851:– In a biological neuron, the dendrites act as the input vector. These dendrites allow the cell to receive signals from a large (>1000) number of neighboring neurons. As in the above mathematical treatment, each dendrite is able to perform "multiplication" by that dendrite's "weight value." The multiplication is accomplished by increasing or decreasing the ratio of synaptic neurotransmitters to signal chemicals introduced into the dendrite in response to the synaptic neurotransmitter. A negative multiplication effect can be achieved by transmitting signal inhibitors (i.e. oppositely charged ions) along the dendrite in response to the reception of synaptic neurotransmitters.
31:
872:
which an axon fires converts directly into the rate at which neighboring cells get signal ions introduced into them. The faster a biological neuron fires, the faster nearby neurons accumulate electrical potential (or lose electrical potential, depending on the "weighting" of the dendrite that connects to the neuron that fired). It is this conversion that allows computer scientists and mathematicians to simulate biological neural networks using artificial neurons which can output distinct values (often from −1 to 1).
867:– The axon gets its signal from the summation behavior which occurs inside the soma. The opening to the axon essentially samples the electrical potential of the solution inside the soma. Once the soma reaches a certain potential, the axon will transmit an all-in signal pulse down its length. In this regard, the axon behaves as the ability for us to connect our artificial neuron to other artificial neurons.
830:
859:– In a biological neuron, the soma acts as the summation function, seen in the above mathematical description. As positive and negative signals (exciting and inhibiting, respectively) arrive in the soma from the dendrites, the positive and negative ions are effectively added in summation, by simple virtue of being mixed together in the solution inside the cell's body.
958:, have been built into a robot, enabling it to learn sensorimotorically within the real world, rather than via simulations or virtually. Moreover, artificial spiking neurons made of soft matter (polymers) can operate in biologically relevant environments and enable the synergetic communication between the artificial and biological domains.
2301:
Wang, Ting; Wang, Ming; Wang, Jianwu; Yang, Le; Ren, Xueyang; Song, Gang; Chen, Shisheng; Yuan, Yuehui; Liu, Ruiqing; Pan, Liang; Li, Zheng; Leow, Wan Ru; Luo, Yifei; Ji, Shaobo; Cui, Zequn; He, Ke; Zhang, Feilong; Lv, Fengting; Tian, Yuanyuan; Cai, Kaiyu; Yang, Bowen; Niu, Jingyi; Zou, Haochen; Liu,
1340:
such as the logistic function also has an easily calculated derivative, which can be important when calculating the weight updates in the network. It thus makes the network more easily manipulable mathematically, and was attractive to early computer scientists who needed to minimize the computational
871:
Unlike most artificial neurons, however, biological neurons fire in discrete pulses. Each time the electrical potential inside the soma reaches a certain threshold, a pulse is transmitted down the axon. This pulsing can be translated into continuous values. The rate (activations per second, etc.) at
2507:
Krauhausen, Imke; Koutsouras, Dimitrios A.; Melianas, Armantas; Keene, Scott T.; Lieberth, Katharina; Ledanseur, Hadrien; Sheelamanthula, Rajendar; Giovannitti, Alexander; Torricelli, Fabrizio; Mcculloch, Iain; Blom, Paul W. M.; Salleo, Alberto; Burgt, Yoeri van de; Gkoupidenis, Paschalis (December
837:
Artificial neurons are designed to mimic aspects of their biological counterparts. However a significant performance gap exists between biological and artificial neural networks. In particular single biological neurons in the human brain with oscillating activation function capable of learning the
207:
Simple artificial neurons, such as the McCulloch–Pitts model, are sometimes described as "caricature models", since they are intended to reflect one or more neurophysiological observations, but without regard to realism. Artificial neurons can also refer to
1620:
model is used. No method of training is defined, since several exist. If a purely functional model were used, the class TLU below would be replaced with a function TLU with input parameters threshold, weights, and inputs that returned a boolean value.
1253:
1584:
154:. Non-monotonic, unbounded and oscillating activation functions with multiple zeros that outperform sigmoidal and ReLU-like activation functions on many tasks have also been recently explored. The thresholding function has inspired building
2190:
Keene, Scott T.; Lubrano, Claudia; Kazemzadeh, Setareh; Melianas, Armantas; Tuchman, Yaakov; Polino, Giuseppina; Scognamiglio, Paola; Cinà, Lucio; Salleo, Alberto; van de Burgt, Yoeri; Santoro, Francesca (September 2020).
