Attention changes the multiheaded attention mechanism. Whereas normally,

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z_e ← layer.layer_norm(z_e) z_e ← layer.multiheaded_attention(z_e, z_e, z_e)

1415: 1061: 744: 587: 500: 296: 266: 211: 206: 161: 103: 14001: 13218: 13189: 12593: 1340:

Since 2020, Transformers have been applied in modalities beyond text, including the

1036:

Transformers were first developed as an improvement over previous architectures for

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Hendrycks, Dan; Gimpel, Kevin (2016-06-27). "Gaussian Error Linear Units (GELUs)".

13757:"Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer" 13662: 13382:"Exploring the limits of transfer learning with a unified text-to-text transformer" 12955: 12798: 12788: 12714: 12581: 12525: 12456: 12415:"Open Sourcing BERT: State-of-the-Art Pre-training for Natural Language Processing" 12383: 12324: 12152: 12124: 9986:{\displaystyle {\tilde {x}}_{1},{\tilde {x}}_{2},{\tilde {x}}_{3},{\tilde {x}}_{4}} 7347: 6837: 6796: 4446: 4155: 2591:

that would be input into the positional encoding function. The original paper uses

2005: 1694: 1687: 1449: 1357: 1248: 1200: 1000:

within the scope of the context window with other (unmasked) tokens via a parallel

772: 525: 475: 385: 369: 339: 201: 196: 146: 136: 34: 14282:"Efficient Memory Management for Large Language Model Serving with PagedAttention" 14188:"FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning" 12652:

Katharopoulos, Angelos; Vyas, Apoorv; Pappas, Nikolaos; Fleuret, François (2020).

12607: 12169: 16274: 16218: 16040: 15682: 15602: 15308: 15119: 15030: 14860:"Phenaki: Variable Length Video Generation from Open Domain Textual Descriptions" 14281: 12108: 11925: 9169: 7319:

z_d ← z_d + z_d_copy z_d ← decoder.final_layer_norm(z_d) output_distributions ←

6824: 6574: 6163: 1212: 1045: 959: 800: 604: 470: 410: 11471:

This approximation can be computed in linear time, as we can compute the matrix

6171:

An encoder consists of an embedding layer, followed by multiple encoder layers.

1259:

recurrence is sufficient for language translation, thus the title "attention is

16248: 16213: 16203: 16028: 15786: 15612: 15220: 14985: 13910:

Proceedings of the 16th International Conference on Spoken Language Translation

12654:"Transformers are RNNs: Fast autoregressive Transformers with linear attention" 12312: 12128: 12075: 11910: 7217:

z_e ← encoder.final_layer_norm(z_e) /* decoder */ z_d ← decoder.tokenizer(t_d)

3132: 2775:{\displaystyle f(t)=\left(e^{it/r^{k}}\right)_{k=0,1,\ldots ,{\frac {d}{2}}-1}} 1746: 1438: 1303: 1057: 993: 820: 351: 88: 14587:"Constructing Transformers For Longer Sequences with Sparse Attention Methods" 14531:"The Reversible Residual Network: Backpropagation Without Storing Activations" 14130:

Dao, Tri; Fu, Dan; Ermon, Stefano; Rudra, Atri; Ré, Christopher (2022-12-06).

13320:. Conference on Computer Vision and Pattern Recognition. pp. 11976–11986. 12954:. Austin, Texas: Association for Computational Linguistics. pp. 551–561. 12703:. Doha, Qatar: Association for Computational Linguistics. pp. 1724–1734. 12585: 3140:

complex multiplication can be implemented as real 2-by-2 matrix multiplication

1700:

The set of all tokens is the vocabulary of the tokenizer, and its size is the

1162:

is an LSTM that takes in a sequence of tokens and turns it into a vector. The

16453: 16193: 16173: 16090: 15769: 15368: 15268: 14859: 14706: 14697: 14132:"FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness" 13978: 13782: 13407: 13072: 13010: 12921: 12537: 12482:

Rumelhart, David E.; McClelland, James L.; Hinton, Geoffrey E. (1987-07-29).

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layer ← encoder.layers /* first sublayer */ z_e_copy ← copy(z_e)

5462:

is a final projection matrix owned by the whole multi-headed attention head.

2620:

The function is in a simpler form when written as a complex function of type

2213: 1509: 1456:

restoring or repairing incomplete or corrupted text. For example, the input,

1096: 973: 739: 668: 550: 281: 166: 14350: 14303: 13644: 12793: 12630: 12567:"Learning to control fast-weight memories: an alternative to recurrent nets" 11854: 10065:

are accepted. The same run of the large model already generated a new token

7181:

z_e ← z_e + z_e_copy /* second sublayer */ z_e_copy ← copy(z_e)

5712:. This may be accomplished before the softmax stage by adding a mask matrix 1610:

Note that "masked" as in "masked language modelling" is not "masked" as in "

1040:, but have found many applications since then. They are used in large-scale 16279: 16110: 15525: 15481: 15161: 15114: 15037:

Phuong, Mary; Hutter, Marcus (2022). "Formal Algorithms for Transformers".

15004: 14720: 13927: 13906:"Transformers without Tears: Improving the Normalization of Self-Attention" 13905: 13667: 12959: 12812: 12545: 9307: 4988:. If the attention head is used in a cross-attention fashion, then usually 2281:{\displaystyle f:\mathbb {R} \to \mathbb {R} ^{d};d\in \mathbb {Z} ,d>0} 1752: 1683: 1030: 14019:

Haviv, Adi; Ram, Ori; Press, Ofir; Izsak, Peter; Levy, Omer (2022-12-05),

13695:"XLNet: Generalized Autoregressive Pretraining for Language Understanding" 12718: 12144: 11109:

Consequently, the one-headed attention, with one query, can be written as

8587:

for the positional encoder on the original transformer. Instead, it is an

4838:. The attention mechanism requires the following three equalities to hold: 1091:

For many years, sequence modelling and generation was done by using plain

16375: 16146: 16055: 16050: 15672: 15650: 15476: 15438: 14969:"Precision information extraction for rare disease epidemiology at scale" 13969: 13942: 13756: 12529: 12313:"Learning to Throw With a Handful of Samples Using Decision Transformers" 12079: 11882: 11800: 11782:-L/14), connected by a linear layer. Only the linear layer is finetuned. 9351: 9331: 8982:. The idea being that the linear bias matrix is a softened mask. Just as 7534:

Transformers may use other positional encoding methods than sinusoidal.

7307:

z_d ← layer.layer_norm(z_d) z_d ← layer.feedforward(z_d)

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is a free parameter that should be significantly larger than the biggest

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which used neurons that multiply the outputs of other neurons, so-called

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Lu, Kevin; Grover, Aditya; Abbeel, Pieter; Mordatch, Igor (2022-06-28).

14562:

Child, Rewon; Gray, Scott; Radford, Alec; Sutskever, Ilya (2019-04-23),

12514:"Learning, invariance, and generalization in high-order neural networks" 12033:

Some architectures, such as RWKV or state space models, avoid the issue.

8330:-dimensional vectors, a RoPE encoder is defined by a sequence of angles 5559:{\displaystyle d_{\text{emb}}=768,n_{\text{head}}=12,d_{\text{head}}=64} 3499:

The attention mechanism used in the Transformer architecture are scaled

3375:{\displaystyle \mathrm {FFN} (x)=\phi (xW^{(1)}+b^{(1)})W^{(2)}+b^{(2)}} 16269: 16228: 16223: 16136: 16045: 15953: 15865: 15845: 15330: 15228: 14945:

Scaling Autoregressive Models for Content-Rich Text-to-Image Generation

14831: 14327: 13651:. Florence, Italy: Association for Computational Linguistics: 276–286. 13333:

Scaling Rectified Flow Transformers for High-Resolution Image Synthesis

13166:"The inside story of how ChatGPT was built from the people who made it" 11943:

chess board positions. Using static evaluation alone (that is, with no

9295: 8300:{\displaystyle {\text{RoPE}}{\big (}z_{m},m{\big )}=e^{im\theta }z_{m}} 8148:

Equivalently, if we write the 2-dimensional vectors as complex numbers

3162:

A Transformer is composed of stacked encoder layers and decoder layers.

1513: 694: 390: 316: 14744:

Liu, Haotian; Li, Chunyuan; Wu, Qingyang; Lee, Yong Jae (2023-12-15).

14529:

Gomez, Aidan N; Ren, Mengye; Urtasun, Raquel; Grosse, Roger B (2017).

6867:

convention. In the post-LN convention, the output of each sublayer is

4212:

are different matrices allows attention to be non-symmetric: if token

3198:

The feedforward network module. It is a two-layered network that maps

2155: 16264: 16233: 16131: 15975: 15938: 15875: 15829: 15824: 15809: 15421: 15250: 15167: 15098: 14417:"Towards 100x Speedup: Full Stack Transformer Inference Optimization" 13852: 13539: 13242: 13101: 12947: 12359: 11971: 11934: 11806: 10801:{\displaystyle \mathbb {E} =e^{-{\frac {\|x-y\|^{2}}{2\sigma ^{2}}}}} 9310:

that supplies transformer-based architectures and pretrained models.

9290:

The transformer model has been implemented in standard deep learning

9029:

original transformer, as well as RoPE and many others, are located).

6466:

stands for "feed-forward network". We can more succinctly write it as

3256:

The feedforward network (FFN) modules in a Transformer are 2-layered

2160: 1023: 853: 634: 14857: 14432:

Accelerating Large Language Model Decoding with Speculative Sampling

14006:

Proceedings of the 34th International Conference on Machine Learning

12696: 12675:(2021). "Linear Transformers Are Secretly Fast Weight Programmers". 12311:

Monastirsky, Maxim; Azulay, Osher; Sintov, Avishai (February 2023).

12277:

Proceedings of the 37th International Conference on Machine Learning

9767:

compute power by computing several tokens in parallel. Similarly to

5034:{\displaystyle X_{\text{query}}\neq X_{\text{key}}=X_{\text{value}}} 4392:

is the weighted sum of the value vectors of all tokens, weighted by

16166: 15998: 15262: 15058: 15043: 14953: 14929: 14904: 14816: 14794: 14773: 14664: 14642: 14621: 14572: 14547: 14485: 14463: 14440: 14401: 14294: 14265: 14243: 14148: 14116: 14091: 14070: 14049: 14029: 13959: 13918: 13885: 13831: 13773: 13736: 13711: 13657: 13555:"Sequence Modeling with Neural Networks (Part 2): Attention Models" 13514: 13428: 13398: 13365: 13341: 13300: 13275: 13250: 13045: 12979: 12893: 12872: 12296: 12256: 12228: 6779:

is the matrix with rows being the output vectors from the encoder.

4154:, which stabilizes gradients during training, and passed through a 1311: 14235: 12851: 12764: 12743: 12709: 12694: 12635:

Proceedings of the Annual Meeting of the Cognitive Science Society

12248:

Decision Transformer: Reinforcement Learning via Sequence Modeling

12207: 9037:

Relative Position Encodings is similar to ALiBi, but more generic:

4715:

where the softmax is applied over each of the rows of the matrix.

1348:. The vision transformer, in turn, stimulated new developments in 992:, and each token is converted into a vector via looking up from a 16289: 16126: 16080: 16003: 15903: 15898: 15850: 15296: 15149: 14681:"Frozen Pretrained Transformers as Universal Computation Engines" 14656: 14286:

Proceedings of the 29th Symposium on Operating Systems Principles

13941:

Dufter, Philipp; Schmitt, Martin; Schütze, Hinrich (2022-06-06).

13289: 12070: 11965: 11944: 11870: 11468:. Similarly for multiple queries, and for multiheaded attention. 9299: 8394:. Then the RoPE encoding is applied to each pair of coordinates. 7519: 7193:

z_e ← layer.layer_norm(z_e) z_e ← layer.feedforward(z_e)

3167: 2309: 1756: 1330: 1292: 1271: 1270:" paper. At the time, the focus of the research was on improving 629: 13825:

Shazeer, Noam (2020-02-01). "GLU Variants Improve Transformer".

12999:"8 Google Employees Invented Modern AI. Here's the Inside Story" 12699:. In Moschitti, Alessandro; Pang, Bo; Daelemans, Walter (eds.). 12068: 12066: 12064: 12062: 12060: 12058: 12056: 12054: 12052: 12050: 4981:{\displaystyle X_{\text{query}}=X_{\text{key}}=X_{\text{value}}} 4935:

If the attention head is used in a self-attention fashion, then

2312:. The full positional encoding defined in the original paper is: 1458:"Thank you ~~ me to your party ~~ week", 16304: 16284: 16156: 15948: 15173: 15109: 15051: 12078:; Shazeer, Noam; Parmar, Niki; Uszkoreit, Jakob; Jones, Llion; 11813: 7232:

z_d ← decoder.embedding(z_d) + decoder.positional_embedding(t)

7142:

z_e ← encoder.embedding(z_e) + encoder.positional_embedding(t)

5651:{\displaystyle W^{O}\in \mathbb {R} ^{(64\times 12)\times 768}} 2216:" and "dog bites man" would be processed exactly the same way. 1353: 1118:. Neural networks using multiplicative units were later called 1018:(LSTM). Later variations have been widely adopted for training 977: 380: 16:

Machine learning algorithm used for natural-language processing

12651: 12352: 12289: 12004: – Series of large language models developed by Google AI 10328:

Sparse attention uses attention graphs that grows slower than

7101:{\displaystyle x+\mathrm {Sublayer} (\mathrm {LayerNorm} (x))} 6953:{\displaystyle \mathrm {LayerNorm} (x+\mathrm {Sublayer} (x))} 2907:{\displaystyle f(t+\Delta t)=\mathrm {diag} (f(\Delta t))f(t)} 2094:{\displaystyle \mathrm {UnEmbed} (x)=\mathrm {softmax} (xW+b)} 1302:(2018) was a bi-directional LSTM that produces contextualized 16105: 16085: 16075: 16070: 16065: 16060: 16023: 15855: 15397: 14685:

Proceedings of the AAAI Conference on Artificial Intelligence

14391:

Leviathan, Yaniv; Kalman, Matan; Matias, Yossi (2023-05-18),

14351:"vLLM: Easy, Fast, and Cheap LLM Serving with PagedAttention" 13190:"Improving language understanding with unsupervised learning" 12751: 12074: 12047: 11980: – Variant of Transformer designed for vision processing 11862: 11846: 11842: 11838: 11713:

are first independently sampled from the normal distribution

11661:

Performer (2022) uses the same Random Feature Attention, but

6085: 5415:

are "projection matrices" owned by individual attention head

5061:

Exact dimension counts within a multiheaded attention module.

1587:

and the model is trained to minimize this loss function. The

624: 619: 346: 15067: 14808: 12946:

Cheng, Jianpeng; Dong, Li; Lapata, Mirella (November 2016).

4372:

could be small). The output of the attention unit for token

1056:, audio, multi-modal processing, robotics, and even playing 16095: 15409: 13330: 12972: 11974: – Variant of Transformer designed for multimodal data 9867:

is indeed the token with the largest log-likelihood in the

9339: 9335: 7500: 5143:

Concretely, let the multiple attention heads be indexed by

1299: 14787: 14760: 14635: 14614: 14257: 13642: 11809:

are a variant of Transformers designed for multimodality.

9993:. These tokens are run through the larger model, and only 5347:

is the concatenation of word embeddings, and the matrices

3402:

is its activation function. The original Transformer used

1958:

The number of dimensions in an embedding vector is called

1591:

are trained for masked token prediction and another task.

1411:. Tasks for pretraining and fine-tuning commonly include: 1072:(bidirectional encoder representations from transformers). 14896: 14561: 14429: 14393:

Fast Inference from Transformers via Speculative Decoding

13999: 13645:"What Does BERT Look at? An Analysis of BERT's Attention" 13034: 12481: 9342:), a 2x speed increase over the original FlashAttention. 2219:

The positional encoding is defined as a function of type

988:". Text is converted to numerical representations called 14966: 13912:. Hong Kong: Association for Computational Linguistics. 11992: – Series of language models developed by Google AI 8226:, then RoPE encoding is just multiplication by an angle: 7015:

In the pre-LN convention, the output of each sublayer is

3495:

Exact dimension counts within an attention head module.

1333:, became unexpectedly popular, triggering a boom around 1325:

of decoder-only Transformers became state of the art in

912:

List of datasets in computer vision and image processing

14108:

Rethinking Positional Encoding in Language Pre-training

13754: 13532: 13420: 13379: 13094: 12310: 12269: 1751:

Each token is converted into an embedding vector via a

14678: 12757: 10587:{\displaystyle \varphi (x)={\frac {1}{\sqrt {D}}}^{T}} 8767: 7985: 7920: 7845: 7426: 6318: 6246: 5914: 3985:{\displaystyle d_{\text{emb, query}}=d_{\text{query}}} 3767:. The matrix of all query vectors is the query matrix: 2140:{\displaystyle (d_{\text{emb}},n_{\text{vocabulary}})} 14528: 14390: 13503: 13313: 13117:"Google: BERT now used on almost every English query" 12948:"Long Short-Term Memory-Networks for Machine Reading" 12670: 12376: 12273:"Stabilizing Transformers for Reinforcement Learning" 12107: 11719: 11667: 11528: 11477: 11428: 11115: 10814: 10697: 10652: 10646:

are independent samples from the normal distribution

10600: 10419: 10374: 10334: 10289: 10253: 10230: 10194: 10134: 10098: 10071: 10035: 9999: 9897: 9873: 9846: 9781: 9580: 9538: 9370: 9240: 9178: 9154: 9043: 9008: 8988: 8943: 8755: 8731: 8711: 8597: 8561: 8403: 8336: 8313: 8232: 8154: 7766: 7746: 7552: 7407: 7379: 7109:

requiring no warm-up, leading to faster convergence.

7021: 6966: 6873: 6758: 6611: 6543: 6472: 6450: 6181: 6137: 6094: 5895: 5781: 5761: 5755:

at entries where the attention link must be cut, and

5738: 5718: 5692: 5672: 5604: 5572: 5501: 5471: 5441: 5421: 5353: 5333: 5169: 5149: 5071: 4994: 4941: 4844: 4817: 4787: 4757: 4727: 4616: 4589: 4562: 4535: 4515: 4495: 4475: 4455: 4428: 4398: 4378: 4338: 4318: 4298: 4292:

is large), this does not necessarily mean that token

4258: 4238: 4218: 4191: 4164: 4129: 4102: 4075: 4051: 4031: 4001: 3958: 3905: 3859: 3816: 3773: 3715: 3688: 3653: 3623: 3596: 3566: 3539: 3512: 3427: 3388: 3266: 3231: 3204: 3107: 2954: 2920: 2832: 2788: 2676: 2626: 2597: 2577: 2557: 2487: 2318: 2294: 2225: 2169: 2107: 2014: 1972: 1867: 1805: 1785: 1765: 1709: 1657: 1522: 14832:"Parti: Pathways Autoregressive Text-to-Image Model" 14766: 14477: 14456: 14084: 13940: 13692: 12950:. In Su, Jian; Duh, Kevin; Carreras, Xavier (eds.). 12835:"Sequence to Sequence Learning with Neural Networks" 12833:

Sutskever, Ilya; Vinyals, Oriol; Le, Quoc V (2014).

11907:

based on requirements expressed in natural language.

10247:

Reformer (2020) reduces the computational load from

7012:

is the function implemented by the sublayer itself.

6828:

Block diagram for the full Transformer architecture.

4610:

respectively. Then we can represent the attention as

3682:

in the query sequence, it is multiplied by a matrix

3409:

The number of neurons in the middle layer is called

2664:{\displaystyle f:\mathbb {R} \to \mathbb {C} ^{d/2}} 2541:{\displaystyle \theta ={\frac {t}{r^{k}}},r=N^{2/d}} 1614:", and "prefixLM" (prefix language modeling) is not 1158:(LSTM). The architecture consists of two parts. The 14918: 13943:"Position Information in Transformers: An Overview" 13267: 12245: 7529: 7494: 6559:is applied to each row of the matrix individually. 4808:. The output dimension of an attention head is its 1759:representation of the token by an embedding matrix 1626:All transformers have the same primary components: 1372: 1364:(2024), are based on the Transformer architecture. 14564:Generating Long Sequences with Sparse Transformers 14018: 12832: 12736: 11750: 11705: 11653: 11514: 11460: 11414: 11101: 10800: 10683: 10638: 10586: 10389: 10356: 10313: 10275: 10236: 10216: 10156: 10120: 10084: 10057: 10021: 9985: 9879: 9859: 9832: 9724: 9564: 9524: 9274: 9226: 9160: 9140: 9017: 8994: 8974: 8929: 8737: 8717: 8697: 8567: 8547: 8386: 8322: 8299: 8218: 8140: 7752: 7732: 7473: 7331:output_distributions.append(decoder.unembed(z_d)) 7100: 7004: 6952: 6820:Transformer decoder with norm-first and norm-last. 6812:Transformer encoder with norm-first and norm-last. 6771: 6744: 6551: 6529: 6458: 6434: 6143: 6123: 6076: 5878: 5767: 5747: 5724: 5704: 5686:, should not have access to the token at position 5678: 5650: 5590: 5558: 5484: 5454: 5427: 5407: 5339: 5319: 5155: 5120: 5033: 4980: 4924: 4830: 4800: 4770: 4740: 4705: 4602: 4575: 4548: 4521: 4501: 4481: 4461: 4434: 4414: 4384: 4364: 4324: 4304: 4284: 4244: 4224: 4204: 4177: 4146: 4115: 4088: 4057: 4037: 4017: 3984: 3944: 3888: 3845: 3802: 3759: 3701: 3674: 3636: 3609: 3579: 3552: 3525: 3456: 3394: 3374: 3244: 3217: 3120: 3093: 2937: 2906: 2815: 2774: 2663: 2609: 2583: 2563: 2540: 2473: 2300: 2280: 2193: 2139: 2093: 1985: 1947: 1853: 1791: 1771: 1722: 1666: 1579: 14750:Advances in Neural Information Processing Systems 14535:Advances in Neural Information Processing Systems 14279: 14136:Advances in Neural Information Processing Systems 13873:Advances in Neural Information Processing Systems 13699:Advances in Neural Information Processing Systems 12839:Advances in Neural Information Processing Systems 12557: 12555: 12200: 12091:Advances in Neural Information Processing Systems 7506:. Other activation functions were developed. The 16451: 13357: 12886: 12865: 12221: 11812:For image generation, notable architectures are 7526:. Other examples include ScaleNorm, or FixNorm. 6786: 1022:(LLM) on large (language) datasets, such as the 14129: 14106:Ke, Guolin; He, Di; Liu, Tie-Yan (2021-03-15), 14063: 14042: 13845: 13283: 12945: 12772: 12645: 12608:http://cogprints.org/1380/1/vdM_correlation.pdf 12170:"Better Language Models and Their Implications" 10183: 8387:{\displaystyle \theta ^{(1)},...,\theta ^{(n)}} 8219:{\displaystyle z_{m}:=x_{m}^{(1)}+ix_{m}^{(2)}} 3760:{\displaystyle q_{i}=x_{i,{\text{query}}}W^{Q}} 3467: 3170:models, the original transformer model used an 1396:Transformers typically are first pretrained by 13037:RWKV: Reinventing RNNs for the Transformer Era 12778: 12552: 12442: 12348: 12346: 9532:with Multi-Query Attention, there is just one 9032: 8583:ALiBi (Attention with Linear Biases) is not a 5121:{\displaystyle \left(W^{Q},W^{K},W^{V}\right)} 4718:The number of dimensions in a query vector is 3457:{\displaystyle d_{\text{ffn}}=4d_{\text{emb}}} 1247:, which are easy to parallelize, and achieved 907:List of datasets for machine-learning research 15541: 15083: 14781: 14348: 14002:"Convolutional Sequence to Sequence Learning" 13902: 13866: 13263: 13261: 12629:Hinton, Geoffrey E.; Plaut, David C. (1987). 12443:Feldman, J. A.; Ballard, D. H. (1982-07-01). 12115:(1 November 1997). "Long Short-Term Memory". 11968: – Family of machine learning approaches 10171: 8540: 8518: 8500: 8477: 8462: 8446: 8428: 8411: 8263: 8240: 7832: 7774: 7513: 6859:There are two common conventions in use: the 5408:{\displaystyle W_{i}^{Q},W_{i}^{K},W_{i}^{V}} 3644:. Similarly for the key and value sequences. 3145: 1207:, which replaced the previous model based on 940: 15555: 15036: 14942: 14802: 14373:: CS1 maint: multiple names: authors list ( 13725: 12600: 12511: 12215: 12082:; Kaiser, Łukasz; Polosukhin, Illia (2017). 11361: 11347: 11248: 11234: 11096: 11055: 11048: 10999: 10992: 10984: 10975: 10934: 10927: 10878: 10871: 10863: 10832: 10820: 10769: 10756: 10736: 10706: 10571: 10552: 10540: 10521: 10506: 10487: 10475: 10456: 7510:used SwiGLU; both GPT-1 and BERT used GELU. 4158:which normalizes the weights. The fact that 3487:Scaled dot-product attention, block diagram. 2468: 2430: 14452: 14450: 13726:Phuong, Mary; Hutter, Marcus (2022-07-19), 12907: 12732: 12730: 12728: 12664: 12631:"Using Fast Weights to Deblur Old Memories" 12628: 12613: 12561: 12445:"Connectionist models and their properties" 12372: 12370: 12343: 12196: 12194: 10404: 9285: 7123:Encoder input t_e Decoder input t_d 5492:, but that is rarely the case in practice. 3182:Both the encoder and decoder layers have a 1630:Tokenizers, which convert text into tokens. 1306:, improving upon the line of research from 1234:Attention (machine learning) § History 1095:(RNNs). A well-cited early example was the 15548: 15534: 15090: 15076: 14743: 13258: 13061:"Was Linguistic A.I. Created by Accident?" 12512:Giles, C. Lee; Maxwell, Tom (1987-12-01). 10364:. For example, BigBird (2020) uses random 6840:for the full Transformer architecture, in 4898: 4871: 3617:, and each entry is a vector of dimension 1227: 947: 933: 15057: 15042: 14994: 14984: 14952: 14928: 14903: 14815: 14793: 14772: 14696: 14663: 14641: 14620: 14571: 14546: 14484: 14462: 14439: 14400: 14293: 14264: 14242: 14147: 14115: 14090: 14069: 14048: 14028: 13968: 13958: 13917: 13884: 13851: 13830: 13772: 13735: 13710: 13666: 13656: 13620:"Keras documentation: GPT2Backbone model" 13538: 13513: 13506:UL2: Unifying Language Learning Paradigms 13427: 13397: 13364: 13340: 13299: 13274: 13249: 13100: 13044: 12978: 12892: 12871: 12850: 12802: 12792: 12763: 12742: 12708: 12358: 12295: 12255: 12227: 12206: 11986: – Type of artificial neural network 11829:The transformer has had great success in 11799:, first turning the speech signal into a 10856: 10699: 5620: 3610:{\displaystyle \ell _{\text{seq, query}}} 3031: 2931: 2643: 2634: 2262: 2242: 2233: 1139: 996:table. At each layer, each token is then 976:architecture developed by researchers at 14447: 13386:The Journal of Machine Learning Research 13353: 13351: 13238: 13236: 12725: 12367: 12191: 11515:{\displaystyle \varphi (k_{i})v_{i}^{T}} 9357: 6831: 6823: 6815: 6807: 6795: 6573: 6162: 6124:{\displaystyle PM_{\text{causal}}P^{-1}} 5056: 5048: 5044: 3490: 3482: 3193: 3157: 3149: 3142:, this is a mere notational difference. 2938:{\displaystyle \Delta t\in \mathbb {R} } 2154: 1400:on a large generic dataset, followed by 1378:training steps), before decaying again. 1060:. It has also led to the development of 958: 14892: 14890: 14853: 14851: 14105: 13824: 12101: 10244:is the number of tokens in a sequence. 9833:{\displaystyle x_{1},x_{2},...,x_{512}} 9761: 9322:, such that each block fits within the 3889:{\displaystyle V=X_{\text{value}}W^{V}} 3810:Similarly, we construct the key matrix 3803:{\displaystyle Q=X_{\text{query}}W^{Q}} 1755:. Equivalently stated, it multiplies a 1474:translation between natural languages ( 16452: 13869:"Root Mean Square Layer Normalization" 13528: 13526: 13524: 13090: 13088: 13058: 12992: 12990: 12690: 12688: 12686: 12024:(2014) further reduced its complexity. 7384:changing the location of normalization 7005:{\displaystyle \mathrm {Sublayer} (x)} 6537:with the implicit convention that the 4509:are defined as the matrices where the 3189: 2150: 1500:Large language model § Evaluation 1452:pretraining tasks. Some examples are: 1243:applied a self-attention mechanism to 15529: 15071: 14501:"Reformer: The Efficient Transformer" 14386: 14384: 13898: 13896: 13797:"Recent Advances in Google Translate" 13750: 13748: 13746: 13583: 13581: 13579: 13499: 13497: 13495: 13493: 13468: 13466: 13441: 13439: 13348: 13233: 13211: 13182: 13142:"Recent Advances in Google Translate" 12901: 12880: 12409: 12407: 12405: 12241: 12239: 10409:Random Feature Attention (2021) uses 7386:, etc. This is also usually used for 6175:individually. Schematically, we have: 5053:Multiheaded attention, block diagram. 3846:{\displaystyle K=X_{\text{key}}W^{K}} 3637:{\displaystyle d_{\text{emb, query}}} 1948:{\displaystyle \mathrm {Embed} (3)=M} 1799:, then the one-hot representation is 1779:. For example, if the input token is 1723:{\displaystyle n_{\text{vocabulary}}} 1611: 1599:are trained by autoregressive tasks. 1329:. In 2022, a chatbot based on GPT-3, 984:mechanism, proposed in a 2017 paper " 16386:Generative adversarial network (GAN) 15510: 14887: 14848: 13867:Zhang, Biao; Sennrich, Rico (2019). 13761:Journal of Machine Learning Research 13292:Rethinking Attention with Performers 12781:Frontiers in Artificial Intelligence 12317:IEEE Robotics and Automation Letters 12164: 12162: 11998: – Type of large language model 10691:. This choice of parameters satisfy 3675:{\displaystyle x_{i,{\text{query}}}} 2163:positional encoding with parameters 1645: 1391: 1344:, speech recognition, robotics, and 15326:Quantum Artificial Intelligence Lab 13587: 13521: 13324: 13085: 12987: 12683: 12491:. Cambridge, Mass: Bradford Books. 12475: 11461:{\displaystyle \sigma =d_{K}^{1/4}} 9002:represent full attention paid, and 6848:The final points of detail are the 5661: 2004:The un-embedding layer is a linear- 1448:report documents a large number of 1066:generative pre-trained transformers 902:Glossary of artificial intelligence 13: 15472:Generative pre-trained transformer 15015: 14921:Zero-Shot Text-to-Image Generation 14414: 14381: 13893: 13743: 13728:Formal Algorithms for Transformers 13576: 13490: 13463: 13436: 13373: 12908:Lewis-Kraus, Gideon (2016-12-14). 12402: 12236: 11996:Generative pre-trained transformer 11579: 11166: 9354:GPUs and new data types like FP8. 9099: 9012: 8653: 7489: 7439: 7082: 7079: 7076: 7073: 7070: 7067: 7064: 7061: 7058: 7050: 7047: 7044: 7041: 7038: 7035: 7032: 7029: 6989: 6986: 6983: 6980: 6977: 6974: 6971: 6968: 6934: 6931: 6928: 6925: 6922: 6919: 6916: 6913: 6899: 6896: 6893: 6890: 6887: 6884: 6881: 6878: 6875: 6594:information flow. This allows for 6009: 5979: 5966: 5946: 5933: 5925: 5843: 5742: 4671: 3274: 3271: 3268: 3055: 3042: 3039: 3036: 3033: 2987: 2921: 2880: 2867: 2864: 2861: 2858: 2845: 2421: 2069: 2066: 2063: 2060: 2057: 2054: 2051: 2034: 2031: 2028: 2025: 2022: 2019: 2016: 1881: 1878: 1875: 1872: 1869: 1733:Some commonly used tokenizers are 1616:"prefixLM" (prefix language model) 1352:. Image and video generators like 14: 16476: 15033:, Harvard NLP group, 3 April 2018 14973:Journal of Translational Medicine 12159: 11751:{\displaystyle N(0,\sigma ^{2}I)} 10684:{\displaystyle N(0,\sigma ^{2}I)} 9313: 9227:{\displaystyle B_{i,j}=B_{i',j'}} 8725:is a real number ("scalar"), and 3945:{\displaystyle W^{Q},W^{K},W^{V}} 3478: 1512:for the task is typically sum of 1205:Google Neural Machine Translation 16424: 16423: 16403: 15509: 15500: 15499: 14960: 14936: 14912: 14824: 13617: 13017:from the original on 20 Mar 2024 12996: 11947:search) transformer achieved an 11765: 10157:{\displaystyle {\tilde {x}}_{4}} 10121:{\displaystyle {\tilde {x}}_{3}} 10058:{\displaystyle {\tilde {x}}_{2}} 10022:{\displaystyle {\tilde {x}}_{1}} 9320:matrix multiplications in blocks 7530:Alternative positional encodings 7495:Alternative activation functions 7447: 7430: 7380:alternative activation functions 6228:combine them into a matrix 6088:considers all masks of the form 4932:but is otherwise unconstrained. 4801:{\displaystyle d_{\text{value}}} 4741:{\displaystyle d_{\text{query}}} 4365:{\displaystyle q_{j}\cdot k_{i}} 4285:{\displaystyle q_{i}\cdot k_{j}} 3899:It is usually the case that all 1737:, WordPiece, and SentencePiece. 1571: conditional on its context 1373:Methods for stabilizing training 14737: 14713: 14672: 14650: 14629: 14608: 14597:from the original on 2021-09-18 14579: 14555: 14522: 14511:from the original on 2020-10-22 14493: 14471: 14423: 14408: 14342: 14320: 14273: 14251: 14229: 14205: 14180: 14156: 14123: 14099: 14078: 14057: 14036: 14012: 13993: 13934: 13860: 13839: 13818: 13807:from the original on 4 Jul 2024 13789: 13719: 13686: 13675:from the original on 2020-10-21 13636: 13611: 13600:from the original on 2020-10-18 13565:from the original on 2020-10-21 13547: 13414: 13307: 13200:from the original on 2023-03-18 13158: 13134: 13109: 13052: 13028: 12966: 12939: 12859: 12826: 12679:. Springer. pp. 9355–9366. 12622: 12505: 12436: 12425:from the original on 2021-01-13 12180:from the original on 2020-12-19 12027: 12015: 11824: 11706:{\displaystyle w_{1},...,w_{D}} 10639:{\displaystyle w_{1},...,w_{D}} 5591:{\displaystyle 12\times 64=768} 5485:{\displaystyle d_{\text{head}}} 4831:{\displaystyle d_{\text{head}}} 4147:{\displaystyle {\sqrt {d_{k}}}} 2420: 1995: 1677: 1621: 1607:are trained by prefixLM tasks. 1291:that contribute to the ongoing 1209:statistical machine translation 1086: 16336:Recurrent neural network (RNN) 16326:Differentiable neural computer 13059:Marche, Stephen (2024-08-23). 12671:Schlag, Imanol; Irie, Kazuki; 12388:10.18653/v1/2020.emnlp-demos.6 12304: 12263: 11745: 11723: 11648: 11613: 11552: 11534: 11494: 11481: 11406: 11393: 11323: 11316: 11293: 11280: 11210: 11203: 11139: 11121: 11093: 11087: 11037: 11031: 10978: 10972: 10966: 10916: 10910: 10860: 10739: 10733: 10727: 10718: 10712: 10703: 10678: 10656: 10575: 10447: 10429: 10423: 10384: 10378: 10351: 10338: 10308: 10293: 10270: 10257: 10211: 10198: 10142: 10106: 10043: 10007: 9971: 9949: 9927: 9905: 9704: 9651: 9636: 9623: 9604: 9586: 9504: 9441: 9426: 9413: 9394: 9376: 9071: 9053: 8625: 8607: 8379: 8373: 8348: 8342: 8211: 8205: 8184: 8178: 8113: 8107: 8077: 8071: 8040: 8034: 8004: 7998: 7964: 7958: 7939: 7933: 7819: 7813: 7795: 7789: 7727: 7712: 7707: 7701: 7683: 7677: 7664: 7658: 7653: 7647: 7629: 7623: 7610: 7604: 7599: 7593: 7575: 7569: 7556: 7553: 7499:The original transformer uses 7338: 7095: 7092: 7086: 7054: 6999: 6993: 6947: 6944: 6938: 6903: 6735: 6732: 6695: 6687: 6672: 6666: 6654: 6636: 6524: 6521: 6503: 6495: 6484: 6478: 6410: 6401: 6382: 6374: 6362: 6353: 6334: 6326: 6303: 6297: 5809: 5791: 5637: 5625: 5304: 5301: 5238: 5230: 5225: 5212: 5193: 5175: 4771:{\displaystyle d_{\text{key}}} 4644: 4626: 3367: 3361: 3348: 3342: 3334: 3329: 3323: 3310: 3304: 3293: 3284: 3278: 3245:{\displaystyle d_{\text{emb}}} 3218:{\displaystyle d_{\text{emb}}} 3088: 3082: 3071: 3068: 3052: 3046: 3000: 2978: 2901: 2895: 2889: 2886: 2877: 2871: 2851: 2836: 2686: 2680: 2638: 2417: 2414: 2408: 2396: 2390: 2381: 2375: 2357: 2350: 2332: 2325: 2319: 2237: 2134: 2108: 2088: 2073: 2044: 2038: 1986:{\displaystyle d_{\text{emb}}} 1939: 1897: 1891: 1885: 1848: 1806: 1574: 1558: 1381:A 2020 paper found that using 1281: 1012:recurrent neural architectures 322:Relevance vector machine (RVM) 1: 16381:Variational autoencoder (VAE) 16341:Long short-term memory (LSTM) 15608:Computational learning theory 15097: 13590:"The Illustrated Transformer" 12461:10.1016/S0364-0213(82)80001-3 12040: 7350:for downstream applications. 