1020:
In the late 1980s, when research on neural networks regained strength, neurons with more continuous shapes started to be considered. The possibility of differentiating the activation function allows the direct use of the
1282:
term. A number of such linear neurons perform a linear transformation of the input vector. This is usually more useful in the first layers of a network. A number of analysis tools exist based on linear models, such as
1475:
motivations and mathematical justifications. It has been demonstrated for the first time in 2011 to enable better training of deeper networks, compared to the widely used activation functions prior to 2011, i.e., the
800:
itself (that is, self-loops are possible). However, an output cannot connect more than once with a single neuron. Self-loops do not cause contradictions, since the network operates in synchronous discrete time-steps.
888:
production. The use of unary in biological networks is presumably due to the inherent simplicity of the coding. Another contributing factor could be that unary coding provides a certain degree of error correction.
978:. Initially, only a simple model was considered, with binary inputs and outputs, some restrictions on the possible weights, and a more flexible threshold value. Since the beginning it was already noticed that any
418:
1270:. It is specially useful in the last layer of a network intended to perform binary classification of the inputs. It can be approximated from other sigmoidal functions by assigning large values to the weights.
2802:
Hahnloser, Richard H. R.; Sarpeshkar, Rahul; Mahowald, Misha A.; Douglas, Rodney J.; Seung, H. Sebastian (2000). "Digital selection and analogue amplification coexist in a cortex-inspired silicon circuit".
2369:
2421:
Fu, Tianda; Liu, Xiaomeng; Gao, Hongyan; Ward, Joy E.; Liu, Xiaorong; Yin, Bing; Wang, Zhongrui; Zhuo, Ye; Walker, David J. F.; Joshua Yang, J.; Chen, Jianhan; Lovley, Derek R.; Yao, Jun (April 20, 2020).
1009:. This model already considered more flexible weight values in the neurons, and was used in machines with adaptive capabilities. The representation of the threshold values as a bias term was introduced by
1353:
algorithm tend to diminish towards zero as activations propagate through layers of sigmoidal neurons, making it difficult to optimize neural networks using multiple layers of sigmoidal neurons.
2581:
Sarkar, Tanmoy; Lieberth, Katharina; Pavlou, Aristea; Frank, Thomas; Mailaender, Volker; McCulloch, Iain; Blom, Paul W. M.; Torriccelli, Fabrizio; Gkoupidenis, Paschalis (7 November 2022).
1139:
448:
1450:
804:
As a simple example, consider a single neuron with threshold 0, and a single inhibitory self-loop. Its output would oscillate between 0 and 1 at every step, acting as a "clock".
1178:
620:
974:
in 1943. The model was specifically targeted as a computational model of the "nerve net" in the brain. As a transfer function, it employed a threshold, equivalent to using the
528:
679:
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791:
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of a biological neuron, and its value propagates to the input of the next layer, through a synapse. It may also exit the system, possibly as part of an output
1055:) of a neuron is chosen to have a number of properties which either enhance or simplify the network containing the neuron. Crucially, for instance, any
982:
could be implemented by networks of such devices, what is easily seen from the fact that one can implement the AND and OR functions, and use them in the
1063:
transfer function has an equivalent single-layer network; a non-linear function is therefore necessary to gain the advantages of a multi-layer network.
2276:
2399:
2042:
1495:
A commonly used variant of the ReLU activation function is the Leaky ReLU which allows a small, positive gradient when the unit is not active:
478:
A MCP neuron is a kind of restricted artificial neuron which operates in discrete time-steps. Each has zero or more inputs, and are written as
62:. The artificial neuron is a function that receives one or more inputs, applies weights to these inputs, and sums them to produce an output.
336:
1779:
Rami A. Alzahrani; Alice C. Parker. "Neuromorphic
Circuits With Neural Modulation Enhancing the Information Content of Neural Signaling".
2482:
2157:
17:
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through neurons, could define dynamical systems with memory, but most of the research concentrated (and still does) on strictly
2724:
2697:
1925:
1900:
1798:
2742:, Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences. PhD thesis, Harvard University, 1974
1025:
and other optimization algorithms for the adjustment of the weights. Neural networks also started to be used as a general
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464:
It has no learning process as such. Its transfer function weights are calculated and threshold value are predetermined.