7112: 6787:Full transformer architecture 3952:are square matrices, meaning 2194:{\displaystyle N=10000,d=100} 1861:, and its embedding vector is 1615: 1350:convolutional neural networks 1321:Starting in 2018, the OpenAI 811:Computational learning theory 375:Expectation–maximization (EM) 16465:Neural network architectures 16361:Convolutional neural network 11921:biological sequence analysis 11795:follow the same pattern for 10184:Alternative attention graphs 7538:positional encoding module. 6791: 6552:{\displaystyle {\text{FFN}}} 6459:{\displaystyle {\text{FFN}}} 3468:Scaled dot-product attention 3130:convolutional neural network 1740: 1082:Timeline of machine learning 980:and based on the multi-head 768:Coefficient of determination 615:Convolutional neural network 327:Support vector machine (SVM) 21:Transformer (disambiguation) 7: 16356:Multilayer perceptron (MLP) 14746:"Visual Instruction Tuning" 12660:. PMLR. pp. 5156–5165. 12084:"Attention is All you Need" 11959: 11831:natural language processing 9565:{\displaystyle W^{K},W^{V}} 9033:Relative Position Encodings 8975:{\displaystyle B_{i,j}=j-i} 7383: 6842:object-oriented programming 5138:feed-forward neural network 4422:, the attention from token 3184:feed-forward neural network 1516:for the masked-out tokens: 1484:The course is jumping well. 1460:might generate the output, 1367: 1327:natural language generation 1042:natural language processing 919:Outline of machine learning 816:Empirical risk minimization 10: 16481: 16432:Artificial neural networks 16346:Gated recurrent unit (GRU) 15572:Differentiable programming 14986:10.1186/s12967-023-04011-y 14541:. Curran Associates, Inc. 13879:. Curran Associates, Inc. 13705:. Curran Associates, Inc. 13474:"Causal language modeling" 13447:"Masked language modeling" 12910:"The Great A.I. Awakening" 12845:. Curran Associates, Inc. 12129:10.1162/neco.1997.9.8.1735 10323:locality-sensitive hashing 10172:Sub-quadratic transformers 9737: 7514:Alternative normalizations 6633:MaskedMultiheadedAttention 6569: 6158: 3709:to produce a query vector 3471: 3225:-dimensional vectors into 3154:One encoder-decoder block. 3146:Encoder-decoder (overview) 1744: 1681: 1497: 1231: 1224:, was proposed for LSTMs. 1143: 1101:vanishing-gradient problem 1079: 1075: 556:Feedforward neural network 307:Artificial neural networks 18: 16399: 16313: 16257: 16186: 16119: 15991: 15891: 15884: 15838: 15802: 15765:Artificial neural network 15745: 15621: 15588:Automatic differentiation 15561: 15495: 15461:Attention Is All You Need 15452: 15431: 15384: 15355: 15348: 15318: 15289: 15282: 15243: 15212: 15183: 15142: 15135: 15128: 15105: 15024:The Annotated transformer 13947:Computational Linguistics 12586:10.1162/neco.1992.4.1.131 12097:. Curran Associates, Inc. 10314:{\displaystyle O(N\ln N)} 9306:is a library produced by 9275:{\displaystyle i-j=i'-j'} 7482:benchmarked comparisons. 7243:1:length(decoder.layers) 7153:1:length(encoder.layers) 6588:encoder-decoder attention 6188:given input vectors 2816:{\displaystyle r=N^{2/d}} 1268:Attention is all you need 1093:recurrent neural networks 986:Attention Is All You Need 539:Artificial neural network 15593:Neuromorphic engineering 15556:Differentiable computing 14698:10.1609/aaai.v36i7.20729 13392:(1): 140:5485–140:5551. 12329:10.1109/LRA.2022.3229266 12008: 11899:named entity recognition 10405:Random Feature Attention 10357:{\displaystyle O(N^{2})} 10325:and reversible layers. 10276:{\displaystyle O(N^{2})} 10217:{\displaystyle O(N^{2})} 9286:Efficient implementation 9018:{\displaystyle -\infty } 8578: 5748:{\displaystyle -\infty } 5598:, its projection matrix 3560:, and the value weights 2212:, as for example, both " 1493: 1420:next-sentence prediction 1398:self-supervised learning 1222:intra-sentence attention 848:Journals and conferences 795:Mathematical foundations 705:Temporal difference (TD) 561:Recurrent neural network 481:Conditional random field 404:Dimensionality reduction 152:Dimensionality reduction 114:Quantum machine learning 109:Neuromorphic engineering 69:Self-supervised learning 64:Semi-supervised learning 16366:Residual neural network 15782:Artificial Intelligence 14304:10.1145/3600006.3613165 13317:A ConvNet for the 2020s 13223:, OpenAI, June 11, 2018 13220:finetune-transformer-lm 12794:10.3389/frai.2020.00040 11951:of 2895, putting it at 11818:variational autoencoder 10411:Fourier random features 7760:. Then RoPE encoding is 7753:{\displaystyle \theta } 7541: 7348:representation learning 6605:Schematically, we have: 2610:{\displaystyle N=10000} 1298:In language modelling, 1228:Parallelizing attention 1106:A key breakthrough was 257:Apprenticeship learning 15336:Tensor Processing Unit 14875:Cite journal requires 14415:Fu, Yao (2023-12-13). 13928:10.5281/zenodo.3525484 11889:document summarization 11760:Gram-Schmidt processed 11752: 11707: 11655: 11516: 11462: 11416: 11103: 10802: 10685: 10640: 10588: 10391: 10358: 10315: 10277: 10238: 10218: 10158: 10122: 10086: 10059: 10023: 9987: 9881: 9861: 9834: 9726: 9566: 9526: 9276: 9228: 9162: 9142: 9019: 8996: 8976: 8931: 8739: 8719: 8699: 8569: 8549: 8388: 8324: 8301: 8220: 8142: 7754: 7740:. Now pick some angle 7734: 7475: 7102: 7006: 6954: 6845: 6829: 6821: 6813: 6801: 6773: 6746: 6579: 6553: 6531: 6460: 6436: 6168: 6145: 6125: 6078: 5880: 5769: 5749: 5726: 5706: 5680: 5652: 5592: 5560: 5486: 5456: 5429: 5409: 5341: 5321: 5157: 5128:matrices is called an 5122: 5062: 5054: 5035: 4982: 4926: 4832: 4802: 4772: 4748:and similarly for the 4742: 4707: 4604: 4577: 4550: 4523: 4503: 4483: 4463: 4436: 4416: 4415:{\displaystyle a_{ij}} 4386: 4366: 4326: 4306: 4286: 4246: 4226: 4206: 4179: 4148: 4117: 4090: 4059: 4039: 4019: 4018:{\displaystyle a_{ij}} 3986: 3946: 3890: 3847: 3804: 3761: 3703: 3676: 3638: 3611: 3581: 3554: 3527: 3496: 3488: 3458: 3396: 3376: 3258:multilayer perceptrons 3253: 3246: 3219: 3163: 3155: 3122: 3095: 2939: 2908: 2817: 2776: 2665: 2611: 2585: 2565: 2542: 2475: 2302: 2282: 2201: 2195: 2141: 2095: 1987: 1949: 1855: 1793: 1773: 1724: 1668: 1581: 1241:decomposable attention 1156:long short-term memory 1146:Seq2seq § History 1140:Attention with seq2seq 1054:reinforcement learning 1016:long short-term memory 965: 806:Bias–variance tradeoff 688:Reinforcement learning 664:Spiking neural network 74:Reinforcement learning 16321:Neural Turing machine 15909:Human image synthesis 14836:sites.research.google 13170:MIT Technology Review 12022:Gated recurrent units 11990:BERT (language model) 11905:writing computer code 11835:large language models 11753: 11708: 11656: 11517: 11463: 11417: 11104: 10803: 10686: 10641: 10589: 10392: 10359: 10316: 10278: 10239: 10219: 10159: 10123: 10087: 10085:{\displaystyle x_{3}} 10060: 10024: 9988: 9882: 9862: 9860:{\displaystyle x_{t}} 9835: 9769:speculative execution 9727: 9567: 9527: 9358:Multi-Query Attention 9277: 9229: 9163: 9143: 9020: 8997: 8977: 8932: 8740: 8720: 8700: 8570: 8550: 8389: 8325: 8302: 8221: 8143: 7755: 7735: 7522:which is used in the 7476: 7398:are encoder-decoder. 7392:instruction following 7364:instruction following 7335:output_distributions 7205:z_e ← z_e + z_e_copy 7103: 7007: 6955: 6835: 6827: 6819: 6811: 6799: 6774: 6772:{\displaystyle H^{E}} 6747: 6577: 6554: 6532: 6461: 6437: 6166: 6146: 6126: 6079: 5881: 5770: 5750: 5727: 5707: 5681: 5653: 5593: 5561: 5487: 5457: 5455:{\displaystyle W^{O}} 5430: 5410: 5342: 5322: 5158: 5123: 5060: 5052: 5045:Multiheaded attention 5036: 4983: 4927: 4833: 4803: 4773: 4743: 4708: 4605: 4603:{\displaystyle v_{i}} 4578: 4576:{\displaystyle k_{i}} 4551: 4549:{\displaystyle q_{i}} 4524: 4504: 4484: 4464: 4437: 4417: 4387: 4367: 4327: 4312:will attend to token 4307: 4287: 4247: 4227: 4207: 4205:{\displaystyle W^{K}} 4180: 4178:{\displaystyle W^{Q}} 4149: 4118: 4116:{\displaystyle k_{j}} 4091: 4089:{\displaystyle q_{i}} 4060: 4040: 4020: 3987: 3947: 3891: 3853:and the value matrix 3848: 3805: 3762: 3704: 3702:{\displaystyle W^{Q}} 3677: 3639: 3612: 3582: 3580:{\displaystyle W^{V}} 3555: 3553:{\displaystyle W^{K}} 3528: 3526:{\displaystyle W^{Q}} 3494: 3486: 3474:Dot-product attention 3459: 3397: 3395:{\displaystyle \phi } 3377: 3252:-dimensional vectors. 3247: 3220: 3197: 3161: 3153: 3123: 3121:{\displaystyle c_{j}} 3096: 2940: 2909: 2818: 2777: 2666: 2612: 2586: 2566: 2543: 2476: 2303: 2283: 2196: 2158: 2142: 2101:The matrix has shape 2096: 1988: 1950: 1856: 1794: 1774: 1745:Further information: 1725: 1669: 1589:BERT series of models 1582: 1429:reading comprehension 1335:large language models 1314:. It was followed by 1168:gated recurrent units 1125:higher-order networks 1020:large language models 962: 642:Neural radiance field 464:Structured prediction 187:Structured prediction 59:Unsupervised learning 16412:Computer programming 16391:Graph neural network 15966:Text-to-video models 15944:Text-to-image models 15792:Large language model 15777:Scientific computing 15583:Statistical manifold 15578:Information geometry 13970:10.1162/coli_a_00445 13668:10.18653/v1/W19-4828 12960:10.18653/v1/D16-1053 12530:10.1364/AO.26.004972 11984:Large language model 11791:Conformer and later 11717: 11665: 11526: 11475: 11426: 11113: 10812: 10695: 10650: 10598: 10417: 10390:{\displaystyle O(N)} 10372: 10366:small-world networks 10332: 10287: 10251: 10228: 10192: 10132: 10096: 10069: 10033: 9997: 9895: 9871: 9844: 9779: 9762:Speculative decoding 9578: 9536: 9373:MultiheadedAttention 9368: 9238: 9176: 9152: 9041: 9006: 8986: 8941: 8753: 8729: 8709: 8595: 8559: 8401: 8334: 8311: 8230: 8152: 7764: 7744: 7550: 7405: 7394:. The models in the 7366:. The models in the 7358:is usually used for 7019: 6964: 6871: 6850:residual connections 6756: 6692:MultiheadedAttention 6609: 6541: 6500:MultiheadedAttention 6470: 6448: 6379:MultiheadedAttention 6331:MultiheadedAttention 6179: 6135: 6092: 5893: 5779: 5759: 5736: 5716: 5690: 5670: 5658:is a square matrix. 5602: 5570: 5499: 5469: 5439: 5419: 5351: 5331: 5172:MultiheadedAttention 5167: 5147: 5069: 4992: 4939: 4842: 4815: 4785: 4755: 4725: 4614: 4587: 4560: 4533: 4529:th rows are vectors 4513: 4493: 4473: 4453: 4426: 4396: 4376: 4336: 4316: 4296: 4256: 4236: 4216: 4189: 4162: 4127: 4100: 4073: 4049: 4029: 3999: 3956: 3903: 3857: 3814: 3771: 3713: 3686: 3651: 3621: 3594: 3564: 3537: 3510: 3425: 3386: 3264: 3229: 3202: 3105: 2952: 2918: 2830: 2786: 2674: 2624: 2595: 2575: 2555: 2485: 2316: 2292: 2223: 2167: 2105: 2012: 1970: 1865: 1803: 1783: 1763: 1707: 1655: 1597:GPT series of models 1563:probability of 1520: 1245:feedforward networks 1217:, originally called 1116:multiplicative units 831:Statistical learning 729:Learning with humans 521:Local outlier factor 19:For other uses, see 15758:In-context learning 15598:Pattern recognition 15467:Future of Go Summit 14507:. 16 January 2020. 12719:10.3115/v1/D14-1179 12673:Schmidhuber, Jürgen 12563:Schmidhuber, Jürgen 12421:. 2 November 2018. 12113:Schmidhuber, Jürgen 12002:T5 (language model) 11926:video understanding 11894:document generation 11878:machine translation 11786:Vision transformers 11511: 11457: 11310: 9671: 9583:MultiQueryAttention 9503: 9482: 9461: 8215: 8188: 8117: 8081: 8044: 8008: 7968: 7943: 7823: 7799: 7711: 7687: 7657: 7633: 7603: 7579: 7504:activation function 6854:layer normalization 5705:{\displaystyle t+1} 5404: 5386: 5368: 5300: 5279: 5258: 3190:Feedforward network 2308:is a positive even 2151:Positional encoding 1605:T5 series of models 1476:machine translation 1383:layer normalization 1276:machine translation 1112:attention mechanism 1062:pre-trained systems 1050:vision transformers 1038:machine translation 1005:attention mechanism 674:Electrochemical RAM 581:reservoir computing 312:Logistic regression 231:Supervised learning 217:Multimodal learning 192:Feature engineering 137:Generative modeling 99:Rule-based learning 94:Curriculum learning 54:Supervised learning 29:Part of a series on 16351:Echo state network 16239:Jürgen Schmidhuber 15934:Facial recognition 15929:Speech recognition 15839:Software libraries 15213:In popular culture 15029:2021-09-22 at the 14332:, vLLM, 2024-06-20 14008:. PMLR: 1243–1252. 13594:jalammar.github.io 13121:Search Engine Land 12914:The New York Times 12574:Neural Computation 12382:. pp. 38–45. 12279:. PMLR: 7487–7498. 12117:Neural Computation 11978:Vision transformer 11797:speech recognition 11748: 11703: 11651: 11512: 11497: 11458: 11435: 11412: 11341: 11296: 11228: 11099: 10798: 10681: 10636: 10584: 10387: 10354: 10311: 10273: 10234: 10214: 10154: 10118: 10082: 10055: 10019: 9983: 9877: 9857: 9830: 9722: 9657: 9562: 9522: 9489: 9468: 9447: 9272: 9224: 9158: 9138: 9136: 9015: 8992: 8972: 8927: 8921: 8735: 8715: 8695: 8693: 8565: 8545: 8384: 8323:{\displaystyle 2n} 8320: 8297: 8216: 8195: 8168: 8138: 8132: 8097: 8061: 8024: 7988: 7971: 7948: 7923: 7909: 7803: 7779: 7750: 7730: 7691: 7667: 7637: 7613: 7583: 7559: 7471: 7465: 7374:are decoder-only. 7098: 7002: 6950: 6846: 6830: 6822: 6814: 6802: 6769: 6742: 6740: 6580: 6578:One decoder layer. 6549: 6527: 6456: 6432: 6430: 6422: 6282: 6169: 6167:One encoder layer. 6153:permutation matrix 6141: 6121: 6074: 6068: 5876: 5874: 5765: 5745: 5722: 5702: 5676: 5648: 5588: 5556: 5482: 5452: 5425: 5405: 5390: 5372: 5354: 5337: 5317: 5286: 5265: 5244: 5153: 5118: 5063: 5055: 5031: 4978: 4922: 4828: 4798: 4768: 4738: 4703: 4701: 4600: 4573: 4546: 4519: 4499: 4479: 4459: 4432: 4412: 4382: 4362: 4322: 4302: 4282: 4242: 4222: 4202: 4175: 4144: 4113: 4086: 4055: 4035: 4015: 3982: 3942: 3886: 3843: 3800: 3757: 3699: 3672: 3634: 3607: 3577: 3550: 3533:, the key weights 3523: 3497: 3489: 3454: 3392: 3372: 3254: 3242: 3215: 3164: 3156: 3118: 3101:for any constants 3091: 3020: 2964: 2935: 2904: 2813: 2772: 2661: 2607: 2581: 2561: 2538: 2471: 2298: 2278: 2202: 2191: 2137: 2091: 1983: 1945: 1851: 1789: 1769: 1735:byte pair encoding 1720: 1667:{\displaystyle xW} 1664: 1577: 1551: 1434:sentiment analysis 1424:question answering 1358:Stable Diffusion 3 1342:vision transformer 1253:textual entailment 1219:intra-attention or 966: 242: • 157:Density estimation 16447: 16446: 16209:Stephen Grossberg 16182: 16181: 15523: 15522: 15448: 15447: 15344: 15343: 15278: 15277: 15239: 15238: 15129:Computer programs 14593:. 25 March 2021. 14329:vllm-project/vllm 14313:979-8-4007-0229-7 14168:crfm.stanford.edu 13196:. June 11, 2018. 12524:(23): 4972–4978. 