74:
70:
458:
1080:
1822:
Maan, A. K.; Jayadevi, D. A.; James, A. P. (1 January 2016). "A Survey of
Memristive Threshold Logic Circuits".
811:
can be simulated by a MCP neural network. Furnished with an infinite tape, MCP neural networks can simulate any
2192:
1315:
2302:
Songrui; Xu, Guoliang; Fan, Xing; Hu, Benhui; Loh, Xian Jun; Wang, Lianhui; Chen, Xiaodong (8 August 2022).
966:
The first artificial neuron was the
Threshold Logic Unit (TLU), or Linear Threshold Unit, first proposed by
3065:
1389:
1311:
1248:{\displaystyle y={\begin{cases}1&{\text{if }}u\geq \theta \\0&{\text{if }}u<\theta \end{cases}}}
944:
917:
2391:
1362:
1346:
569:
2934:
2249:
1287:, and they can all be used in neural networks with this linear neuron. The bias term allows us to make
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One important and pioneering artificial neural network that used the linear threshold function was the
921:
1471:
was first introduced to a dynamical network by
Hahnloser et al. in a 2000 paper in Nature with strong
1368:
481:
59:
2051:
1579:{\displaystyle f(x)={\begin{cases}x&{\text{if }}x>0,\\ax&{\text{otherwise}}.\end{cases}}}
1524:
1193:
2980:
Samardak, A.; Nogaret, A.; Janson, N. B.; Balanov, A. G.; Farrer, I.; Ritchie, D. A. (2009-06-05).
628:
213:
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Neuron and myelinated axon, with signal flow from inputs at dendrites to outputs at axon terminals
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of this transfer function is binary, depending on whether the input meets a specified threshold,
987:
983:
975:
824:
147:
1026:
940:
43:
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2714:
1172:. The "signal" is sent, i.e. the output is set to one, if the activation meets the threshold.
755:
710:
426:
1342:
1295:
1056:
2687:
1980:
Gidon, Albert; Zolnik, Timothy Adam; Fidzinski, Pawel; Bolduan, Felix; Papoutsi, Athanasia;
897:
There is research and development into physical artificial neurons – organic and inorganic.
2993:
2812:
2521:
2435:
2204:
2089:
1997:
1841:
995:
808:
2583:"An organic artificial spiking neuron for in situ neuromorphic sensing and biointerfacing"
8:
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119:
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2510:"Organic neuromorphic electronics for sensorimotor integration and learning in robotics"
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2001:
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2023:
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1804:
1489:
1481:
1033:
has been rediscovered several times but its first development goes back to the work of
931:
may enable construction of artificial neurons which function at voltages of biological
625:
In a MCP neural network, all the neurons operate in synchronous discrete time-steps of
533:
139:
47:
2913:
2135:
Potluri, Pushpa Sree (26 November 2014). "Error
Correction Capacity of Unary Coding".
169:
The artificial neuron transfer function should not be confused with a linear system's
3009:
2836:
2828:
2776:
2720:
2693:
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2614:
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2015:
1981:
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1808:
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1613:
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1299:
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954:, coated with an ion-rich gel to enable a material to carry an electric charge like
3005:
3001:
2968:
2952:
2848:
2820:
2768:
2652:
2641:"Artificial neurons emulate biological counterparts to enable synergetic operation"
2604:
2594:
2545:
2537:
2529:
2453:
2443:
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2317:
2212:
2165:
2107:
2097:
2005:
1954:
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1337:
1331:
1022:
1006:
979:
967:
932:
905:
151:
127:
92:
66:
1070:
refers in all cases to the weighted sum of all the inputs to the neuron, i.e. for
748:
if the number of firing excitatory inputs is at least equal to the threshold, and
2392:"Researchers unveil electronics that mimic the human brain in efficient learning"
2041:
Squire, L.; Albright, T.; Bloom, F.; Gage, F.; Spitzer, N., eds. (October 2007).
1986:"Dendritic action potentials and computation in human layer 2/3 cortical neurons"
1617:
1350:
1030:
209:
88:
1596:
is a small positive constant (in the original paper the value 0.01 was used for
2656:
2599:
2582:
2448:
2321:
1853:
1754:
1616:
inputs (true or false), and returns a single boolean output when activated. An
1010:
855:
812:
55:
3036:
2216:
2169:
1278:
In this case, the output unit is simply the weighted sum of its inputs plus a
30:
3054:
2878:
2832:
2780:
2664:
2618:
2339:
2224:
2078:"Motor pathway convergence predicts syllable repertoire size in oscine birds"
1966:
1861:
1759:
1460:
1319:
1303:
159:
2982:"Noise-Controlled Signal Transmission in a Multithread Semiconductor Neuron"
2102:
2010:
1985:
1789:
3013:
2956:
2840:
2559:
2533:
2467:
2232:
2121:
2019:
1869:
1345:. However, recent work has shown sigmoid neurons to be less effective than
1263:
971:
881:
839:
2905:
2752:
2739:
1034:
2981:
2959:(1943). "A logical calculus of the ideas immanent in nervous activity".
2876:
2609:
2541:
2330:
2972:
2901:
2277:"Artificial neuron swaps dopamine with rat brain cells like a real one"
1958:
1890:
1609:
1472:
1267:
1262:
and often shows up in many other models. It performs a division of the
1259:
1002:
913:
909:
473:
155:
2824:
2250:"Researchers develop artificial synapse that works with living cells"
1942:
936:
928:
847:
413:{\displaystyle y_{k}=\varphi \left(\sum _{j=0}^{m}w_{kj}x_{j}\right)}
163:
131:
103:
2772:
2756:
1781:
Proceedings of
International Conference on Neuromorphic Systems 2020
447:
2864:
Permitted and
Forbidden Sets in Symmetric Threshold-Linear Networks
1984:; Holtkamp, Martin; Vida, Imre; Larkum, Matthew Evan (2020-01-03).
1836:
991:
901:
885:
78:
2801:
2141:
2044:
Neural network models of birdsong production, learning, and coding
443:(phi) is the transfer function (commonly a threshold function).
166:
have been extensively used to develop such logic in recent times.
2506:
1307:
1014:
951:
908:
rather than electrical signals) and communicate with natural rat
130:, but they may also take the form of other non-linear functions,
796:
Each output can be the input to an arbitrary number of neurons,
2935:
2362:"Scientists create tiny devices that work like the human brain"
2193:"A biohybrid synapse with neurotransmitter-mediated plasticity"
1783:. Art. 19. New York: Association for Computing Machinery.
955:
51:
2483:"Lego Robot with an Organic 'Brain' Learns to Navigate a Maze"
2189:
1943:"A logical calculus of the ideas immanent in nervous activity"
1341:
load of their simulations. It was previously commonly seen in
162:
resembling brain processing. For example, new devices such as
2757:"Backpropagation through time: what it does and how to do it"
2050:. New Encyclopedia of Neuroscience: Elservier. Archived from
900:
For example, some artificial neurons can receive and release
2979:
1778:
990:. Researchers also soon realized that cyclic networks, with
1979:
1572:
1241:
863:
454:
96:
1349:
neurons. The reason is that the gradients computed by the
829:
2580:
1824:
IEEE Transactions on Neural
Networks and Learning Systems
2689:
Discrete
Mathematics of Neural Networks: Selected Topics
2149:
2040:
158:
referred to as threshold logic; applicable to building
2933:
Andrew L. Maas, Awni Y. Hannun, Andrew Y. Ng (2014).
2861:
1503:
1392:
1181:
1083:
758:
713:
687:
631:
572:
536:
484:
429:
339:
65:
The design of the artificial neuron was inspired by
2303:
1941:McCulloch, Warren S.; Pitts, Walter (1943-12-01).
1578:
1459:is the input to a neuron. This is also known as a
1444:
1247:
1133:
785:
740:
699:
673:
614:
542:
522:
435:
412:
106:, and the sum is often added to a term known as a
2712:
2158:"Making computer chips act more like brain cells"
1821:
280:input is assigned the value +1, which makes it a
58:. Artificial neurons are the elementary units of
3052:
2716:Data Classification: Algorithms and Applications
2300:
1891:F. C. Hoppensteadt and E. M. Izhikevich (1997).
1421:
1029:model. The best known training algorithm called
998:because of the smaller difficulty they present.
223:) that are similar to natural physical neurons.