12498:978-0-262-68053-0 12449:Cognitive Science 11776:transfer learning 11646: 11598: 11597: 11561: 11532: 11410: 11332: 11219: 11185: 11184: 11148: 11119: 10794: 10445: 10444: 10237:{\displaystyle N} 10145: 10109: 10046: 10010: 9974: 9952: 9930: 9908: 9880:{\displaystyle t} 9649: 9633: 9614: 9584: 9439: 9423: 9404: 9374: 9161:{\displaystyle B} 9118: 9117: 9080: 9051: 8995:{\displaystyle 0} 8749:matrix defined by 8738:{\displaystyle B} 8718:{\displaystyle s} 8672: 8671: 8634: 8605: 8568:{\displaystyle k} 8514: 8473: 8442: 8407: 8236: 7770: 7460: 7415: 7372:Chinchilla series 6693: 6685: 6664: 6634: 6547: 6501: 6493: 6476: 6454: 6380: 6372: 6332: 6324: 6295: 6229: 6189: 6144:{\displaystyle P} 6105: 5903: 5862: 5861: 5818: 5789: 5768:{\displaystyle 0} 5725:{\displaystyle M} 5679:{\displaystyle t} 5547: 5528: 5509: 5479: 5428:{\displaystyle i} 5340:{\displaystyle X} 5327:where the matrix 5236: 5222: 5203: 5173: 5156:{\displaystyle i} 5028: 5015: 5002: 4975: 4962: 4949: 4919: 4906: 4892: 4879: 4865: 4852: 4825: 4795: 4765: 4735: 4690: 4689: 4653: 4624: 4522:{\displaystyle i} 4502:{\displaystyle V} 4482:{\displaystyle K} 4462:{\displaystyle Q} 4435:{\displaystyle i} 4385:{\displaystyle i} 4325:{\displaystyle i} 4305:{\displaystyle j} 4245:{\displaystyle j} 4232:attends to token 4225:{\displaystyle i} 4142: 4058:{\displaystyle j} 4038:{\displaystyle i} 3979: 3966: 3873: 3830: 3787: 3743: 3668: 3631: 3604: 3451: 3435: 3411:intermediate size 3239: 3212: 3011: 2955: 2762: 2584:{\displaystyle k} 2564:{\displaystyle N} 2509: 2301:{\displaystyle d} 2131: 2118: 1980: 1792:{\displaystyle 3} 1772:{\displaystyle M} 1717: 1646:following section 1572: 1564: 1548: 1534: 1526: 1466:me to your party 1416:language modeling 1392:Pretrain-finetune 1289:generative models 1120:sigma-pi networks 957: 956: 762:Model diagnostics 745:Human-in-the-loop 588:Boltzmann machine 501:Anomaly detection 297:Linear regression 212:Ontology learning 207:Grammar induction 182:Semantic analysis 177:Association rules 162:Anomaly detection 104:Neuro-symbolic AI 16472: 16437:Machine learning 16427: 16426: 16407: 16162:Action selection 16152:Self-driving car 15959:Stable Diffusion 15924:Speech synthesis 15889: 15888: 15753:Machine learning 15629:Gradient descent 15550: 15543: 15536: 15527: 15526: 15513: 15512: 15503: 15502: 15487:Google Workspace 15353: 15352: 15287: 15286: 15283:Machine learning 15140: 15139: 15133: 15132: 15092: 15085: 15078: 15069: 15068: 15063: 15061: 15048: 15046: 15022:Alexander Rush, 15009: 15008: 14998: 14988: 14964: 14958: 14957: 14956: 14940: 14934: 14933: 14932: 14916: 14910: 14909: 14907: 14894: 14885: 14884: 14878: 14873: 14871: 14863: 14855: 14846: 14845: 14843: 14842: 14828: 14822: 14821: 14819: 14806: 14800: 14799: 14797: 14785: 14779: 14778: 14776: 14764: 14758: 14757: 14741: 14735: 14734: 14732: 14731: 14717: 14711: 14710: 14700: 14691:(7): 7628–7636. 14676: 14670: 14669: 14667: 14654: 14648: 14647: 14645: 14633: 14627: 14626: 14624: 14612: 14606: 14605: 14603: 14602: 14583: 14577: 14576: 14575: 14559: 14553: 14552: 14550: 14526: 14520: 14519: 14517: 14516: 14497: 14491: 14490: 14488: 14475: 14469: 14468: 14466: 14454: 14445: 14444: 14443: 14427: 14421: 14420: 14412: 14406: 14405: 14404: 14388: 14379: 14378: 14372: 14364: 14362: 14361: 14346: 14340: 14339: 14338: 14337: 14324: 14318: 14317: 14297: 14277: 14271: 14270: 14268: 14255: 14249: 14248: 14246: 14233: 14227: 14226: 14224: 14223: 14209: 14203: 14202: 14200: 14199: 14184: 14178: 14177: 14175: 14174: 14160: 14154: 14153: 14151: 14127: 14121: 14120: 14119: 14103: 14097: 14096: 14094: 14082: 14076: 14075: 14073: 14061: 14055: 14054: 14052: 14040: 14034: 14033: 14032: 14016: 14010: 14009: 13997: 13991: 13990: 13972: 13962: 13938: 13932: 13931: 13921: 13900: 13891: 13890: 13888: 13864: 13858: 13857: 13855: 13843: 13837: 13836: 13834: 13822: 13816: 13815: 13813: 13812: 13803:. June 8, 2020. 13793: 13787: 13786: 13776: 13752: 13741: 13740: 13739: 13723: 13717: 13716: 13714: 13690: 13684: 13683: 13681: 13680: 13670: 13660: 13640: 13634: 13633: 13631: 13630: 13615: 13609: 13608: 13606: 13605: 13585: 13574: 13573: 13571: 13570: 13551: 13545: 13544: 13542: 13530: 13519: 13518: 13517: 13501: 13488: 13487: 13485: 13484: 13470: 13461: 13460: 13458: 13457: 13443: 13434: 13433: 13431: 13418: 13412: 13411: 13401: 13377: 13371: 13370: 13368: 13355: 13346: 13345: 13344: 13328: 13322: 13321: 13311: 13305: 13304: 13303: 13287: 13281: 13280: 13278: 13265: 13256: 13255: 13253: 13240: 13231: 13230: 13229: 13228: 13215: 13209: 13208: 13206: 13205: 13186: 13180: 13179: 13177: 13176: 13162: 13156: 13155: 13153: 13152: 13138: 13132: 13131: 13129: 13128: 13113: 13107: 13106: 13104: 13092: 13083: 13082: 13080: 13079: 13056: 13050: 13049: 13048: 13032: 13026: 13025: 13023: 13022: 12994: 12985: 12984: 12982: 12970: 12964: 12963: 12943: 12937: 12936: 12934: 12933: 12924:. Archived from 12905: 12899: 12898: 12896: 12884: 12878: 12877: 12875: 12863: 12857: 12856: 12854: 12830: 12824: 12823: 12806: 12796: 12776: 12770: 12769: 12767: 12755: 12749: 12748: 12746: 12734: 12723: 12722: 12712: 12692: 12681: 12680: 12668: 12662: 12661: 12649: 12643: 12642: 12626: 12620: 12617: 12611: 12604: 12598: 12597: 12571: 12559: 12550: 12549: 12509: 12503: 12502: 12490: 12479: 12473: 12472: 12440: 12434: 12433: 12431: 12430: 12411: 12400: 12399: 12374: 12365: 12364: 12362: 12350: 12341: 12340: 12308: 12302: 12301: 12299: 12287: 12281: 12280: 12267: 12261: 12260: 12259: 12243: 12234: 12233: 12231: 12219: 12213: 12212: 12210: 12198: 12189: 12188: 12186: 12185: 12166: 12157: 12156: 12123:(8): 1735–1780. 12109:Hochreiter, Sepp 12105: 12099: 12098: 12088: 12072: 12034: 12031: 12025: 12019: 11758:, then they are 11757: 11755: 11754: 11749: 11741: 11740: 11712: 11710: 11709: 11704: 11702: 11701: 11677: 11676: 11660: 11658: 11657: 11652: 11647: 11645: 11644: 11635: 11633: 11625: 11624: 11603: 11599: 11596: 11595: 11586: 11585: 11584: 11583: 11582: 11568: 11562: 11559: 11533: 11530: 11521: 11519: 11518: 11513: 11510: 11505: 11493: 11492: 11467: 11465: 11464: 11459: 11456: 11452: 11443: 11421: 11419: 11418: 11413: 11411: 11409: 11405: 11404: 11389: 11388: 11387: 11386: 11374: 11369: 11368: 11359: 11358: 11340: 11331: 11330: 11311: 11309: 11304: 11292: 11291: 11276: 11275: 11274: 11273: 11261: 11256: 11255: 11246: 11245: 11227: 11218: 11217: 11198: 11190: 11186: 11183: 11182: 11173: 11172: 11171: 11170: 11169: 11155: 11149: 11146: 11120: 11117: 11108: 11106: 11105: 11100: 11083: 11082: 11081: 11080: 11068: 11063: 11062: 11027: 11026: 11025: 11024: 11012: 11007: 11006: 10962: 10961: 10960: 10959: 10947: 10942: 10941: 10906: 10905: 10904: 10903: 10891: 10886: 10885: 10859: 10851: 10850: 10849: 10848: 10839: 10807: 10805: 10804: 10799: 10797: 10796: 10795: 10793: 10792: 10791: 10778: 10777: 10776: 10754: 10702: 10690: 10688: 10687: 10682: 10674: 10673: 10645: 10643: 10642: 10637: 10635: 10634: 10610: 10609: 10593: 10591: 10590: 10585: 10583: 10582: 10564: 10563: 10533: 10532: 10499: 10498: 10468: 10467: 10446: 10440: 10436: 10396: 10394: 10393: 10388: 10363: 10361: 10360: 10355: 10350: 10349: 10320: 10318: 10317: 10312: 10282: 10280: 10279: 10274: 10269: 10268: 10243: 10241: 10240: 10235: 10223: 10221: 10220: 10215: 10210: 10209: 10178:Long Range Arena 10163: 10161: 10160: 10155: 10153: 10152: 10147: 10146: 10138: 10127: 10125: 10124: 10119: 10117: 10116: 10111: 10110: 10102: 10091: 10089: 10088: 10083: 10081: 10080: 10064: 10062: 10061: 10056: 10054: 10053: 10048: 10047: 10039: 10028: 10026: 10025: 10020: 10018: 10017: 10012: 10011: 10003: 9992: 9990: 9989: 9984: 9982: 9981: 9976: 9975: 9967: 9960: 9959: 9954: 9953: 9945: 9938: 9937: 9932: 9931: 9923: 9916: 9915: 9910: 9909: 9901: 9886: 9884: 9883: 9878: 9866: 9864: 9863: 9858: 9856: 9855: 9839: 9837: 9836: 9831: 9829: 9828: 9804: 9803: 9791: 9790: 9731: 9729: 9728: 9723: 9721: 9720: 9711: 9707: 9703: 9702: 9687: 9686: 9670: 9665: 9650: 9647: 9640: 9639: 9635: 9634: 9631: 9615: 9612: 9585: 9582: 9571: 9569: 9568: 9563: 9561: 9560: 9548: 9547: 9531: 9529: 9528: 9523: 9521: 9520: 9511: 9507: 9502: 9497: 9481: 9476: 9460: 9455: 9440: 9437: 9430: 9429: 9425: 9424: 9421: 9405: 9402: 9375: 9372: 9281: 9279: 9278: 9273: 9271: 9260: 9233: 9231: 9230: 9225: 9223: 9222: 9221: 9210: 9194: 9193: 9167: 9165: 9164: 9159: 9147: 9145: 9144: 9139: 9137: 9130: 9126: 9119: 9116: 9115: 9106: 9105: 9104: 9103: 9102: 9088: 9081: 9078: 9052: 9049: 9024: 9022: 9021: 9016: 9001: 8999: 8998: 8993: 8981: 8979: 8978: 8973: 8959: 8958: 8937:in other words, 8936: 8934: 8933: 8928: 8926: 8925: 8744: 8742: 8741: 8736: 8724: 8722: 8721: 8716: 8704: 8702: 8701: 8696: 8694: 8687: 8683: 8673: 8670: 8669: 8660: 8659: 8658: 8657: 8656: 8642: 8635: 8632: 8606: 8603: 8574: 8572: 8571: 8566: 8555:for any integer 8554: 8552: 8551: 8546: 8544: 8543: 8522: 8521: 8515: 8512: 8510: 8509: 8504: 8503: 8481: 8480: 8474: 8471: 8466: 8465: 8450: 8449: 8443: 8440: 8438: 8437: 8432: 8431: 8415: 8414: 8408: 8405: 8393: 8391: 8390: 8385: 8383: 8382: 8352: 8351: 8329: 8327: 8326: 8321: 8306: 8304: 8303: 8298: 8296: 8295: 8286: 8285: 8267: 8266: 8254: 8253: 8244: 8243: 8237: 8234: 8225: 8223: 8222: 8217: 8214: 8203: 8187: 8176: 8164: 8163: 8147: 8145: 8144: 8139: 8137: 8136: 8116: 8105: 8080: 8069: 8043: 8032: 8007: 7996: 7976: 7975: 7967: 7956: 7942: 7931: 7914: 7913: 7836: 7835: 7822: 7811: 7798: 7787: 7778: 7777: 7771: 7768: 7759: 7757: 7756: 7751: 7739: 7737: 7736: 7733:{\displaystyle } 7731: 7710: 7699: 7686: 7675: 7656: 7645: 7632: 7621: 7602: 7591: 7578: 7567: 7480: 7478: 7477: 7472: 7470: 7469: 7462: 7461: 7458: 7450: 7433: 7417: 7416: 7413: 7107: 7105: 7104: 7099: 7085: 7053: 7011: 7009: 7008: 7003: 6992: 6959: 6957: 6956: 6951: 6937: 6902: 6838:object hierarchy 6778: 6776: 6775: 6770: 6768: 6767: 6751: 6749: 6748: 6743: 6741: 6731: 6730: 6718: 6717: 6705: 6694: 6691: 6686: 6683: 6665: 6662: 6635: 6632: 6623: 6558: 6556: 6555: 6550: 6548: 6545: 6536: 6534: 6533: 6528: 6502: 6499: 6494: 6491: 6477: 6474: 6465: 6463: 6462: 6457: 6455: 6452: 6441: 6439: 6438: 6433: 6431: 6427: 6426: 6409: 6408: 6381: 6378: 6373: 6370: 6361: 6360: 6333: 6330: 6325: 6322: 6296: 6293: 6287: 6286: 6272: 6271: 6258: 6257: 6230: 6227: 6215: 6214: 6202: 6201: 6190: 6187: 6150: 6148: 6147: 6142: 6130: 6128: 6127: 6122: 6120: 6119: 6107: 6106: 6103: 6083: 6081: 6080: 6075: 6073: 6072: 5905: 5904: 5901: 5885: 5883: 5882: 5877: 5875: 5868: 5864: 5863: 5860: 5859: 5850: 5849: 5848: 5847: 5846: 5832: 5819: 5816: 5790: 5787: 5775:at other places: 5774: 5772: 5771: 5766: 5754: 5752: 5751: 5746: 5731: 5729: 5728: 5723: 5711: 5709: 5708: 5703: 5685: 5683: 5682: 5677: 5662:Masked attention 5657: 5655: 5654: 5649: 5647: 5646: 5623: 5614: 5613: 5597: 5595: 5594: 5589: 5565: 5563: 5562: 5557: 5549: 5548: 5545: 5530: 5529: 5526: 5511: 5510: 5507: 5491: 5489: 5488: 5483: 5481: 5480: 5477: 5461: 5459: 5458: 5453: 5451: 5450: 5434: 5432: 5431: 5426: 5414: 5412: 5411: 5406: 5403: 5398: 5385: 5380: 5367: 5362: 5346: 5344: 5343: 5338: 5326: 5324: 5323: 5318: 5316: 5315: 5299: 5294: 5278: 5273: 5257: 5252: 5237: 5234: 5229: 5228: 5224: 5223: 5220: 5204: 5201: 5174: 5171: 5162: 5160: 5159: 5154: 5127: 5125: 5124: 5119: 5117: 5113: 5112: 5111: 5099: 5098: 5086: 5085: 5040: 5038: 5037: 5032: 5030: 5029: 5026: 5017: 5016: 5013: 5004: 5003: 5000: 4987: 4985: 4984: 4979: 4977: 4976: 4973: 4964: 4963: 4960: 4951: 4950: 4947: 4931: 4929: 4928: 4923: 4921: 4920: 4917: 4908: 4907: 4904: 4894: 4893: 4890: 4881: 4880: 4877: 4867: 4866: 4863: 4854: 4853: 4850: 4837: 4835: 4834: 4829: 4827: 4826: 4823: 4807: 4805: 4804: 4799: 4797: 4796: 4793: 4777: 4775: 4774: 4769: 4767: 4766: 4763: 4747: 4745: 4744: 4739: 4737: 4736: 4733: 4712: 4710: 4709: 4704: 4702: 4695: 4691: 4688: 4687: 4678: 4677: 4676: 4675: 4674: 4660: 4654: 4651: 4625: 4622: 4609: 4607: 4606: 4601: 4599: 4598: 4582: 4580: 4579: 4574: 4572: 4571: 4555: 4553: 4552: 4547: 4545: 4544: 4528: 4526: 4525: 4520: 4508: 4506: 4505: 4500: 4488: 4486: 4485: 4480: 4468: 4466: 4465: 4460: 4447:softmax function 4441: 4439: 4438: 4433: 4421: 4419: 4418: 4413: 4411: 4410: 4391: 4389: 4388: 4383: 4371: 4369: 4368: 4363: 4361: 4360: 4348: 4347: 4331: 4329: 4328: 4323: 4311: 4309: 4308: 4303: 4291: 4289: 4288: 4283: 4281: 4280: 4268: 4267: 4251: 4249: 4248: 4243: 4231: 4229: 4228: 4223: 4211: 4209: 4208: 4203: 4201: 4200: 4184: 4182: 4181: 4176: 4174: 4173: 4153: 4151: 4150: 4145: 4143: 4141: 4140: 4131: 4122: 4120: 4119: 4114: 4112: 4111: 4095: 4093: 4092: 4087: 4085: 4084: 4064: 4062: 4061: 4056: 4044: 4042: 4041: 4036: 4024: 4022: 4021: 4016: 4014: 4013: 3991: 3989: 3988: 3983: 3981: 3980: 3977: 3968: 3967: 3964: 3951: 3949: 3948: 3943: 3941: 3940: 3928: 3927: 3915: 3914: 3895: 3893: 3892: 3887: 3885: 3884: 3875: 3874: 3871: 3852: 3850: 3849: 3844: 3842: 3841: 3832: 3831: 3828: 3809: 3807: 3806: 3801: 3799: 3798: 3789: 3788: 3785: 3766: 3764: 3763: 3758: 3756: 3755: 3746: 3745: 3744: 3741: 3725: 3724: 3708: 3706: 3705: 3700: 3698: 3697: 3681: 3679: 3678: 3673: 3671: 3670: 3669: 3666: 3647:For each vector 3643: 3641: 3640: 3635: 3633: 3632: 3629: 3616: 3614: 3613: 3608: 3606: 3605: 3602: 3586: 3584: 3583: 3578: 3576: 3575: 3559: 3557: 3556: 3551: 3549: 3548: 3532: 3530: 3529: 3524: 3522: 3521: 3463: 3461: 3460: 3455: 3453: 3452: 3449: 3437: 3436: 3433: 3419:feedforward size 3401: 3399: 3398: 3393: 3381: 3379: 3378: 3373: 3371: 3370: 3352: 3351: 3333: 3332: 3314: 3313: 3277: 3251: 3249: 3248: 3243: 3241: 3240: 3237: 3224: 3222: 3221: 3216: 3214: 3213: 3210: 3127: 3125: 3124: 3119: 3117: 3116: 3100: 3098: 3097: 3092: 3078: 3074: 3067: 3066: 3045: 3030: 3029: 3019: 2999: 2998: 2974: 2973: 2963: 2944: 2942: 2941: 2936: 2934: 2913: 2911: 2910: 2905: 2870: 2822: 2820: 2819: 2814: 2812: 2811: 2807: 2781: 2779: 2778: 2773: 2771: 2770: 2763: 2755: 2728: 2724: 2723: 2722: 2721: 2712: 2670: 2668: 2667: 2662: 2660: 2659: 2655: 2646: 2637: 2616: 2614: 2613: 2608: 2590: 2588: 2587: 2582: 2570: 2568: 2567: 2562: 2547: 2545: 2544: 2539: 2537: 2536: 2532: 2510: 2508: 2507: 2495: 2480: 2478: 2477: 2472: 2458: 2374: 2373: 2343: 2342: 2307: 2305: 2304: 2299: 2287: 2285: 2284: 2279: 2265: 2251: 2250: 2245: 2236: 2200: 2198: 2197: 2192: 2146: 2144: 2143: 2138: 2133: 2132: 2129: 2120: 2119: 2116: 2100: 2098: 2097: 2092: 2072: 2037: 1992: 1990: 1989: 1984: 1982: 1981: 1978: 1954: 1952: 1951: 1946: 1884: 1860: 1858: 1857: 1854:{\displaystyle } 1852: 1798: 1796: 1795: 1790: 1778: 1776: 1775: 1770: 1729: 1727: 1726: 1721: 1719: 1718: 1715: 1688:Lexical analysis 1673: 1671: 1670: 1665: 1612:masked attention 1586: 1584: 1583: 1578: 1573: 1570: 1565: 1562: 1550: 1549: 1546: 1527: 1524: 1514:log-perplexities 1450:natural language 1203:was revamped to 1201:Google Translate 949: 942: 935: 896:Related articles 773:Confusion matrix 526:Isolation forest 471:Graphical models 250: 249: 202:Learning to rank 197:Feature learning 35:Machine learning 26: 25: 16480: 16479: 16475: 16474: 16473: 16471: 16470: 16469: 16460:Google software 16450: 16449: 16448: 16443: 16395: 16309: 16275:Google DeepMind 16253: 16219:Geoffrey Hinton 16178: 16115: 16041:Project Debater 15987: 15885:Implementations 15880: 15834: 15798: 15741: 15683:Backpropagation 15617: 15603:Tensor calculus 15557: 15554: 15524: 15519: 15491: 15444: 15427: 15385:Language models 15380: 15340: 15314: 15290:Neural networks 15274: 15235: 15208: 15179: 15124: 15120:Google DeepMind 15101: 15096: 15066: 15031:Wayback Machine 15018: 15016:Further reading 15013: 15012: 14965: 14961: 14941: 14937: 14917: 14913: 14895: 14888: 14876: 14874: 14865: 14864: 14856: 14849: 14840: 14838: 14830: 14829: 14825: 14807: 14803: 14786: 14782: 14765: 14761: 14742: 14738: 14729: 14727: 14719: 14718: 14714: 14677: 14673: 14655: 14651: 14634: 14630: 14613: 14609: 14600: 14598: 14585: 14584: 14580: 14560: 14556: 14527: 14523: 14514: 14512: 14499: 14498: 14494: 14476: 14472: 14455: 14448: 14428: 14424: 14413: 14409: 14389: 14382: 14366: 14365: 14359: 14357: 14347: 14343: 14335: 14333: 14326: 14325: 14321: 14314: 14278: 14274: 14256: 14252: 14234: 14230: 14221: 14219: 14211: 14210: 14206: 14197: 14195: 14186: 14185: 14181: 14172: 14170: 14164:"Stanford CRFM" 14162: 14161: 14157: 14142:: 16344–16359. 