27:Mathematical function conceived as a crude model
884:is used in the neural circuits responsible for
467:
2951:
2685:
1940:
1383:defined as the positive part of its argument:
1040:
231:For a given artificial neuron k, let there be
219:
2855:
2795:
176:An artificial neuron may be referred to as a
3041:] neuron mimicks function of human cells
2706:
2420:
945:direct communication with biological neurons
892:
609:
579:
91:, and its output is analogous to a neuron's
2679:
1612:implementation of a single TLU which takes
1134:{\displaystyle u=\sum _{i=1}^{n}w_{i}x_{i}}
2870:
1488:) and its more practical counterpart, the
950:Organic neuromorphic circuits made out of
2608:
2598:
2549:
2457:
2447:
2329:
2305:"A chemically mediated artificial neuron"
2254:Stanford University via medicalxpress.com
2140:
2111:
2101:
2009:
1918:Computation: Finite and Infinite Machines
1835:
1788:
1336:A fairly simple non-linear function, the
2927:
828:
126:. The transfer functions usually have a
29:
2155:
2134:
1947:The Bulletin of Mathematical Biophysics
1603:
14:
3053:
2751:
2474:
1915:
935:and could be used to directly process
2884:Deep sparse rectifier neural networks
2075:
1445:{\displaystyle f(x)=x^{+}=\max(0,x),}
1273:
566:. An MCP neuron also has a threshold
2921:Neural Networks: Tricks of the Trade
2424:"Bioinspired bio-voltage memristors"
818:
2961:Bulletin of Mathematical Biophysics
2480:
2372:from the original on April 24, 2020
235: + 1 inputs with signals
204:, depending on the structure used.
24:
3046:McCulloch-Pitts Neurons (Overview)
2944:
2713:Charu C. Aggarwal (25 July 2014).
2162:Knowable Magazine | Annual Reviews
615:{\displaystyle b\in \{0,1,2,...\}}
307:actual inputs to the neuron: from
226:
135:
102:Usually, each input is separately
75:inhibitory postsynaptic potentials
71:excitatory postsynaptic potentials
25:
3082:
3030:
2651:(11): 721–722. 10 November 2022.
2402:from the original on May 28, 2020
2076:Moore, J.M.; et al. (2011).
1916:Minsky, Marvin Lee (1967-01-01).
1909:
114:), before being passed through a
2862:R Hahnloser; H.S. Seung (2001).
2156:Kleiner, Kurt (25 August 2022).
1893:Weakly connected neural networks
1467:in electrical engineering. This
1159:
530:. It has one output, written as
446:
2919:. In G. Orr; K. Müller (eds.).
2894:
2877:Xavier Glorot; Antoine Bordes;
2745:
2733:
2686:Martin Anthony (January 2001).
2633:
2574:
2500:
2414:
2384:
2354:
2294:
2269:
2183:
1592:is the input to the neuron and
523:{\displaystyle x_{1},...,x_{n}}
453:The output is analogous to the
95:which is transmitted along its
87:, its weights are analogous to
3006:10.1103/physrevlett.102.226802
2128:
2069:
2034:
1973:
1934:
1884:
1815:
1772:
1513:
1507:
1436:
1424:
1402:
1396:
1316:Independent component analysis
774:
762:
752:inhibitory inputs are firing;
729:
717:
707:, the output of the neuron is
110:(loosely corresponding to the
69:. Its inputs are analogous to
13:
1:
1765:
674:{\displaystyle t=0,1,2,3,...}
2719:. CRC Press. pp. 209–.
1377:ReLU (Rectified Linear Unit)
1356:
1312:Principal component analysis
916:, with potential for use in
468:McCulloch–Pitts (MCP) neuron
7:
1748:
1712:T + weights(i)
1363:Rectifier (neural networks)
1041:Types of transfer functions
875:
558:. The output can either be
550:. Each input can be either
217:
34:Artificial neuron structure
10:
3087:
3061:Artificial neural networks
2657:10.1038/s41928-022-00862-3
2600:10.1038/s41928-022-00859-y
2449:10.1038/s41467-020-15759-y
2322:10.1038/s41928-022-00803-0
2247:University press release:
2082:Proc. Natl. Acad. Sci. USA
1854:10.1109/TNNLS.2016.2547842
1608:The following is a simple
1369:artificial neural networks
1360:
1329:
1325:
1044:
961:
822:
471:
60:artificial neural networks
2217:10.1038/s41563-020-0703-y
2170:10.1146/knowable-082422-1
1258:This function is used in
893:Physical artificial cells
190:linear threshold function
927:Low-power biocompatible
880:Research has shown that
786:{\displaystyle y(t+1)=0}
741:{\displaystyle y(t+1)=1}
436:{\displaystyle \varphi }
214:neuromorphic engineering
140:monotonically increasing
2986:Physical Review Letters
2761:Proceedings of the IEEE
2103:10.1073/pnas.1102077108
2011:10.1126/science.aax6239
1895:. Springer. p. 4.
1790:10.1145/3407197.3407204
1465:half-wave rectification
1156:is a vector of inputs.
1051:The transfer function (
988:conjunctive normal form
976:Heaviside step function
842:have been discovered.
825:Biological neuron model
2534:10.1126/sciadv.abl5068
1580:
1480:(which is inspired by
1446:
1343:multilayer perceptrons
1289:affine transformations
1249:
1135:
1110:
1027:function approximation
941:neuromorphic computing
834:
787:
742:
701:
675:
616:
544:
524:
437:
414:
381:
138:. They are also often
35:
18:McCulloch–Pitts neuron
2692:. SIAM. pp. 3–.
2428:Nature Communications
1581:
1447:
1296:Linear transformation
1250:
1136:
1090:
1057:multilayer perceptron
996:feed-forward networks
832:
788:
743:
702:
676:
617:
545:
525:
438:
415:
361:
134:linear functions, or
44:mathematical function
33:
2953:McCulloch, Warren S.
2914:"Efficient BackProp"
2908:; Genevieve B. Orr;
1604:Pseudocode algorithm
1501:
1463:and is analogous to
1390:
1179:
1081:
809:finite state machine
756:
711:
685:
629:
570:
534:
482:
427:
337:
3066:American inventions
3037:Artifical [
2998:2009PhRvL.102v6802S
2910:Klaus-Robert Müller
2817:2000Natur.405..947H
2526:2021SciA....7.5068K
2487:Scientific American
2440:2020NatCo..11.1861F
2209:2020NatMa..19..969K
2094:2011PNAS..10816440M
2088:(39): 16440–16445.
2002:2020Sci...367...83G
1846:2016arXiv160407121M
1486:logistic regression
1469:activation function
1381:activation function
1053:activation function
700:{\displaystyle t+1}
303:. This leaves only
120:activation function
116:non-linear function
112:threshold potential
2973:10.1007/bf02478259
2645:Nature Electronics
2587:Nature Electronics
2368:. April 20, 2020.
2310:Nature Electronics
1982:Poirazi, Panayiota
1959:10.1007/BF02478259
1576:
1571:
1490:hyperbolic tangent
1482:probability theory
1442:
1367:In the context of
1274:Linear combination
1245:
1240:
1131:
937:biosensing signals
835:
783:
738:
697:
671:
612:
540:
520:
433:
410:
326:The output of the
36:
2811:(6789): 947–951.
2767:(10): 1550–1560.
2726:978-1-4665-8674-1
2699:978-0-89871-480-7
2481:Bolakhe, Saugat.
1927:978-0-13-165563-8
1920:. Prentice Hall.
1902:978-0-387-94948-2
1830:(99): 1734–1746.
1800:978-1-4503-8851-1
1722:T > threshold
1677:number T
1564:
1535:
1300:Harmonic analysis
1285:harmonic analysis
1227:
1204:
1047:Transfer function
933:action potentials
819:Biological models
543:{\displaystyle y}
171:transfer function
124:transfer function
40:artificial neuron
16:(Redirected from
3078:
3025:
2976:
2938:
2931:
2925:
2924:
2918:
2898:
2892:
2891:
2889:
2874:
2868:
2867:
2859:
2853:
2852:
2825:10.1038/35016072
2799:
2793:
2792:
2749:
2743:
2737:
2731:
2730:
2710:
2704:
2703:
2683:
2677:
2676:
2637:
2631:
2630:
2612:
2602:
2578:
2572:
2571:
2553:
2520:(50): eabl5068.