14128: 14124: 14104: 14100: 14083: 14079: 14062: 14058: 14041: 14037: 14017: 14013: 13998: 13994: 13939: 13935: 13901: 13894: 13865: 13861: 13844: 13840: 13823: 13819: 13810: 13808: 13801:Google Research 13795: 13794: 13790: 13753: 13744: 13724: 13720: 13691: 13687: 13678: 13676: 13641: 13637: 13628: 13626: 13616: 13612: 13603: 13601: 13586: 13577: 13568: 13566: 13553: 13552: 13548: 13531: 13522: 13502: 13491: 13482: 13480: 13472: 13471: 13464: 13455: 13453: 13445: 13444: 13437: 13419: 13415: 13378: 13374: 13356: 13349: 13329: 13325: 13312: 13308: 13288: 13284: 13266: 13259: 13241: 13234: 13226: 13224: 13217: 13216: 13212: 13203: 13201: 13188: 13187: 13183: 13174: 13172: 13164: 13163: 13159: 13150: 13148: 13146:research.google 13140: 13139: 13135: 13126: 13124: 13115: 13114: 13110: 13093: 13086: 13077: 13075: 13057: 13053: 13033: 13029: 13020: 13018: 12995: 12988: 12971: 12967: 12944: 12940: 12931: 12929: 12906: 12902: 12885: 12881: 12864: 12860: 12831: 12827: 12777: 12773: 12756: 12752: 12735: 12726: 12693: 12684: 12669: 12665: 12650: 12646: 12627: 12623: 12618: 12614: 12605: 12601: 12569: 12560: 12553: 12510: 12506: 12499: 12488: 12480: 12476: 12441: 12437: 12428: 12426: 12413: 12412: 12403: 12375: 12368: 12351: 12344: 12309: 12305: 12288: 12284: 12268: 12264: 12244: 12237: 12220: 12216: 12199: 12192: 12183: 12181: 12168: 12167: 12160: 12106: 12102: 12086: 12076:Vaswani, Ashish 12073: 12048: 12043: 12038: 12037: 12032: 12028: 12020: 12016: 12011: 11962: 11931:protein folding 11827: 11768: 11736: 11732: 11718: 11715: 11714: 11697: 11693: 11672: 11668: 11666: 11663: 11662: 11640: 11636: 11634: 11629: 11620: 11616: 11591: 11587: 11578: 11577: 11573: 11569: 11567: 11563: 11558: 11529: 11527: 11524: 11523: 11506: 11501: 11488: 11484: 11476: 11473: 11472: 11448: 11444: 11439: 11427: 11424: 11423: 11400: 11396: 11382: 11378: 11370: 11364: 11360: 11354: 11350: 11346: 11342: 11336: 11326: 11322: 11312: 11305: 11300: 11287: 11283: 11269: 11265: 11257: 11251: 11247: 11241: 11237: 11233: 11229: 11223: 11213: 11209: 11199: 11197: 11178: 11174: 11165: 11164: 11160: 11156: 11154: 11150: 11145: 11116: 11114: 11111: 11110: 11076: 11072: 11064: 11058: 11054: 11047: 11043: 11020: 11016: 11008: 11002: 10998: 10991: 10987: 10955: 10951: 10943: 10937: 10933: 10926: 10922: 10899: 10895: 10887: 10881: 10877: 10870: 10866: 10855: 10844: 10840: 10835: 10819: 10815: 10813: 10810: 10809: 10787: 10783: 10779: 10772: 10768: 10755: 10753: 10749: 10745: 10698: 10696: 10693: 10692: 10669: 10665: 10651: 10648: 10647: 10630: 10626: 10605: 10601: 10599: 10596: 10595: 10578: 10574: 10559: 10555: 10528: 10524: 10494: 10490: 10463: 10459: 10435: 10418: 10415: 10414: 10407: 10373: 10370: 10369: 10368:which grows as 10345: 10341: 10333: 10330: 10329: 10288: 10285: 10284: 10264: 10260: 10252: 10249: 10248: 10229: 10226: 10225: 10205: 10201: 10193: 10190: 10189: 10186: 10174: 10148: 10137: 10136: 10135: 10133: 10130: 10129: 10112: 10101: 10100: 10099: 10097: 10094: 10093: 10076: 10072: 10070: 10067: 10066: 10049: 10038: 10037: 10036: 10034: 10031: 10030: 10013: 10002: 10001: 10000: 9998: 9995: 9994: 9977: 9966: 9965: 9964: 9955: 9944: 9943: 9942: 9933: 9922: 9921: 9920: 9911: 9900: 9899: 9898: 9896: 9893: 9892: 9872: 9869: 9868: 9851: 9847: 9845: 9842: 9841: 9824: 9820: 9799: 9795: 9786: 9782: 9780: 9777: 9776: 9764: 9754:to KV caching. 9740: 9716: 9712: 9698: 9694: 9682: 9678: 9666: 9661: 9646: 9645: 9641: 9630: 9626: 9616: 9611: 9610: 9581: 9579: 9576: 9575: 9556: 9552: 9543: 9539: 9537: 9534: 9533: 9516: 9512: 9498: 9493: 9477: 9472: 9456: 9451: 9436: 9435: 9431: 9420: 9416: 9406: 9401: 9400: 9371: 9369: 9366: 9365: 9360: 9316: 9288: 9264: 9253: 9239: 9236: 9235: 9214: 9203: 9202: 9198: 9183: 9179: 9177: 9174: 9173: 9170:Toeplitz matrix 9153: 9150: 9149: 9135: 9134: 9111: 9107: 9098: 9097: 9093: 9089: 9087: 9086: 9082: 9077: 9048: 9044: 9042: 9039: 9038: 9035: 9007: 9004: 9003: 8987: 8984: 8983: 8948: 8944: 8942: 8939: 8938: 8920: 8919: 8914: 8909: 8904: 8899: 8893: 8892: 8887: 8882: 8874: 8866: 8857: 8856: 8851: 8846: 8841: 8833: 8824: 8823: 8818: 8813: 8808: 8803: 8794: 8793: 8788: 8783: 8778: 8773: 8763: 8762: 8754: 8751: 8750: 8730: 8727: 8726: 8710: 8707: 8706: 8692: 8691: 8665: 8661: 8652: 8651: 8647: 8643: 8641: 8640: 8636: 8631: 8602: 8598: 8596: 8593: 8592: 8581: 8560: 8557: 8556: 8539: 8538: 8517: 8516: 8511: 8505: 8499: 8498: 8497: 8476: 8475: 8470: 8461: 8460: 8445: 8444: 8439: 8433: 8427: 8426: 8425: 8410: 8409: 8404: 8402: 8399: 8398: 8372: 8368: 8341: 8337: 8335: 8332: 8331: 8312: 8309: 8308: 8291: 8287: 8275: 8271: 8262: 8261: 8249: 8245: 8239: 8238: 8233: 8231: 8228: 8227: 8204: 8199: 8177: 8172: 8159: 8155: 8153: 8150: 8149: 8131: 8130: 8106: 8101: 8070: 8065: 8058: 8057: 8033: 8028: 7997: 7992: 7981: 7980: 7970: 7969: 7957: 7952: 7945: 7944: 7932: 7927: 7916: 7915: 7908: 7907: 7893: 7878: 7877: 7860: 7841: 7840: 7831: 7830: 7812: 7807: 7788: 7783: 7773: 7772: 7767: 7765: 7762: 7761: 7745: 7742: 7741: 7700: 7695: 7676: 7671: 7646: 7641: 7622: 7617: 7592: 7587: 7568: 7563: 7551: 7548: 7547: 7544: 7532: 7516: 7497: 7492: 7490:Subsequent work 7464: 7463: 7457: 7453: 7451: 7446: 7443: 7442: 7434: 7429: 7422: 7421: 7412: 7408: 7406: 7403: 7402: 7388:text generation 7360:text generation 7341: 7336: 7115: 7057: 7028: 7020: 7017: 7016: 6967: 6965: 6962: 6961: 6912: 6874: 6872: 6869: 6868: 6794: 6789: 6763: 6759: 6757: 6754: 6753: 6739: 6738: 6726: 6722: 6713: 6709: 6698: 6690: 6682: 6675: 6661: 6658: 6657: 6631: 6624: 6616: 6612: 6610: 6607: 6606: 6572: 6544: 6542: 6539: 6538: 6498: 6490: 6473: 6471: 6468: 6467: 6451: 6449: 6446: 6445: 6429: 6428: 6421: 6420: 6414: 6413: 6404: 6400: 6377: 6369: 6366: 6365: 6356: 6352: 6329: 6321: 6314: 6313: 6306: 6292: 6289: 6288: 6281: 6280: 6274: 6273: 6267: 6263: 6260: 6259: 6253: 6249: 6242: 6241: 6234: 6226: 6223: 6222: 6210: 6206: 6197: 6193: 6191: 6186: 6182: 6180: 6177: 6176: 6161: 6136: 6133: 6132: 6112: 6108: 6102: 6098: 6093: 6090: 6089: 6067: 6066: 6061: 6056: 6051: 6046: 6040: 6039: 6034: 6029: 6024: 6019: 6013: 6012: 6004: 5999: 5994: 5989: 5983: 5982: 5974: 5969: 5961: 5956: 5950: 5949: 5941: 5936: 5928: 5920: 5910: 5909: 5900: 5896: 5894: 5891: 5890: 5873: 5872: 5855: 5851: 5842: 5841: 5837: 5833: 5831: 5824: 5820: 5815: 5788:MaskedAttention 5786: 5782: 5780: 5777: 5776: 5760: 5757: 5756: 5737: 5734: 5733: 5717: 5714: 5713: 5691: 5688: 5687: 5671: 5668: 5667: 5664: 5624: 5619: 5618: 5609: 5605: 5603: 5600: 5599: 5571: 5568: 5567: 5544: 5540: 5525: 5521: 5506: 5502: 5500: 5497: 5496: 5476: 5472: 5470: 5467: 5466: 5446: 5442: 5440: 5437: 5436: 5420: 5417: 5416: 5399: 5394: 5381: 5376: 5363: 5358: 5352: 5349: 5348: 5332: 5329: 5328: 5311: 5307: 5295: 5290: 5274: 5269: 5253: 5248: 5233: 5219: 5215: 5205: 5200: 5199: 5170: 5168: 5165: 5164: 5148: 5145: 5144: 5107: 5103: 5094: 5090: 5081: 5077: 5076: 5072: 5070: 5067: 5066: 5047: 5025: 5021: 5012: 5008: 4999: 4995: 4993: 4990: 4989: 4972: 4968: 4959: 4955: 4946: 4942: 4940: 4937: 4936: 4916: 4912: 4903: 4899: 4889: 4885: 4876: 4872: 4862: 4858: 4849: 4845: 4843: 4840: 4839: 4822: 4818: 4816: 4813: 4812: 4792: 4788: 4786: 4783: 4782: 4762: 4758: 4756: 4753: 4752: 4732: 4728: 4726: 4723: 4722: 4700: 4699: 4683: 4679: 4670: 4669: 4665: 4661: 4659: 4655: 4650: 4621: 4617: 4615: 4612: 4611: 4594: 4590: 4588: 4585: 4584: 4567: 4563: 4561: 4558: 4557: 4540: 4536: 4534: 4531: 4530: 4514: 4511: 4510: 4494: 4491: 4490: 4474: 4471: 4470: 4454: 4451: 4450: 4442:to each token. 4427: 4424: 4423: 4403: 4399: 4397: 4394: 4393: 4377: 4374: 4373: 4356: 4352: 4343: 4339: 4337: 4334: 4333: 4317: 4314: 4313: 4297: 4294: 4293: 4276: 4272: 4263: 4259: 4257: 4254: 4253: 4237: 4234: 4233: 4217: 4214: 4213: 4196: 4192: 4190: 4187: 4186: 4169: 4165: 4163: 4160: 4159: 4136: 4132: 4130: 4128: 4125: 4124: 4107: 4103: 4101: 4098: 4097: 4080: 4076: 4074: 4071: 4070: 4050: 4047: 4046: 4030: 4027: 4026: 4006: 4002: 4000: 3997: 3996: 3976: 3972: 3963: 3959: 3957: 3954: 3953: 3936: 3932: 3923: 3919: 3910: 3906: 3904: 3901: 3900: 3880: 3876: 3870: 3866: 3858: 3855: 3854: 3837: 3833: 3827: 3823: 3815: 3812: 3811: 3794: 3790: 3784: 3780: 3772: 3769: 3768: 3751: 3747: 3740: 3733: 3729: 3720: 3716: 3714: 3711: 3710: 3693: 3689: 3687: 3684: 3683: 3665: 3658: 3654: 3652: 3649: 3648: 3628: 3624: 3622: 3619: 3618: 3601: 3597: 3595: 3592: 3591: 3571: 3567: 3565: 3562: 3561: 3544: 3540: 3538: 3535: 3534: 3517: 3513: 3511: 3508: 3507: 3481: 3476: 3470: 3448: 3444: 3432: 3428: 3426: 3423: 3422: 3387: 3384: 3383: 3360: 3356: 3341: 3337: 3322: 3318: 3303: 3299: 3267: 3265: 3262: 3261: 3236: 3232: 3230: 3227: 3226: 3209: 3205: 3203: 3200: 3199: 3192: 3172:encoder-decoder 3148: 3112: 3108: 3106: 3103: 3102: 3062: 3058: 3032: 3025: 3021: 3015: 3010: 3006: 2994: 2990: 2969: 2965: 2959: 2953: 2950: 2949: 2930: 2919: 2916: 2915: 2857: 2831: 2828: 2827: 2803: 2799: 2795: 2787: 2784: 2783: 2754: 2729: 2717: 2713: 2708: 2701: 2697: 2693: 2692: 2675: 2672: 2671: 2651: 2647: 2642: 2641: 2633: 2625: 2622: 2621: 2596: 2593: 2592: 2576: 2573: 2572: 2556: 2553: 2552: 2528: 2524: 2520: 2503: 2499: 2494: 2486: 2483: 2482: 2454: 2360: 2356: 2335: 2331: 2317: 2314: 2313: 2293: 2290: 2289: 2261: 2246: 2241: 2240: 2232: 2224: 2221: 2220: 2168: 2165: 2164: 2159:A diagram of a 2153: 2128: 2124: 2115: 2111: 2106: 2103: 2102: 2050: 2015: 2013: 2010: 2009: 1998: 1977: 1973: 1971: 1968: 1967: 1966:and written as 1868: 1866: 1863: 1862: 1804: 1801: 1800: 1784: 1781: 1780: 1764: 1761: 1760: 1749: 1743: 1714: 1710: 1708: 1705: 1704: 1702:vocabulary size 1690: 1682:Main articles: 1680: 1656: 1653: 1652: 1624: 1569: 1561: 1545: 1538: 1523: 1521: 1518: 1517: 1502: 1496: 1394: 1375: 1370: 1304:word embeddings 1284: 1236: 1230: 1214:avant la lettre 1148: 1142: 1089: 1084: 1078: 1046:computer vision 1014:(RNNs) such as 953: 924: 923: 897: 889: 888: 849: 841: 840: 801:Kernel machines 796: 788: 787: 763: 755: 754: 735:Active learning 730: 722: 721: 690: 680: 679: 605:Diffusion model 541: 531: 530: 503: 493: 492: 466: 456: 455: 411:Factor analysis 406: 396: 395: 379: 342: 332: 331: 252: 251: 235: 234: 233: 222: 221: 127: 119: 118: 84:Online learning 49: 37: 24: 17: 12: 11: 5: 16478: 16468: 16467: 16462: 16445: 16444: 16442: 16441: 16440: 16439: 16434: 16421: 16420: 16419: 16414: 16400: 16397: 16396: 16394: 16393: 16388: 16383: 16378: 16373: 16368: 16363: 16358: 16353: 16348: 16343: 16338: 16333: 16328: 16323: 16317: 16315: 16311: 16310: 16308: 16307: 16302: 16297: 16292: 16287: 16282: 16277: 16272: 16267: 16261: 16259: 16255: 16254: 16252: 16251: 16249:Ilya Sutskever 16246: 16241: 16236: 16231: 16226: 16221: 16216: 16214:Demis Hassabis 16211: 16206: 16204:Ian Goodfellow 16201: 16196: 16190: 16188: 16184: 16183: 16180: 16179: 16177: 16176: 16171: 16170: 16169: 16159: 16154: 16149: 16144: 16139: 16134: 16129: 16123: 16121: 16117: 16116: 16114: 16113: 16108: 16103: 16098: 16093: 16088: 16083: 16078: 16073: 16068: 16063: 16058: 16053: 16048: 16043: 16038: 16033: 16032: 16031: 16021: 16016: 16011: 16006: 16001: 15995: 15993: 15989: 15988: 15986: 15985: 15980: 15979: 15978: 15973: 15963: 15962: 15961: 15956: 15951: 15941: 15936: 15931: 15926: 15921: 15916: 15911: 15906: 15901: 15895: 15893: 15886: 15882: 15881: 15879: 15878: 15873: 15868: 15863: 15858: 15853: 15848: 15842: 15840: 15836: 15835: 15833: 15832: 15827: 15822: 15817: 15812: 15806: 15804: 15800: 15799: 15797: 15796: 15795: 15794: 15787:Language model 15784: 15779: 15774: 15773: 15772: 15762: 15761: 15760: 15749: 15747: 15743: 15742: 15740: 15739: 15737:Autoregression 15734: 15729: 15728: 15727: 15717: 15715:Regularization 15712: 15711: 15710: 15705: 15700: 15690: 15685: 15680: 15678:Loss functions 15675: 15670: 15665: 15660: 15655: 15654: 15653: 15643: 15638: 15637: 15636: 15625: 15623: 15619: 15618: 15616: 15615: 15613:Inductive bias 15610: 15605: 15600: 15595: 15590: 15585: 15580: 15575: 15567: 15565: 15559: 15558: 15553: 15552: 15545: 15538: 15530: 15521: 15520: 15518: 15517: 15507: 15496: 15493: 15492: 15490: 15489: 15484: 15479: 15474: 15469: 15464: 15456: 15454: 15450: 15449: 15446: 15445: 15443: 15442: 15435: 15433: 15429: 15428: 15426: 15425: 15419: 15413: 15407: 15401: 15395: 15388: 15386: 15382: 15381: 15379: 15378: 15372: 15366: 15359: 15357: 15350: 15346: 15345: 15342: 15341: 15339: 15338: 15333: 15328: 15322: 15320: 15316: 15315: 15313: 15312: 15306: 15300: 15293: 15291: 15284: 15280: 15279: 15276: 15275: 15273: 15272: 15266: 15260: 15254: 15247: 15245: 15241: 15240: 15237: 15236: 15234: 15233: 15225: 15216: 15214: 15210: 15209: 15207: 15206: 15200: 15194: 15187: 15185: 15181: 15180: 15178: 15177: 15171: 15165: 15159: 15153: 15146: 15144: 15137: 15130: 15126: 15125: 15123: 15122: 15117: 15112: 15106: 15103: 15102: 15095: 15094: 15087: 15080: 15072: 15065: 15064: 15049: 15034: 15019: 15017: 15014: 15011: 15010: 14959: 14935: 14911: 14886: 14877:|journal= 14847: 14823: 14801: 14780: 14759: 14756:: 34892–34916. 14736: 14712: 14671: 14649: 14628: 14607: 14591:Google AI Blog 14578: 14554: 14521: 14505:Google AI Blog 14492: 14470: 14446: 14422: 14407: 14380: 14341: 14319: 14312: 14272: 14250: 14228: 14204: 14179: 14155: 14122: 14098: 14077: 14056: 14035: 14011: 13992: 13953:(3): 733–763. 13933: 13892: 13859: 13838: 13817: 13788: 13742: 13718: 13685: 13635: 13610: 13588:Alammar, Jay. 13575: 13561:. 2016-04-18. 13546: 13520: 13489: 13478:huggingface.co 13462: 13451:huggingface.co 13435: 13413: 13372: 13347: 13323: 13306: 13282: 13257: 13232: 13210: 13181: 13157: 13133: 13108: 13084: 13065:The New Yorker 13051: 13027: 12997:Levy, Steven. 12986: 12965: 12938: 12928:on 24 May 2023 12900: 12879: 12858: 12825: 12771: 12750: 12724: 12682: 12663: 12644: 12621: 12612: 12599: 12580:(1): 131–139. 12551: 12518:Applied Optics 12504: 12497: 12474: 12455:(3): 205–254. 12435: 12419:Google AI Blog 12401: 12366: 12342: 12323:(2): 576–583. 12303: 12282: 12262: 12235: 12214: 12190: 12176:. 2019-02-14. 12158: 12100: 12080:Gomez, Aidan N 12045: 12044: 12042: 12039: 12036: 12035: 12026: 12013: 12012: 12010: 12007: 12006: 12005: 11999: 11993: 11987: 11981: 11975: 11969: 11961: 11958: 11957: 11956: 11938: 11928: 11923: 11914: 11913: 11911:speech-to-text 11908: 11902: 11896: 11891: 11886: 11880: 11826: 11823: 11767: 11764: 11747: 11744: 11739: 11735: 11731: 11728: 11725: 11722: 11700: 11696: 11692: 11689: 11686: 11683: 11680: 11675: 11671: 11650: 11643: 11639: 11632: 11628: 11623: 11619: 11615: 11612: 11609: 11606: 11602: 11594: 11590: 11581: 11576: 11572: 11566: 11557: 11554: 11551: 11548: 11545: 11542: 11539: 11536: 11509: 11504: 11500: 11496: 11491: 11487: 11483: 11480: 11455: 11451: 11447: 11442: 11438: 11434: 11431: 11408: 11403: 11399: 11395: 11392: 11385: 11381: 11377: 11373: 11367: 11363: 11357: 11353: 11349: 11345: 11339: 11335: 11329: 11325: 11321: 11318: 11315: 11308: 11303: 11299: 11295: 11290: 11286: 11282: 11279: 11272: 11268: 11264: 11260: 11254: 11250: 11244: 11240: 11236: 11232: 11226: 11222: 11216: 11212: 11208: 11205: 11202: 11196: 11193: 11189: 11181: 11177: 11168: 11163: 11159: 11153: 11144: 11141: 11138: 11135: 11132: 11129: 11126: 11123: 11098: 11095: 11092: 11089: 11086: 11079: 11075: 11071: 11067: 11061: 11057: 11053: 11050: 11046: 11042: 11039: 11036: 11033: 11030: 11023: 11019: 11015: 11011: 11005: 11001: 10997: 10994: 10990: 10986: 10983: 10980: 10977: 10974: 10971: 10968: 10965: 10958: 10954: 10950: 10946: 10940: 10936: 10932: 10929: 10925: 10921: 10918: 10915: 10912: 10909: 10902: 10898: 10894: 10890: 10884: 10880: 10876: 10873: 10869: 10865: 10862: 10858: 10854: 10847: 10843: 10838: 10834: 10831: 10828: 10825: 10822: 10818: 10790: 10786: 10782: 10775: 10771: 10767: 10764: 10761: 10758: 10752: 10748: 10744: 10741: 10738: 10735: 10732: 10729: 10726: 10723: 10720: 10717: 10714: 10711: 10708: 10705: 10701: 10680: 10677: 10672: 10668: 10664: 10661: 10658: 10655: 10633: 10629: 10625: 10622: 10619: 10616: 10613: 10608: 10604: 10581: 10577: 10573: 10570: 10567: 10562: 10558: 10554: 10551: 10548: 10545: 10542: 10539: 10536: 10531: 10527: 10523: 10520: 10517: 10514: 10511: 10508: 10505: 10502: 10497: 10493: 10489: 10486: 10483: 10480: 10477: 10474: 10471: 10466: 10462: 10458: 10455: 10452: 10449: 10443: 10439: 10434: 10431: 10428: 10425: 10422: 10406: 10403: 10386: 10383: 10380: 10377: 10353: 10348: 10344: 10340: 10337: 10310: 10307: 10304: 10301: 10298: 10295: 10292: 10272: 10267: 10263: 10259: 10256: 10233: 10213: 10208: 10204: 10200: 10197: 10185: 10182: 10173: 10170: 10151: 10144: 10141: 10115: 10108: 10105: 10079: 10075: 10052: 10045: 10042: 10016: 10009: 10006: 9980: 9973: 9970: 9963: 9958: 9951: 9948: 9941: 9936: 9929: 9926: 9919: 9914: 9907: 9904: 9876: 9854: 9850: 9827: 9823: 9819: 9816: 9813: 9810: 9807: 9802: 9798: 9794: 9789: 9785: 9763: 9760: 9748:PagedAttention 9739: 9736: 9719: 9715: 9710: 9706: 9701: 9697: 9693: 9690: 9685: 9681: 9677: 9674: 9669: 9664: 9660: 9656: 9653: 9644: 9638: 9629: 9625: 9622: 9619: 9609: 9606: 9603: 9600: 9597: 9594: 9591: 9588: 9559: 9555: 9551: 9546: 9542: 9519: 9515: 9510: 9506: 9501: 9496: 9492: 9488: 9485: 9480: 9475: 9471: 9467: 9464: 9459: 9454: 9450: 9446: 9443: 9434: 9428: 9419: 9415: 9412: 9409: 9399: 9396: 9393: 9390: 9387: 9384: 9381: 9378: 9359: 9356: 9315: 9314:FlashAttention 9312: 9287: 9284: 9270: 9267: 9263: 9259: 9256: 9252: 9249: 9246: 9243: 9220: 9217: 9213: 9209: 9206: 9201: 9197: 9192: 9189: 9186: 9182: 9157: 9133: 9129: 9125: 9122: 9114: 9110: 9101: 9096: 9092: 9085: 9076: 9073: 9070: 9067: 9064: 9061: 9058: 9055: 9047: 9046: 9034: 9031: 9014: 9011: 8991: 8971: 8968: 8965: 8962: 8957: 8954: 8951: 8947: 8924: 8918: 8915: 8913: 8910: 8908: 8905: 8903: 8900: 8898: 8895: 8894: 8891: 8888: 8886: 8883: 8881: 8878: 8875: 8873: 8870: 8867: 8865: 8862: 8859: 8858: 8855: 8852: 8850: 8847: 8845: 8842: 8840: 8837: 8834: 8832: 8829: 8826: 8825: 8822: 8819: 8817: 8814: 8812: 8809: 8807: 8804: 8802: 8799: 8796: 8795: 8792: 8789: 8787: 8784: 8782: 8779: 8777: 8774: 8772: 8769: 8768: 8766: 8761: 8758: 8734: 8714: 8690: 8686: 8682: 8679: 8676: 8668: 8664: 8655: 8650: 8646: 8639: 8630: 8627: 8624: 8621: 8618: 8615: 8612: 8609: 8601: 8600: 8580: 8577: 8564: 8542: 8537: 8534: 8531: 8528: 8525: 8520: 8508: 8502: 8496: 8493: 8490: 8487: 8484: 8479: 8469: 8464: 8459: 8456: 8453: 8448: 8436: 8430: 8424: 8421: 8418: 8413: 8381: 8378: 8375: 8371: 8367: 8364: 8361: 8358: 8355: 8350: 8347: 8344: 8340: 8319: 8316: 8307:For a list of 8294: 8290: 8284: 8281: 8278: 8274: 8270: 8265: 8260: 8257: 8252: 8248: 8242: 8213: 8210: 8207: 8202: 8198: 8194: 8191: 8186: 8183: 8180: 8175: 8171: 8167: 8162: 8158: 8135: 8129: 8126: 8123: 8120: 8115: 8112: 8109: 8104: 8100: 8096: 8093: 8090: 8087: 8084: 8079: 8076: 8073: 8068: 8064: 8060: 8059: 8056: 8053: 8050: 8047: 8042: 8039: 8036: 8031: 8027: 8023: 8020: 8017: 8014: 8011: 8006: 8003: 8000: 7995: 7991: 7987: 7986: 7984: 7979: 7974: 7966: 7963: 7960: 7955: 7951: 7947: 7946: 7941: 7938: 7935: 7930: 7926: 7922: 7921: 7919: 7912: 7906: 7903: 7900: 7897: 7894: 7892: 7889: 7886: 7883: 7880: 7879: 7876: 7873: 7870: 7867: 7864: 7861: 7859: 7856: 7853: 7850: 7847: 7846: 7844: 7839: 7834: 7829: 7826: 7821: 7818: 7815: 7810: 7806: 7802: 7797: 7794: 7791: 7786: 7782: 7776: 7749: 7729: 7726: 7723: 7720: 7717: 7714: 7709: 7706: 7703: 7698: 7694: 7690: 7685: 7682: 7679: 7674: 7670: 7666: 7663: 7660: 7655: 7652: 7649: 7644: 7640: 7636: 7631: 7628: 7625: 7620: 7616: 7612: 7609: 7606: 7601: 7598: 7595: 7590: 7586: 7582: 7577: 7574: 7571: 7566: 7562: 7558: 7555: 7543: 7540: 7531: 7528: 7515: 7512: 7496: 7493: 7491: 7488: 7468: 7456: 7452: 7449: 7445: 7444: 7441: 7438: 7435: 7432: 7428: 7427: 7425: 7420: 7411: 7340: 7337: 7327:1:length(z_d) 7315:1:length(z_d) 7303:1:length(z_d) 7291:1:length(z_d) 7279:1:length(z_d) 7267:1:length(z_d) 7255:1:length(z_d) 7228:1:length(z_d) 7213:1:length(z_e) 7201:1:length(z_e) 7189:1:length(z_e) 7177:1:length(z_e) 7165:1:length(z_e) 7138:1:length(z_e) 7119: 7114: 7111: 7097: 7094: 7091: 7088: 7084: 7081: 7078: 7075: 7072: 7069: 7066: 7063: 7060: 7056: 7052: 7049: 7046: 7043: 7040: 7037: 7034: 7031: 7027: 7024: 7001: 6998: 6995: 6991: 6988: 6985: 6982: 6979: 6976: 6973: 6970: 6949: 6946: 6943: 6940: 6936: 6933: 6930: 6927: 6924: 6921: 6918: 6915: 6911: 6908: 6905: 6901: 6898: 6895: 6892: 6889: 6886: 6883: 6880: 6877: 6793: 6790: 6788: 6785: 6766: 6762: 6737: 6734: 6729: 6725: 6721: 6716: 6712: 6708: 6704: 6701: 6697: 6689: 6681: 6678: 6676: 6674: 6671: 6668: 6660: 6659: 6656: 6653: 6650: 6647: 6644: 6641: 6638: 6630: 6627: 6625: 6622: 6619: 6615: 6614: 6596:autoregressive 6571: 6568: 6526: 6523: 6520: 6517: 6514: 6511: 6508: 6505: 6497: 6489: 6486: 6483: 6480: 6425: 6419: 6416: 6415: 6412: 6407: 6403: 6399: 6396: 6393: 6390: 6387: 6384: 6376: 6368: 6367: 6364: 6359: 6355: 6351: 6348: 6345: 6342: 6339: 6336: 6328: 6320: 6319: 6317: 6312: 6309: 6307: 6305: 6302: 6299: 6291: 6290: 6285: 6279: 6276: 6275: 6270: 6266: 6262: 6261: 6256: 6252: 6248: 6247: 6245: 6240: 6237: 6235: 6233: 6225: 6224: 6221: 6218: 6213: 6209: 6205: 6200: 6196: 6192: 6185: 6184: 6160: 6157: 6140: 6118: 6115: 6111: 6101: 6097: 6071: 6065: 6062: 6060: 6057: 6055: 6052: 6050: 6047: 6045: 6042: 6041: 6038: 6035: 6033: 6030: 6028: 6025: 6023: 6020: 6018: 6015: 6014: 6011: 6008: 6005: 6003: 6000: 5998: 5995: 5993: 5990: 5988: 5985: 5984: 5981: 5978: 5975: 5973: 5970: 5968: 5965: 5962: 5960: 5957: 5955: 5952: 5951: 5948: 5945: 5942: 5940: 5937: 5935: 5932: 5929: 5927: 5924: 5921: 5919: 5916: 5915: 5913: 5908: 5899: 5871: 5867: 5858: 5854: 5845: 5840: 5836: 5830: 5827: 5823: 5814: 5811: 5808: 5805: 5802: 5799: 5796: 5793: 5785: 5784: 5764: 5744: 5741: 5721: 5701: 5698: 5695: 5675: 5663: 5660: 5645: 5642: 5639: 5636: 5633: 5630: 5627: 5622: 5617: 5612: 5608: 5587: 5584: 5581: 5578: 5575: 5555: 5552: 5543: 5539: 5536: 5533: 5524: 5520: 5517: 5514: 5505: 5475: 5449: 5445: 5424: 5402: 5397: 5393: 5389: 5384: 5379: 5375: 5371: 5366: 5361: 5357: 5336: 5314: 5310: 5306: 5303: 5298: 5293: 5289: 5285: 5282: 5277: 5272: 5268: 5264: 5261: 5256: 5251: 5247: 5243: 5240: 5232: 5227: 5218: 5214: 5211: 5208: 5198: 5195: 5192: 5189: 5186: 5183: 5180: 5177: 5163:, then we have 5152: 5130:attention head 5116: 5110: 5106: 5102: 5097: 5093: 5089: 5084: 5080: 5075: 5046: 5043: 5024: 5020: 5011: 5007: 4998: 4971: 4967: 4958: 4954: 4945: 4915: 4911: 4902: 4897: 4888: 4884: 4875: 4870: 4861: 4857: 4848: 4821: 4810:head dimension 4791: 4761: 4731: 4698: 4694: 4686: 4682: 4673: 4668: 4664: 4658: 4649: 4646: 4643: 4640: 4637: 4634: 4631: 4628: 4620: 4619: 4597: 4593: 4570: 4566: 4543: 4539: 4518: 4498: 4478: 4458: 4431: 4409: 4406: 4402: 4381: 4359: 4355: 4351: 4346: 4342: 4321: 4301: 4279: 4275: 4271: 4266: 4262: 4241: 4221: 4199: 4195: 4172: 4168: 4139: 4135: 4110: 4106: 4083: 4079: 4054: 4034: 4012: 4009: 4005: 3975: 3971: 3962: 3939: 3935: 3931: 3926: 3922: 3918: 3913: 3909: 3883: 3879: 3869: 3865: 3862: 3840: 3836: 3826: 3822: 3819: 3797: 3793: 3783: 3779: 3776: 3754: 3750: 3739: 3736: 3732: 3728: 3723: 3719: 3696: 3692: 3664: 3661: 3657: 3627: 3600: 3574: 3570: 3547: 3543: 3520: 3516: 3480: 3479:Attention head 3477: 3472:Main article: 3469: 3466: 3447: 3443: 3440: 3431: 3391: 3369: 3366: 3363: 3359: 3355: 3350: 3347: 3344: 3340: 3336: 3331: 3328: 3325: 3321: 3317: 3312: 3309: 3306: 3302: 3298: 3295: 3292: 3289: 3286: 3283: 3280: 3276: 3273: 3270: 3235: 3208: 3191: 3188: 3147: 3144: 3133:language model 3115: 3111: 3090: 3087: 3084: 3081: 3077: 3073: 3070: 3065: 3061: 3057: 3054: 3051: 3048: 3044: 3041: 3038: 3035: 3028: 3024: 3018: 3014: 3009: 3005: 3002: 2997: 2993: 2989: 2986: 2983: 2980: 2977: 2972: 2968: 2962: 2958: 2933: 2929: 2926: 2923: 2903: 2900: 2897: 2894: 2891: 2888: 2885: 2882: 2879: 2876: 2873: 2869: 2866: 2863: 2860: 2856: 2853: 2850: 2847: 2844: 2841: 2838: 2835: 2810: 2806: 2802: 2798: 2794: 2791: 2769: 2766: 2761: 2758: 2753: 2750: 2747: 2744: 2741: 2738: 2735: 2732: 2727: 2720: 2716: 2711: 2707: 2704: 2700: 2696: 2691: 2688: 2685: 2682: 2679: 2658: 2654: 2650: 2645: 2640: 2636: 2632: 2629: 2606: 2603: 2600: 2580: 2560: 2535: 2531: 2527: 2523: 2519: 2516: 2513: 2506: 2502: 2498: 2493: 2490: 2470: 2467: 2464: 2461: 2457: 2453: 2450: 2447: 2444: 2441: 2438: 2435: 2432: 2429: 2426: 2423: 2419: 2416: 2413: 2410: 2407: 2404: 2401: 2398: 2395: 2392: 2389: 2386: 2383: 2380: 2377: 2372: 2369: 2366: 2363: 2359: 2355: 2352: 2349: 2346: 2341: 2338: 2334: 2330: 2327: 2324: 2321: 2297: 2277: 2274: 2271: 2268: 2264: 2260: 2257: 2254: 2249: 2244: 2239: 2235: 2231: 2228: 2190: 2187: 2184: 2181: 2178: 2175: 2172: 2152: 2149: 2136: 2127: 2123: 2114: 2110: 2090: 2087: 2084: 2081: 2078: 2075: 2071: 2068: 2065: 2062: 2059: 2056: 2053: 2049: 2046: 2043: 2040: 2036: 2033: 2030: 2027: 2024: 2021: 2018: 1997: 1994: 1976: 1964:embedding size 1944: 1941: 1938: 1935: 1932: 1929: 1926: 1923: 1920: 1917: 1914: 1911: 1908: 1905: 1902: 1899: 1896: 1893: 1890: 1887: 1883: 1880: 1877: 1874: 1871: 1850: 1847: 1844: 1841: 1838: 1835: 1832: 1829: 1826: 1823: 1820: 1817: 1814: 1811: 1808: 1788: 1768: 1747:Word embedding 1742: 1739: 1713: 1679: 1676: 1663: 1660: 1642: 1641: 1638: 1634: 1631: 1623: 1620: 1576: 1568: 1560: 1557: 1554: 1544: 1541: 1537: 1533: 1530: 1495: 1492: 1487: 1486: 1479: 1472: 1446:T5 transformer 1442: 1441: 1436: 1431: 1426: 1421: 1418: 1393: 1390: 1374: 1371: 1369: 1366: 1283: 1280: 1232:Main article: 1229: 1226: 1144:Main article: 1141: 1138: 1088: 1085: 1077: 1074: 998:contextualized 994:word embedding 955: 954: 952: 951: 944: 937: 929: 926: 925: 922: 921: 916: 915: 914: 904: 898: 895: 894: 891: 890: 887: 886: 881: 876: 871: 866: 861: 856: 850: 847: 846: 843: 842: 839: 838: 833: 828: 823: 821:Occam learning 818: 813: 808: 803: 797: 794: 793: 790: 789: 786: 785: 780: 778:Learning curve 775: 770: 764: 761: 760: 757: 756: 753: 752: 747: 742: 737: 731: 728: 727: 724: 723: 720: 719: 718: 717: 707: 702: 697: 691: 686: 685: 682: 681: 678: 677: 671: 666: 661: 656: 655: 654: 644: 639: 638: 637: 632: 627: 622: 612: 607: 602: 597: 596: 595: 585: 584: 583: 578: 573: 568: 558: 553: 548: 542: 537: 536: 533: 532: 529: 528: 523: 518: 510: 504: 499: 498: 495: 494: 491: 490: 489: 488: 483: 478: 467: 462: 461: 458: 457: 454: 453: 448: 443: 438: 433: 428: 423: 418: 413: 407: 402: 401: 398: 397: 394: 393: 388: 383: 377: 372: 367: 359: 354: 349: 343: 338: 337: 334: 333: 330: 329: 324: 319: 314: 309: 304: 299: 294: 286: 285: 284: 279: 274: 264: 262:Decision trees 259: 253: 239:classification 229: 228: 227: 224: 223: 220: 219: 214: 209: 204: 199: 194: 189: 184: 179: 174: 169: 164: 159: 154: 149: 144: 139: 134: 132:Classification 128: 125: 124: 121: 120: 117: 116: 111: 106: 101: 96: 91: 89:Batch learning 86: 81: 76: 71: 66: 61: 56: 50: 47: 46: 43: 42: 31: 30: 15: 9: 6: 4: 3: 2: 16477: 16466: 16463: 16461: 16458: 16457: 16455: 16438: 16435: 16433: 16430: 16429: 16422: 16418: 16415: 16413: 16410: 16409: 16406: 16402: 16401: 16398: 16392: 16389: 16387: 16384: 16382: 16379: 16377: 16374: 16372: 16369: 16367: 16364: 16362: 16359: 16357: 16354: 16352: 16349: 16347: 16344: 16342: 16339: 16337: 16334: 16332: 16329: 16327: 16324: 16322: 16319: 16318: 16316: 16314:Architectures 16312: 16306: 16303: 16301: 16298: 16296: 16293: 16291: 16288: 16286: 16283: 16281: 16278: 16276: 16273: 16271: 16268: 16266: 16263: 16262: 16260: 16258:Organizations 16256: 16250: 16247: 16245: 16242: 16240: 16237: 16235: 16232: 16230: 16227: 16225: 16222: 16220: 16217: 16215: 16212: 16210: 16207: 16205: 16202: 16200: 16197: 16195: 16194:Yoshua Bengio 16192: 16191: 16189: 16185: 16175: 16174:Robot control 16172: 16168: 16165: 16164: 16163: 16160: 16158: 16155: 16153: 16150: 16148: 16145: 16143: 16140: 16138: 16135: 16133: 16130: 16128: 16125: 16124: 16122: 16118: 16112: 16109: 16107: 16104: 16102: 16099: 16097: 16094: 16092: 16091:Chinchilla AI 16089: 16087: 16084: 16082: 16079: 16077: 16074: 16072: 16069: 16067: 16064: 16062: 16059: 16057: 16054: 16052: 16049: 16047: 16044: 16042: 16039: 16037: 16034: 16030: 16027: 16026: 16025: 16022: 16020: 16017: 16015: 16012: 16010: 16007: 16005: 16002: 16000: 15997: 15996: 15994: 15990: 15984: 15981: 15977: 15974: 15972: 15969: 15968: 15967: 15964: 15960: 15957: 15955: 15952: 15950: 15947: 15946: 15945: 15942: 15940: 15937: 15935: 15932: 15930: 15927: 15925: 15922: 15920: 15917: 15915: 15912: 15910: 15907: 15905: 15902: 15900: 15897: 15896: 15894: 15890: 15887: 15883: 15877: 15874: 15872: 15869: 15867: 15864: 15862: 15859: 15857: 15854: 15852: 15849: 15847: 15844: 15843: 15841: 15837: 15831: 15828: 15826: 15823: 15821: 15818: 15816: 15813: 15811: 15808: 15807: 15805: 15801: 15793: 15790: 15789: 15788: 15785: 15783: 15780: 15778: 15775: 15771: 15770:Deep learning 15768: 15767: 15766: 15763: 15759: 15756: 15755: 15754: 15751: 15750: 15748: 15744: 15738: 15735: 15733: 15730: 15726: 15723: 15722: 15721: 15718: 15716: 15713: 15709: 15706: 15704: 15701: 15699: 15696: 15695: 15694: 15691: 15689: 15686: 15684: 15681: 15679: 15676: 15674: 15671: 15669: 15666: 15664: 15661: 15659: 15658:Hallucination 15656: 15652: 15649: 15648: 15647: 15644: 15642: 15639: 15635: 15632: 15631: 15630: 15627: 15626: 15624: 15620: 15614: 15611: 15609: 15606: 15604: 15601: 15599: 15596: 15594: 15591: 15589: 15586: 15584: 15581: 15579: 15576: 15574: 15573: 15569: 15568: 15566: 15564: 15560: 15551: 15546: 15544: 15539: 15537: 15532: 15531: 15528: 15516: 15508: 15506: 15498: 15497: 15494: 15488: 15485: 15483: 15480: 15478: 15475: 15473: 15470: 15468: 15465: 15462: 15458: 15457: 15455: 15451: 15440: 15437: 15436: 15434: 15430: 15423: 15420: 15417: 15414: 15411: 15408: 15405: 15402: 15399: 15396: 15393: 15390: 15389: 15387: 15383: 15376: 15373: 15370: 15367: 15364: 15361: 15360: 15358: 15354: 15351: 15349:Generative AI 15347: 15337: 15334: 15332: 15329: 15327: 15324: 15323: 15321: 15317: 15310: 15307: 15304: 15301: 15298: 15295: 15294: 15292: 15288: 15285: 15281: 15270: 15269:AlphaGeometry 15267: 15264: 15261: 15258: 15255: 15252: 15249: 15248: 15246: 15242: 15231: 15230: 15226: 15223: 15222: 15218: 15217: 15215: 15211: 15204: 15201: 15198: 15195: 15192: 15189: 15188: 15186: 15182: 15175: 15172: 15169: 15166: 15163: 15160: 15157: 15154: 15151: 15148: 15147: 15145: 15141: 15138: 15134: 15131: 15127: 15121: 15118: 15116: 15113: 15111: 15108: 15107: 15104: 15100: 15093: 15088: 15086: 15081: 15079: 15074: 15073: 15070: 15060: 15055: 15050: 15045: 15040: 15035: 15032: 15028: 15025: 15021: 15020: 15006: 15002: 14997: 14992: 14987: 14982: 14978: 14974: 14970: 14963: 14955: 14950: 14946: 14939: 14931: 14926: 14922: 14915: 14906: 14901: 14893: 14891: 14882: 14869: 14861: 14854: 14852: 14837: 14833: 14827: 14818: 14813: 14805: 14796: 14791: 14784: 14775: 14770: 14763: 14755: 14751: 14747: 14740: 14726: 14722: 14716: 14708: 14704: 14699: 14694: 14690: 14686: 14682: 14675: 14666: 14661: 14653: 14644: 14639: 14632: 14623: 14618: 14611: 14596: 14592: 14588: 14582: 14574: 14569: 14565: 14558: 14549: 14544: 14540: 14536: 14532: 14525: 14510: 14506: 14502: 14496: 14487: 14482: 14474: 14465: 14460: 14453: 14451: 14442: 14437: 14433: 14426: 14418: 14411: 14403: 14398: 14394: 14387: 14385: 14376: 14370: 14356: 14352: 14345: 14331: 14330: 14323: 14315: 14309: 14305: 14301: 14296: 14291: 14287: 14283: 14276: 14267: 14262: 14254: 14245: 14240: 14232: 14218: 14214: 14208: 14193: 14192:Princeton NLP 14189: 14183: 14169: 14165: 14159: 14150: 14145: 14141: 14137: 14133: 14126: 14118: 14113: 14109: 14102: 14093: 14088: 14081: 14072: 14067: 14060: 14051: 14046: 14039: 14031: 14026: 14022: 14015: 14007: 14003: 13996: 13988: 13984: 13980: 13976: 13971: 13966: 13961: 13956: 13952: 13948: 13944: 13937: 13929: 13925: 13920: 13915: 13911: 13907: 13899: 13897: 13887: 13882: 13878: 13874: 13870: 13863: 13854: 13849: 13842: 13833: 13828: 13821: 13806: 13802: 13798: 13792: 13784: 13780: 13775: 13770: 13767:(140): 1–67. 13766: 13762: 13758: 13751: 13749: 13747: 13738: 13733: 13729: 13722: 13713: 13708: 13704: 13700: 13696: 13689: 13674: 13669: 13664: 13659: 13654: 13650: 13646: 13639: 13625: 13621: 13618:Team, Keras. 13614: 13599: 13595: 13591: 13584: 13582: 13580: 13564: 13560: 13556: 13550: 13541: 13536: 13529: 13527: 13525: 13516: 13511: 13507: 13500: 13498: 13496: 13494: 13479: 13475: 13469: 13467: 13452: 13448: 13442: 13440: 13430: 13425: 13417: 13409: 13405: 13400: 13395: 13391: 13387: 13383: 13376: 13367: 13362: 13354: 13352: 13343: 13338: 13334: 13327: 13319: 13318: 13310: 13302: 13297: 13293: 13286: 13277: 13272: 13264: 13262: 13252: 13247: 13239: 13237: 13222: 13221: 13214: 13199: 13195: 13191: 13185: 13171: 13167: 13161: 13147: 13143: 13137: 13122: 13118: 13112: 13103: 13098: 13091: 13089: 13074: 13070: 13066: 13062: 13055: 13047: 13042: 13038: 13031: 13016: 13012: 13008: 13004: 13000: 12993: 12991: 12981: 12976: 12969: 12961: 12957: 12953: 12949: 12942: 12927: 12923: 12919: 12915: 12911: 12904: 12895: 12890: 12883: 12874: 12869: 12862: 12853: 12848: 12844: 12840: 12836: 12829: 12822: 12818: 12814: 12810: 12805: 12800: 12795: 12790: 12786: 12782: 12775: 12766: 12761: 12754: 12745: 12740: 12733: 12731: 12729: 12720: 12716: 12711: 12706: 12702: 12698: 12691: 12689: 12687: 12678: 12674: 12667: 12659: 12655: 12648: 12640: 12636: 12632: 12625: 12616: 12609: 12603: 12595: 12591: 12587: 12583: 12579: 12575: 12568: 12564: 12558: 12556: 12547: 12543: 12539: 12535: 12531: 12527: 12523: 12519: 12515: 12508: 12500: 12494: 12487: 12486: 12478: 12470: 12466: 12462: 12458: 12454: 12450: 12446: 12439: 12424: 12420: 12416: 12410: 12408: 12406: 12397: 12393: 12389: 12385: 12381: 12373: 12371: 12361: 12356: 12349: 12347: 12338: 12334: 12330: 12326: 12322: 12318: 12314: 12307: 12298: 12293: 12286: 12278: 12274: 12266: 12258: 12253: 12249: 12242: 12240: 12230: 12225: 12218: 12209: 12204: 12197: 12195: 12179: 12175: 12171: 12165: 12163: 12154: 12150: 12146: 12142: 12138: 12134: 12130: 12126: 12122: 12118: 12114: 12110: 12104: 12096: 12092: 12085: 12081: 12077: 12071: 12069: 12067: 12065: 12063: 12061: 12059: 12057: 12055: 12053: 12051: 12046: 12030: 12023: 12018: 12014: 12003: 12000: 11997: 11994: 11991: 11988: 11985: 11982: 11979: 11976: 11973: 11970: 11967: 11964: 11963: 11954: 11950: 11946: 11942: 11939: 11936: 11932: 11929: 11927: 11924: 11922: 11919: 11918: 11917: 11912: 11909: 11906: 11903: 11900: 11897: 11895: 11892: 11890: 11887: 11884: 11881: 11879: 11876: 11875: 11874: 11872: 11868: 11864: 11860: 11856: 11852: 11848: 11844: 11840: 11836: 11832: 11822: 11819: 11815: 11810: 11808: 11804: 11802: 11798: 11794: 11789: 11787: 11783: 11781: 11777: 11771: 11766:Multimodality 11763: 11761: 11742: 11737: 11733: 11729: 11726: 11720: 11698: 11694: 11690: 11687: 11684: 11681: 11678: 11673: 11669: 11641: 11637: 11630: 11626: 11621: 11617: 11610: 11607: 11604: 11600: 11592: 11588: 11574: 11570: 11564: 11555: 11549: 11546: 11543: 11540: 11537: 11507: 11502: 11498: 11489: 11485: 11478: 11469: 11453: 11449: 11445: 11440: 11436: 11432: 11429: 11401: 11397: 11390: 11383: 11379: 11375: 11371: 11365: 11355: 11351: 11343: 11337: 11333: 11327: 11319: 11313: 11306: 11301: 11297: 11288: 11284: 11277: 11270: 11266: 11262: 11258: 11252: 11242: 11238: 11230: 11224: 11220: 11214: 11206: 11200: 11194: 11191: 11187: 11179: 11175: 11161: 11157: 11151: 11142: 11136: 11133: 11130: 11127: 11124: 11090: 11084: 11077: 11073: 11069: 11065: 11059: 11051: 11044: 11040: 11034: 11028: 11021: 11017: 11013: 11009: 11003: 10995: 10988: 10981: 10969: 10963: 10956: 10952: 10948: 10944: 10938: 10930: 10923: 10919: 10913: 10907: 10900: 10896: 10892: 10888: 10882: 10874: 10867: 10852: 10845: 10841: 10836: 10829: 10826: 10823: 10816: 10788: 10784: 10780: 10773: 10765: 10762: 10759: 10750: 10746: 10742: 10730: 10724: 10721: 10715: 10709: 10675: 10670: 10666: 10662: 10659: 10653: 10631: 10627: 10623: 10620: 10617: 10614: 10611: 10606: 10602: 10579: 10568: 10565: 10560: 10556: 10549: 10546: 10543: 10537: 10534: 10529: 10525: 10518: 10515: 10512: 10509: 10503: 10500: 10495: 10491: 10484: 10481: 10478: 10472: 10469: 10464: 10460: 10453: 10450: 10441: 10437: 10432: 10426: 10420: 10412: 10402: 10398: 10381: 10375: 10367: 10346: 10342: 10335: 10326: 10324: 10305: 10302: 10299: 10296: 10290: 10265: 10261: 10254: 10245: 10231: 10206: 10202: 10195: 10181: 10179: 10169: 10165: 10149: 10139: 10113: 10103: 10077: 10073: 10050: 10040: 10014: 10004: 9978: 9968: 9961: 9956: 9946: 9939: 9934: 9924: 9917: 9912: 9902: 9888: 9874: 9852: 9848: 9825: 9821: 9817: 9814: 9811: 9808: 9805: 9800: 9796: 9792: 9787: 9783: 9772: 9770: 9759: 9755: 9753: 9752:memory paging 9749: 9745: 9735: 9732: 9717: 9713: 9708: 9699: 9695: 9691: 9688: 9683: 9679: 9675: 9672: 9667: 9662: 9658: 9654: 9642: 9627: 9620: 9617: 9607: 9601: 9598: 9595: 9592: 9589: 9573: 9557: 9553: 9549: 9544: 9540: 9517: 9513: 9508: 9499: 9494: 9490: 9486: 9483: 9478: 9473: 9469: 9465: 9462: 9457: 9452: 9448: 9444: 9432: 9417: 9410: 9407: 9397: 9391: 9388: 9385: 9382: 9379: 9363: 9355: 9353: 9347: 9343: 9341: 9337: 9333: 9327: 9325: 9321: 9311: 9309: 9305: 9301: 9297: 9293: 9283: 9268: 9265: 9261: 9257: 9254: 9250: 9247: 9244: 9241: 9218: 9215: 9211: 9207: 9204: 9199: 9195: 9190: 9187: 9184: 9180: 9171: 9155: 9131: 9127: 9123: 9120: 9112: 9108: 9094: 9090: 9083: 9074: 9068: 9065: 9062: 9059: 9056: 9030: 9026: 9009: 8989: 8969: 8966: 8963: 8960: 8955: 8952: 8949: 8945: 8922: 8916: 8911: 8906: 8901: 8896: 8889: 8884: 8879: 8876: 8871: 8868: 8863: 8860: 8853: 8848: 8843: 8838: 8835: 8830: 8827: 8820: 8815: 8810: 8805: 8800: 8797: 8790: 8785: 8780: 8775: 8770: 8764: 8759: 8756: 8748: 8732: 8712: 8688: 8684: 8680: 8677: 8674: 8666: 8662: 8648: 8644: 8637: 8628: 8622: 8619: 8616: 8613: 8610: 8590: 8586: 8576: 8562: 8535: 8532: 8529: 8526: 8523: 8506: 8494: 8491: 8488: 8485: 8482: 8467: 8457: 8454: 8451: 8434: 8422: 8419: 8416: 8395: 8376: 8369: 8365: 8362: 8359: 8356: 8353: 8345: 8338: 8317: 8314: 8292: 8288: 8282: 8279: 8276: 8272: 8268: 8258: 8255: 8250: 8246: 8208: 8200: 8196: 8192: 8189: 8181: 8173: 8169: 8165: 8160: 8156: 8133: 8127: 8124: 8121: 8118: 8110: 8102: 8098: 8094: 8091: 8088: 8085: 8082: 8074: 8066: 8062: 8054: 8051: 8048: 8045: 8037: 8029: 8025: 8021: 8018: 8015: 8012: 8009: 8001: 7993: 7989: 7982: 7977: 7972: 7961: 7953: 7949: 7936: 7928: 7924: 7917: 7910: 7904: 7901: 7898: 7895: 7890: 7887: 7884: 7881: 7874: 7871: 7868: 7865: 7862: 7857: 7854: 7851: 7848: 7842: 7837: 7827: 7824: 7816: 7808: 7804: 7800: 7792: 7784: 7780: 7747: 7724: 7721: 7718: 7715: 7704: 7696: 7692: 7688: 7680: 7672: 7668: 7661: 7650: 7642: 7638: 7634: 7626: 7618: 7614: 7607: 7596: 7588: 7584: 7580: 7572: 7564: 7560: 7539: 7535: 7527: 7525: 7521: 7511: 7509: 7505: 7502: 7487: 7483: 7466: 7454: 7436: 7423: 7418: 7409: 7399: 7397: 7393: 7389: 7385: 7381: 7375: 7373: 7369: 7365: 7361: 7355: 7353: 7349: 7344: 7334: 7330: 7326: 7322: 7318: 7314: 7310: 7306: 7302: 7298: 7294: 7290: 7286: 7282: 7278: 7274: 7270: 7266: 7262: 7258: 7254: 7250: 7246: 7242: 7238: 7235: 7231: 7227: 7223: 7220: 7216: 7212: 7208: 7204: 7200: 7196: 7192: 7188: 7184: 7180: 7176: 7172: 7168: 7164: 7160: 7156: 7152: 7148: 7145: 7141: 7137: 7133: 7130: 7126: 7122: 7118: 7110: 7089: 7025: 7022: 7013: 6996: 6941: 6909: 6906: 6866: 6862: 6857: 6855: 6851: 6843: 6839: 6834: 6826: 6818: 6810: 6806: 6798: 6784: 6780: 6764: 6760: 6727: 6723: 6719: 6714: 6710: 6706: 6702: 6699: 6679: 6677: 6669: 6651: 6648: 6645: 6642: 6639: 6628: 6626: 6620: 6617: 6603: 6599: 6597: 6591: 6589: 6583: 6576: 6567: 6564: 6560: 6518: 6515: 6512: 6509: 6506: 6487: 6481: 6442: 6423: 6417: 6405: 6397: 6394: 6391: 6388: 6385: 6357: 6349: 6346: 6343: 6340: 6337: 6315: 6310: 6308: 6300: 6283: 6277: 6268: 6264: 6254: 6250: 6243: 6238: 6236: 6231: 6219: 6216: 6211: 6207: 6203: 6198: 6194: 6172: 6165: 6156: 6154: 6138: 6116: 6113: 6109: 6099: 6095: 6087: 6069: 6063: 6058: 6053: 6048: 6043: 6036: 6031: 6026: 6021: 6016: 6006: 6001: 5996: 5991: 5986: 5976: 5971: 5963: 5958: 5953: 5943: 5938: 5930: 5922: 5917: 5911: 5906: 5897: 5887: 5869: 5865: 5856: 5852: 5838: 5834: 5828: 5825: 5821: 5812: 5806: 5803: 5800: 5797: 5794: 5762: 5739: 5719: 5699: 5696: 5693: 5673: 5659: 5643: 5640: 5634: 5631: 5628: 5615: 5610: 5606: 5585: 5582: 5579: 5576: 5573: 5553: 5550: 5541: 5537: 5534: 5531: 5522: 5518: 5515: 5512: 5503: 5493: 5473: 5463: 5447: 5443: 5422: 5400: 5395: 5391: 5387: 5382: 5377: 5373: 5369: 5364: 5359: 5355: 5334: 5312: 5308: 5296: 5291: 5287: 5283: 5280: 5275: 5270: 5266: 5262: 5259: 5254: 5249: 5245: 5241: 5216: 5209: 5206: 5196: 5190: 5187: 5184: 5181: 5178: 5150: 5141: 5139: 5135: 5131: 5114: 5108: 5104: 5100: 5095: 5091: 5087: 5082: 5078: 5073: 5059: 5051: 5042: 5022: 5018: 5009: 5005: 4996: 4969: 4965: 4956: 4952: 4943: 4933: 4913: 4909: 4900: 4895: 4886: 4882: 4873: 4868: 4859: 4855: 4846: 4819: 4811: 4789: 4781: 4759: 4751: 4729: 4721: 4716: 4713: 4696: 4692: 4684: 4680: 4666: 4662: 4656: 4647: 4641: 4638: 4635: 4632: 4629: 4595: 4591: 4568: 4564: 4541: 4537: 4516: 4496: 4476: 4456: 4448: 4443: 4429: 4407: 4404: 4400: 4379: 4357: 4353: 4349: 4344: 4340: 4319: 4299: 4277: 4273: 4269: 4264: 4260: 4239: 4219: 4197: 4193: 4170: 4166: 4157: 4137: 4133: 4108: 4104: 4081: 4077: 4068: 4052: 4032: 4010: 4007: 4003: 3993: 3973: 3969: 3960: 3937: 3933: 3929: 3924: 3920: 3916: 3911: 3907: 3897: 3881: 3877: 3867: 3863: 3860: 3838: 3834: 3824: 3820: 3817: 3795: 3791: 3781: 3777: 3774: 3752: 3748: 3737: 3734: 3730: 3726: 3721: 3717: 3694: 3690: 3662: 3659: 3655: 3645: 3625: 3598: 3588: 3572: 3568: 3545: 3541: 3518: 3514: 3505: 3502: 3493: 3485: 3475: 3465: 3445: 3441: 3438: 3429: 3420: 3416: 3412: 3407: 3405: 3389: 3364: 3357: 3353: 3345: 3338: 3326: 3319: 3315: 3307: 3300: 3296: 3290: 3287: 3281: 3259: 3233: 3206: 3196: 3187: 3185: 3180: 3176: 3173: 3169: 3166:Like earlier 3160: 3152: 3143: 3141: 3136: 3134: 3131: 3113: 3109: 3085: 3079: 3075: 3063: 3059: 3049: 3026: 3022: 3016: 3012: 3007: 3003: 2995: 2991: 2984: 2981: 2975: 2970: 2966: 2960: 2956: 2946: 2927: 2924: 2898: 2892: 2883: 2874: 2854: 2848: 2842: 2839: 2833: 2824: 2808: 2804: 2800: 2796: 2792: 2789: 2767: 2764: 2759: 2756: 2751: 2748: 2745: 2742: 2739: 2736: 2733: 2730: 2725: 2718: 2714: 2709: 2705: 2702: 2698: 2694: 2689: 2683: 2677: 2656: 2652: 2648: 2630: 2627: 2618: 2604: 2601: 2598: 2578: 2558: 2549: 2533: 2529: 2525: 2521: 2517: 2514: 2511: 2504: 2500: 2496: 2491: 2488: 2465: 2462: 2459: 2455: 2451: 2448: 2445: 2442: 2439: 2436: 2433: 2427: 2424: 2411: 2405: 2402: 2399: 2393: 2387: 2384: 2378: 2370: 2367: 2364: 2361: 2353: 2347: 2344: 2339: 2336: 2328: 2322: 2311: 2295: 2275: 2272: 2269: 2266: 2258: 2255: 2252: 2247: 2229: 2226: 2217: 2215: 2214:man bites dog 2211: 2207: 2188: 2185: 2182: 2179: 2176: 2173: 2170: 2162: 2157: 2148: 2125: 2121: 2112: 2085: 2082: 2079: 2076: 2047: 2041: 2007: 2002: 1993: 1974: 1965: 1961: 1956: 1942: 1936: 1933: 1930: 1927: 1924: 1921: 1918: 1915: 1912: 1909: 1906: 1903: 1900: 1894: 1888: 1845: 1842: 1839: 1836: 1833: 1830: 1827: 1824: 1821: 1818: 1815: 1812: 1809: 1786: 1766: 1758: 1754: 1748: 1738: 1736: 1731: 1711: 1703: 1698: 1696: 1689: 1685: 1675: 1661: 1658: 1649: 1647: 1639: 1635: 1632: 1629: 1628: 1627: 1619: 1617: 1613: 1608: 1606: 1600: 1598: 1592: 1590: 1566: 1555: 1552: 1547:masked tokens 1542: 1539: 1535: 1531: 1528: 1515: 1511: 1510:loss function 1506: 1501: 1491: 1485: 1480: 1477: 1473: 1471: 1469: 1465: 1459: 1455: 1454: 1453: 1451: 1447: 1440: 1437: 1435: 1432: 1430: 1427: 1425: 1422: 1419: 1417: 1414: 1413: 1412: 1410: 1406: 1403: 1399: 1389: 1387: 1384: 1379: 1365: 1363: 1359: 1355: 1351: 1347: 1343: 1338: 1336: 1332: 1328: 1324: 1319: 1317: 1313: 1309: 1305: 1301: 1296: 1294: 1290: 1279: 1277: 1273: 1269: 1264: 1262: 1258: 1254: 1250: 1246: 1242: 1235: 1225: 1223: 1220: 1216: 1215: 1210: 1206: 1202: 1197: 1194: 1192: 1188: 1183: 1181: 1176: 1171: 1169: 1165: 1161: 1157: 1152: 1147: 1137: 1134: 1129: 1127: 1126: 1121: 1117: 1113: 1109: 1104: 1102: 1098: 1097:Elman network 1094: 1083: 1073: 1071: 1067: 1063: 1059: 1055: 1051: 1047: 1043: 1039: 1034: 1032: 1028: 1025: 1021: 1017: 1013: 1008: 1006: 1003: 999: 995: 991: 987: 983: 979: 975: 974:deep learning 971: 961: 950: 945: 943: 938: 936: 931: 930: 928: 927: 920: 917: 913: 910: 909: 908: 905: 903: 900: 899: 893: 892: 885: 882: 880: 877: 875: 872: 870: 867: 865: 862: 860: 857: 855: 852: 851: 845: 844: 837: 834: 832: 829: 827: 824: 822: 819: 817: 814: 812: 809: 807: 804: 802: 799: 798: 792: 791: 784: 781: 779: 776: 774: 771: 769: 766: 765: 759: 758: 751: 748: 746: 743: 741: 740:Crowdsourcing 738: 736: 733: 732: 726: 725: 716: 713: 712: 711: 708: 706: 703: 701: 698: 696: 693: 692: 689: 684: 683: 675: 672: 670: 669:Memtransistor 667: 665: 662: 660: 657: 653: 650: 649: 648: 645: 643: 640: 636: 633: 631: 628: 626: 623: 621: 618: 617: 616: 613: 611: 608: 606: 603: 601: 598: 594: 591: 590: 589: 586: 582: 579: 577: 574: 572: 569: 567: 564: 563: 562: 559: 557: 554: 552: 551:Deep learning 549: 547: 544: 543: 540: 535: 534: 527: 524: 522: 519: 517: 515: 511: 509: 506: 505: 502: 497: 496: 487: 486:Hidden Markov 484: 482: 479: 477: 474: 473: 472: 469: 468: 465: 460: 459: 452: 449: 447: 444: 442: 439: 437: 434: 432: 429: 427: 424: 422: 419: 417: 414: 412: 409: 408: 405: 400: 399: 392: 389: 387: 384: 382: 378: 376: 373: 371: 368: 366: 364: 360: 358: 355: 353: 350: 348: 345: 344: 341: 336: 335: 328: 325: 323: 320: 318: 315: 313: 310: 308: 305: 303: 300: 298: 295: 293: 291: 287: 283: 282:Random forest 280: 278: 275: 273: 270: 269: 268: 265: 263: 260: 258: 255: 254: 247: 246: 241: 240: 232: 226: 225: 218: 215: 213: 210: 208: 205: 203: 200: 198: 195: 193: 190: 188: 185: 183: 180: 178: 175: 173: 170: 168: 167:Data cleaning 165: 163: 160: 158: 155: 153: 150: 148: 145: 143: 140: 138: 135: 133: 130: 129: 123: 122: 115: 112: 110: 107: 105: 102: 100: 97: 95: 92: 90: 87: 85: 82: 80: 79:Meta-learning 77: 75: 72: 70: 67: 65: 62: 60: 57: 55: 52: 51: 45: 44: 41: 36: 33: 32: 28: 27: 22: 16280:Hugging Face 16244:David Silver 15892:Audio–visual 15746:Applications 15725:Augmentation 15570: 15482:Google Pixel 15302: 15227: 15219: 15184:Competitions 15162:AlphaGo Zero 15115:Google Brain 14976: 14972: 14962: 14944: 14938: 14920: 14914: 14868:cite journal 14839:. 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Many 11828: 11825:Applications 11811: 11805: 11790: 11784: 11772: 11769: 11470: 10408: 10399: 10327: 10246: 10187: 10177: 10175: 10166: 9889: 9887:-th output. 9773: 9765: 9756: 9747: 9743: 9741: 9733: 9574: 9364: 9361: 9348: 9344: 9328: 9317: 9308:Hugging Face 9304:Transformers 9303: 9289: 9036: 9027: 8746: 8588: 8584: 8582: 8396: 7545: 7536: 7533: 7524:Llama series 7517: 7508:Llama series 7498: 7484: 7400: 7376: 7356: 7345: 7342: 7332: 7328: 7324: 7320: 7316: 7312: 7308: 7304: 7300: 7296: 7292: 7288: 7284: 7280: 7276: 7272: 7268: 7264: 7260: 7256: 7252: 7248: 7244: 7240: 7236: 7233: 7229: 7225: 7221: 7218: 7214: 7210: 7206: 7202: 7198: 7194: 7190: 7186: 7182: 7178: 7174: 7170: 7166: 7162: 7158: 7154: 7150: 7146: 7143: 7139: 7135: 7131: 7128: 7124: 7120: 7116: 7014: 6864: 6860: 6858: 6847: 6803: 6781: 6663:DecoderLayer 6604: 6600: 6592: 6587: 6584: 6581: 6565: 6561: 6475:EncoderLayer 6443: 6294:EncoderLayer 6173: 6170: 6151:is a random 5888: 5665: 5494: 5464: 5142: 5129: 5064: 4934: 4809: 4779: 4749: 4719: 4717: 4714: 4444: 3994: 3898: 3646: 3589: 3498: 3418: 3414: 3410: 3408: 3406:activation. 3255: 3181: 3177: 3171: 3165: 3137: 2947: 2825: 2619: 2550: 2218: 2210:bag of words 2205: 2203: 2003: 1999: 1996:Un-embedding 1963: 1959: 1957: 1753:lookup table 1750: 1732: 1701: 1699: 1691: 1684:Tokenization 1678:Tokenization 1650: 1643: 1625: 1622:Architecture 1609: 1601: 1593: 1507: 1503: 1488: 1483: 1467: 1464:for inviting 1463: 1461: 1457: 1443: 1439:paraphrasing 1395: 1385: 1380: 1376: 1360:(2024), and 1339: 1320: 1308:bag of words 1297: 1285: 1265: 1260: 1256: 1240: 1237: 1221: 1218: 1213: 1198: 1195: 1190: 1186: 1184: 1179: 1174: 1172: 1163: 1159: 1153: 1149: 1130: 1123: 1119: 1115: 1105: 1090: 1087:Predecessors 1035: 1031:Common Crawl 1009: 969: 967: 964:Transformer. 826:PAC learning 513: 362: 357:Hierarchical 289: 243: 237: 16428:Categories 16376:Autoencoder 16331:Transformer 16199:Alex Graves 16147:OpenAI Five 16051:IBM Watsonx 15673:Convolution 15651:Overfitting 15477:Google Labs 15303:Transformer 14259:Pathways". 11953:grandmaster 11883:time series 11801:spectrogram 10092:to replace 9172:, that is, 8747:linear bias 8585:replacement 7339:Terminology 5065:One set of 4067:dot product 4025:from token 3501:dot-product 3417:(BERT), or 3415:filter size 1960:hidden size 1462:"Thank you 1405:fine-tuning 1282:AI boom era 1133:fast weight 1068:(GPTs) and 970:transformer 710:Multi-agent 647:Transformer 546:Autoencoder 302:Naive Bayes 40:data mining 16454:Categories 16417:Technology 16270:EleutherAI 16229:Fei-Fei Li 16224:Yann LeCun 16137:Q-learning 16120:Decisional 16046:IBM Watson 15954:Midjourney 15846:TensorFlow 15693:Activation 15646:Regression 15641:Clustering 15404:Chinchilla 15331:TensorFlow 15229:The MANIAC 15059:2405.00208 15044:2207.09238 14979:(1): 157. 14954:2206.10789 14930:2102.12092 14905:2301.00704 14841:2024-08-09 14817:2107.14795 14795:2103.03206 14774:2212.04356 14730:2024-08-11 14665:2006.03555 14643:2103.02143 14622:2105.14103 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12429:2019-08-25 12297:2212.04356 12257:2106.01345 12229:1508.04025 12184:2019-08-25 12041:References 11941:evaluating 11885:prediction 11851:AlbertAGPT 11807:Perceivers 9744:KV caching 9296:TensorFlow 9292:frameworks 8589:additional 7368:GPT series 7113:Pseudocode 6836:Schematic 4864:seq, value 4780:value size 4720:query size 3965:emb, query 3630:emb, query 3603:seq, query 2161:sinusoidal 2130:vocabulary 1716:vocabulary 1498:See also: 1402:supervised 1346:multimodal 1323:GPT series 1251:result in 1187:fixed-size 1080:See also: 1064:, such as 1002:multi-head 695:Q-learning 593:Restricted 391:Mean shift 340:Clustering 317:Perceptron 245:regression 147:Clustering 142:Regression 16300:MIT CSAIL 16265:Anthropic 16234:Andrew Ng 16132:AlphaZero 15976:VideoPoet 15939:AlphaFold 15876:MindSpore 15830:SpiNNaker 15825:Memristor 15732:Diffusion 15708:Rectifier 15688:Batchnorm 15668:Attention 15663:Adversary 15422:VideoPoet 15363:Assistant 15257:AlphaStar 15251:AlphaFold 15197:Lee Sedol 15168:AlphaZero 15099:Google AI 14725:lmsys.org 14707:2374-3468 14355:vLLM Blog 13987:231986066 13979:0891-2017 13783:1533-7928 13408:1532-4435 13073:0028-792X 13011:1059-1028 12922:0362-4331 12852:1409.3215 12821:220252321 12765:1412.3555 12744:1409.3215 12710:1406.1078 12677:ICML 2021 12658:ICML 2020 12538:0003-6935 12469:0364-0213 12396:208117506 12337:2377-3766 12208:1409.0473 12137:0899-7667 11972:Perceiver 11935:AlphaFold 11933:(such as 11734:σ 11608:≈ 11531:Attention 11479:φ 11430:σ 11391:φ 11380:σ 11362:‖ 11348:‖ 11334:∑ 11314:φ 11278:φ 11267:σ 11249:‖ 11235:‖ 11221:∑ 11201:φ 11195:≈ 11118:Attention 11097:⟩ 11085:φ 11074:σ 11056:‖ 11049:‖ 11029:φ 11018:σ 11000:‖ 10993:‖ 10985:⟨ 10982:≈ 10976:⟩ 10964:φ 10953:σ 10935:‖ 10928:‖ 10908:φ 10897:σ 10879:‖ 10872:‖ 10864:⟨ 10842:σ 10833:⟩ 10821:⟨ 10785:σ 10770:‖ 10763:− 10757:‖ 10751:− 10737:⟩ 10725:φ 10710:φ 10707:⟨ 10667:σ 10572:⟩ 10553:⟨ 10550:⁡ 10541:⟩ 10522:⟨ 10519:⁡ 10513:⋯ 10507:⟩ 10488:⟨ 10485:⁡ 10476:⟩ 10457:⟨ 10454:⁡ 10421:φ 10321:by using 10303:⁡ 10143:~ 10107:~ 10044:~ 10008:~ 9972:~ 9950:~ 9928:~ 9906:~ 9648:Attention 9621:∈ 9438:Attention 9411:∈ 9262:− 9245:− 9234:whenever 9050:Attention 9013:∞ 9010:− 8967:− 8917:⋱ 8912:⋮ 8907:⋮ 8902:⋮ 8897:⋮ 8890:⋯ 8877:− 8869:− 8861:− 8854:⋯ 8836:− 8828:− 8821:⋯ 8798:− 8791:⋯ 8604:Attention 8370:θ 8339:θ 8283:θ 8128:θ 8122:⁡ 8092:θ 8086:⁡ 8055:θ 8049:⁡ 8022:− 8019:θ 8013:⁡ 7905:θ 7899:⁡ 7891:θ 7885:⁡ 7875:θ 7869:⁡ 7863:− 7858:θ 7852:⁡ 7748:θ 7440:∞ 7437:− 7396:T5 series 6792:Sublayers 6418:⋮ 6278:⋮ 6220:… 6114:− 6059:… 6037:⋮ 6032:⋱ 6027:⋮ 6022:⋮ 6017:⋮ 6010:∞ 6007:− 6002:… 5980:∞ 5977:− 5972:… 5967:∞ 5964:− 5947:∞ 5944:− 5939:… 5934:∞ 5931:− 5926:∞ 5923:− 5743:∞ 5740:− 5641:× 5632:× 5616:∈ 5577:× 5235:Attention 5210:∈ 5006:≠ 4860:ℓ 4847:ℓ 4623:Attention 4350:⋅ 4270:⋅ 4045:to token 3599:ℓ 3504:attention 3390:ϕ 3291:ϕ 3056:Δ 3013:∑ 2988:Δ 2957:∑ 2928:∈ 2922:Δ 2881:Δ 2846:Δ 2765:− 2749:… 2639:→ 2489:θ 2463:− 2446:… 2428:∈ 2422:∀ 2412:θ 2406:⁡ 2394:θ 2388:⁡ 2259:∈ 2238:→ 1937:… 1846:… 1741:Embedding 1695:tokenizer 1637:variants. 1556:⁡ 1543:∈ 1536:∑ 1532:− 1199:In 2016, 1191:RNNsearch 1024:Knowledge 982:attention 854:ECML PKDD 836:VC theory 783:ROC curve 715:Self-play 635:DeepDream 476:Bayes net 267:Ensembles 48:Paradigms 16408:Portals 16167:Auto-GPT 15999:Word2vec 15803:Hardware 15720:Datasets 15622:Concepts 15505:Category 15453:See also 15356:Chatbots 15263:AlphaDev 15143:Versions 15027:Archived 15005:36855134 14595:Archived 14509:Archived 14369:cite web 14217:TOGETHER 13805:Archived 13673:Archived 13624:keras.io 13598:Archived 13563:Archived 13198:Archived 13015:Archived 12813:33733157 12594:16683347 12565:(1992). 12546:20523475 12423:Archived 12178:Archived 11960:See also 11837:such as 11814:DALL-E 1 9750:applies 9572:, thus: 9294:such as 9269:′ 9258:′ 9219:′ 9208:′ 7414:prefixLM 7321:for each 7309:for each 7297:for each 7285:for each 7273:for each 7261:for each 7249:for each 7207:for each 7195:for each 7183:for each 7171:for each 7159:for each 6863:and the 6703:′ 6621:′ 6131:, where 5732:that is 5140:layers. 5134:parallel 4851:seq, key 4750:key size 4069:between 2288:, where 1409:The Pile 1368:Training 1356:(2021), 1312:word2vec 277:Boosting 126:Problems 16290:Meta AI 16127:AlphaGo 16111:PanGu-Σ 16081:ChatGPT 16056:Granite 16004:Seq2seq 15983:Whisper 15904:WaveNet 15899:AlexNet 15871:Flux.jl 15851:PyTorch 15703:Sigmoid 15698:Softmax 15563:General 15515:Commons 15369:Sparrow 15297:WaveNet 15221:AlphaGo 15191:Fan Hui 15150:AlphaGo 15136:AlphaGo 14996:9972634 12804:7861254 12153:1915014 12145:9377276 11966:seq2seq 11945:Minimax 11871:ChatGPT 11867:RoBERTa 11793:Whisper 11560:softmax 11147:softmax 9738:Caching 9300:PyTorch 9079:softmax 8745:is the 8633:softmax 7520:RMSNorm 7125:output: 6861:post-LN 6570:Decoder 6159:Encoder 5817:softmax 4652:softmax 4156:softmax 4065:is the 3992:, etc. 3413:(GPT), 3168:seq2seq 2310:integer 2006:softmax 1757:one-hot 1331:ChatGPT 1293:AI boom 1272:seq2seq 1257:without 1164:decoder 1160:encoder 1076:History 859:NeurIPS 676:(ECRAM) 630:AlexNet 272:Bagging 16305:Huawei 16285:OpenAI 16187:People 16157:MuZero 16019:Gemini 16014:Claude 15949:DALL-E 15861:Theano 15441:(2024) 15424:(2024) 15418:(2023) 15416:Gemini 15412:(2022) 15406:(2022) 15400:(2021) 15394:(2018) 15377:(2023) 15375:Gemini 15371:(2022) 15365:(2016) 15311:(2022) 15305:(2017) 15299:(2016) 15271:(2024) 15265:(2023) 15259:(2019) 15253:(2018) 15232:(2023) 15224:(2017) 15205:(2017) 15203:Ke Jie 15199:(2016) 15193:(2015) 15176:(2019) 15174:MuZero 15170:(2017) 15164:(2017) 15158:(2016) 15156:Master 15152:(2015) 15110:Google 15003: 14993: 14705: 14310: 13985: 13977: 13781: 13559:Indico 13406: 13071: 13009: 12920: 12819: 12811: 12801: 12787:: 40, 12592: 12544: 12536: 12495: 12467: 12394: 12335: 12174:OpenAI 12151: 12143: 12135: 11955:level. 11855:Claude 11422:where 10594:where 10224:where 10128:, and 9613:Concat 9403:Concat 9334:GPUs ( 9148:where 8705:Here, 7459:causal 7333:return 7121:input: 6960:where 6865:pre-LN 6844:style. 6752:where 6444:where 6104:causal 5902:causal 5566:Since 5435:, and 5202:Concat 4583:, and 4332:(i.e. 4252:(i.e. 3382:where 2914:where 2782:where 2551:Here, 2481:where 2008:layer: 1470:week". 1386:before 1354:DALL-E 1027:corpus 990:tokens 978:Google 652:Vision 508:RANSAC 386:OPTICS 381:DBSCAN 365:-means 172:AutoML 16371:Mamba 16142:SARSA 16106:LLaMA 16101:BLOOM 16086:GPT-J 16076:GPT-4 16071:GPT-3 16066:GPT-2 16061:GPT-1 16024:LaMDA 15856:Keras 15432:Other 15398:LaMDA 15319:Other 15244:Other 15054:arXiv 15039:arXiv 14949:arXiv 14925:arXiv 14900:arXiv 14812:arXiv 14790:arXiv 14769:arXiv 14660:arXiv 14638:arXiv 14617:arXiv 14568:arXiv 14543:arXiv 14481:arXiv 14459:arXiv 14436:arXiv 14397:arXiv 14290:arXiv 14261:arXiv 14239:arXiv 14144:arXiv 14112:arXiv 14087:arXiv 14066:arXiv 14045:arXiv 14025:arXiv 13983:S2CID 13955:arXiv 13914:arXiv 13881:arXiv 13848:arXiv 13827:arXiv 13769:arXiv 13732:arXiv 13707:arXiv 13653:arXiv 13535:arXiv 13510:arXiv 13424:arXiv 13394:arXiv 13361:arXiv 13337:arXiv 13296:arXiv 13271:arXiv 13246:arXiv 13097:arXiv 13041:arXiv 13003:Wired 12975:arXiv 12889:arXiv 12868:arXiv 12847:arXiv 12817:S2CID 12760:arXiv 12739:arXiv 12705:arXiv 12590:S2CID 12570:(PDF) 12489:(PDF) 12392:S2CID 12355:arXiv 12292:arXiv 12252:arXiv 12224:arXiv 12203:arXiv 12149:S2CID 12087:(PDF) 12009:Notes 11901:(NER) 11863:XLNet 11847:GPT-4 11843:GPT-3 11839:GPT-2 10808:, or 9632:heads 9422:heads 9324:cache 9168:is a 8579:ALiBi 6086:XLNet 5221:heads 5027:value 5001:query 4974:value 4948:query 4905:value 4878:query 4794:value 4734:query 3978:query 3872:value 3786:query 3742:query 3667:query 2605:10000 2206:where 2177:10000 1494:Tasks 1180:fixed 1058:chess 972:is a 874:IJCAI 700:SARSA 659:Mamba 625:LeNet 620:U-Net 446:t-SNE 370:Fuzzy 347:BIRCH 16295:Mila 16096:PaLM 16029:Bard 16009:BERT 15992:Text 15971:Sora 15439:Vids 15410:PaLM 15392:BERT 15309:Gato 15001:PMID 14881:help 14703:ISSN 14375:link 14308:ISBN 13975:ISSN 13779:ISSN 13404:ISSN 13069:ISSN 13007:ISSN 12918:ISSN 12809:PMID 12542:PMID 12534:ISSN 12493:ISBN 12465:ISSN 12333:ISSN 12141:PMID 12133:ISSN 11869:and 11859:BERT 10029:and 9352:H100 9340:BF16 9336:FP16 9332:A100 9298:and 8513:RoPE 8472:RoPE 8441:RoPE 8406:RoPE 8235:RoPE 7769:RoPE 7542:RoPE 7501:ReLU 7390:and 7370:and 7362:and 7352:BERT 7237:each 7222:each 7147:each 7132:each 6852:and 5546:head 5527:head 5478:head 4918:head 4824:head 4778:and 4489:and 4185:and 4096:and 3404:ReLU 2273:> 1686:and 1603:The 1525:Loss 1468:last 1444:The 1362:Sora 1316:BERT 1310:and 1300:ELMo 1274:for 1249:SOTA 1175:last 1108:LSTM 1070:BERT 1029:and 884:JMLR 869:ICLR 864:ICML 750:RLHF 566:LSTM 352:CURE 38:and 16036:NMT 15919:OCR 15914:HWR 15866:JAX 15820:VPU 15815:TPU 15810:IPU 15634:SGD 14991:PMC 14981:doi 14693:doi 14300:doi 13965:doi 13924:doi 13663:doi 12956:doi 12799:PMC 12789:doi 12715:doi 12582:doi 12526:doi 12457:doi 12384:doi 12325:doi 12125:doi 11949:Elo 11780:ViT 10547:sin 10516:cos 10482:sin 10451:cos 10283:to 9826:512 8119:sin 8083:cos 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6392:H 6389:, 6386:H 6383:( 6375:( 6363:) 6358:0 6354:) 6350:H 6347:, 6344:H 6341:, 6338:H 6335:( 6327:( 6316:[ 6311:= 6304:) 6301:H 6298:( 6284:] 6269:1 6265:h 6255:0 6251:h 6244:[ 6239:= 6232:H 6217:, 6212:1 6208:h 6204:, 6199:0 6195:h 6139:P 6117:1 6110:P 6100:M 6096:P 6070:] 6064:0 6054:0 6049:0 6044:0 5997:0 5992:0 5987:0 5959:0 5954:0 5918:0 5912:[ 5907:= 5898:M 5870:V 5866:) 5857:k 5853:d 5844:T 5839:K 5835:Q 5829:+ 5826:M 5822:( 5813:= 5810:) 5807:V 5804:, 5801:K 5798:, 5795:Q 5792:( 5763:0 5720:M 5700:1 5697:+ 5694:t 5674:t 5638:) 5626:( 5621:R 5611:O 5607:W 5583:= 5551:= 5542:d 5538:, 5532:= 5523:n 5519:, 5513:= 5504:d 5474:d 5448:O 5444:W 5423:i 5401:V 5396:i 5392:W 5388:, 5383:K 5378:i 5374:W 5370:, 5365:Q 5360:i 5356:W 5335:X 5313:O 5309:W 5305:) 5302:) 5297:V 5292:i 5288:W 5284:X 5281:, 5276:K 5271:i 5267:W 5263:X 5260:, 5255:Q 5250:i 5246:W 5242:X 5239:( 5231:( 5226:] 5217:n 5213:[ 5207:i 5197:= 5194:) 5191:V 5188:, 5185:K 5182:, 5179:Q 5176:( 5151:i 5115:) 5109:V 5105:W 5101:, 5096:K 5092:W 5088:, 5083:Q 5079:W 5074:( 5023:X 5019:= 5010:X 4997:X 4970:X 4966:= 4957:X 4953:= 4944:X 4914:d 4910:= 4901:d 4896:, 4887:d 4883:= 4874:d 4869:, 4856:= 4820:d 4790:d 4760:d 4730:d 4697:V 4693:) 4685:k 4681:d 4672:T 4667:K 4663:Q 4657:( 4648:= 4645:) 4642:V 4639:, 4636:K 4633:, 4630:Q 4627:( 4596:i 4592:v 4569:i 4565:k 4542:i 4538:q 4517:i 4497:V 4477:K 4457:Q 4430:i 4408:j 4405:i 4401:a 4380:i 4358:i 4354:k 4345:j 4341:q 4320:i 4300:j 4278:j 4274:k 4265:i 4261:q 4240:j 4220:i 4198:K 4194:W 4171:Q 4167:W 4138:k 4134:d 4109:j 4105:k 4082:i 4078:q 4053:j 4033:i 4011:j 4008:i 4004:a 3974:d 3970:= 3961:d 3938:V 3934:W 3930:, 3925:K 3921:W 3917:, 3912:Q 3908:W 3882:V 3878:W 3868:X 3864:= 3861:V 3839:K 3835:W 3825:X 3821:= 3818:K 3796:Q 3792:W 3782:X 3778:= 3775:Q 3753:Q 3749:W 3738:, 3735:i 3731:x 3727:= 3722:i 3718:q 3695:Q 3691:W 3663:, 3660:i 3656:x 3626:d 3573:V 3569:W 3546:K 3542:W 3519:Q 3515:W 3446:d 3442:4 3439:= 3430:d 3368:) 3365:2 3362:( 3358:b 3354:+ 3349:) 3346:2 3343:( 3339:W 3335:) 3330:) 3327:1 3324:( 3320:b 3316:+ 3311:) 3308:1 3305:( 3301:W 3297:x 3294:( 3288:= 3285:) 3282:x 3279:( 3275:N 3272:F 3269:F 3260:: 3234:d 3207:d 3114:j 3110:c 3089:) 3086:t 3083:( 3080:f 3076:) 3072:) 3069:) 3064:j 3060:t 3053:( 3050:f 3047:( 3043:g 3040:a 3037:i 3034:d 3027:j 3023:c 3017:j 3008:( 3004:= 3001:) 2996:j 2992:t 2985:+ 2982:t 2979:( 2976:f 2971:j 2967:c 2961:j 2932:R 2925:t 2902:) 2899:t 2896:( 2893:f 2890:) 2887:) 2884:t 2878:( 2875:f 2872:( 2868:g 2865:a 2862:i 2859:d 2855:= 2852:) 2849:t 2843:+ 2840:t 2837:( 2834:f 2809:d 2805:/ 2801:2 2797:N 2793:= 2790:r 2768:1 2760:2 2757:d 2752:, 2746:, 2743:1 2740:, 2737:0 2734:= 2731:k 2726:) 2719:k 2715:r 2710:/ 2706:t 2703:i 2699:e 2695:( 2690:= 2687:) 2684:t 2681:( 2678:f 2657:2 2653:/ 2649:d 2644:C 2635:R 2631:: 2628:f 2602:= 2599:N 2579:k 2559:N 2534:d 2530:/ 2526:2 2522:N 2518:= 2515:r 2512:, 2505:k 2501:r 2497:t 2492:= 2469:} 2466:1 2460:2 2456:/ 2452:d 2449:, 2443:, 2440:1 2437:, 2434:0 2431:{ 2425:k 2418:) 2415:) 2409:( 2400:, 2397:) 2391:( 2382:( 2379:= 2376:) 2371:1 2368:+ 2365:k 2362:2 2358:) 2354:t 2351:( 2348:f 2345:, 2340:k 2337:2 2333:) 2329:t 2326:( 2323:f 2320:( 2296:d 2276:0 2270:d 2267:, 2263:Z 2256:d 2253:; 2248:d 2243:R 2234:R 2230:: 2227:f 2186:= 2183:d 2180:, 2174:= 2171:N 2135:) 2126:n 2122:, 2113:d 2109:( 2089:) 2086:b 2083:+ 2080:W 2077:x 2074:( 2070:x 2067:a 2064:m 2061:t 2058:f 2055:o 2052:s 2048:= 2045:) 2042:x 2039:( 2035:d 2032:e 2029:b 2026:m 2023:E 2020:n 2017:U 1975:d 1943:M 1940:] 1934:, 1931:0 1928:, 1925:0 1922:, 1919:1 1916:, 1913:0 1910:, 1907:0 1904:, 1901:0 1898:[ 1895:= 1892:) 1889:3 1886:( 1882:d 1879:e 1876:b 1873:m 1870:E 1849:] 1843:, 1840:0 1837:, 1834:0 1831:, 1828:1 1825:, 1822:0 1819:, 1816:0 1813:, 1810:0 1807:[ 1787:3 1767:M 1712:n 1662:W 1659:x 1575:) 1567:t 1559:( 1540:t 1529:= 1478:) 1048:( 948:e 941:t 934:v 514:k 363:k 290:k 248:) 236:( 23:.

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