2514:Science Advances
2504:
2498:
2497:
2495:
2493:
2478:
2472:
2471:
2461:
2451:
2418:
2412:
2411:
2409:
2407:
2388:
2382:
2381:
2379:
2377:
2358:
2352:
2351:
2333:
2307:
2298:
2292:
2291:
2289:
2287:
2273:
2267:
2264:
2262:
2260:
2244:
2197:Nature Materials
2187:
2181:
2180:
2178:
2176:
2153:
2147:
2146:
2144:
2132:
2126:
2125:
2115:
2105:
2073:
2067:
2066:
2064:
2062:
2056:
2049:
2038:
2032:
2031:
2013:
1977:
1971:
1970:
1938:
1932:
1931:
1913:
1907:
1906:
1888:
1882:
1881:
1839:
1819:
1813:
1812:
1792:
1776:
1585:
1583:
1582:
1577:
1575:
1574:
1565:
1562:
1536:
1533:
1478:logistic sigmoid
1451:
1449:
1448:
1443:
1417:
1416:
1347:rectified linear
1338:sigmoid function
1332:Sigmoid function
1254:
1252:
1251:
1246:
1244:
1243:
1228:
1225:
1205:
1202:
1150:synaptic weights
1140:
1138:
1137:
1132:
1130:
1129:
1120:
1119:
1109:
1104:
1023:gradient descent
1007:Frank Rosenblatt
980:boolean function
968:Warren McCulloch
906:chemical signals
792:
790:
789:
784:
747:
745:
744:
739:
706:
704:
703:
698:
680:
678:
677:
672:
621:
619:
618:
613:
549:
547:
546:
541:
529:
527:
526:
521:
519:
518:
494:
493:
450:
442:
440:
439:
434:
419:
417:
416:
411:
409:
405:
404:
403:
394:
393:
380:
375:
349:
348:
222:
210:artificial cells
178:semi-linear unit
93:action potential
86:
85:
67:neural circuitry
21:
3086:
3085:
3081:
3080:
3079:
3077:
3076:
3075:
3051:
3050:
3033:
3028:
2947:
2945:Further reading
2942:
2941:
2932:
2928:
2916:
2899:
2895:
2887:
2875:
2871:
2860:
2856:
2800:
2796:
2773:10.1109/5.58337
2750:
2746:
2738:
2734:
2727:
2711:
2707:
2700:
2684:
2680:
2639:
2638:
2634:
2593:(11): 774–783.
2579:
2575:
2505:
2501:
2491:
2489:
2479:
2475:
2419:
2415:
2405:
2403:
2390:
2389:
2385:
2375:
2373:
2366:The Independent
2360:
2359:
2355:
2299:
2295:
2285:
2283:
2275:
2274:
2270:
2258:
2256:
2248:
2188:
2184:
2174:
2172:
2154:
2150:
2133:
2129:
2074:
2070:
2060:
2058:
2054:
2047:
2039:
2035:
1996:(6473): 83–87.
1978:
1974:
1939:
1935:
1928:
1914:
1910:
1903:
1889:
1885:
1820:
1816:
1801:
1777:
1773:
1768:
1751:
1746:
1652:function member
1618:object-oriented
1606:
1570:
1569:
1561:
1559:
1550:
1549:
1532:
1530:
1520:
1519:
1502:
1499:
1498:
1412:
1408:
1391:
1388:
1387:
1365:
1359:
1351:backpropagation
1334:
1328:
1276:
1266:of inputs by a
1239:
1238:
1224:
1222:
1216:
1215:
1201:
1199:
1189:
1188:
1180:
1177:
1176:
1162:
1148:is a vector of
1125:
1121:
1115:
1111:
1105:
1094:
1082:
1079:
1078:
1049:
1043:
1031:backpropagation
1005:, developed by
964:
895:
878:
827:
821:
757:
754:
753:
712:
709:
708:
686:
683:
682:
630:
627:
626:
571:
568:
567:
535:
532:
531:
514:
510:
489:
485:
483:
480:
479:
476:
470:
428:
425:
424:
399:
395:
386:
382:
376:
365:
360:
356:
344:
340:
338:
335:
334:
322:
313:
302:
293:
279:
273:. Usually, the
272:
266:
260:
256:
250:
241:
229:
227:Basic structure
194:McCulloch–Pitts
89:synaptic weight
83:
82:
46:conceived as a
28:
23:
22:
15:
12:
11:
5:
3084:
3074:
3073:
3071:Bioinspiration
3068:
3063:
3049:
3048:
3043:
3032:
3031:External links
3029:
3027:
3026:
2992:(22): 226802.
2977:
2967:(4): 115–133.
2948:
2946:
2943:
2940:
2939:
2926:
2893:
2869:
2854:
2794:
2744:
2732:
2725:
2705:
2698:
2678:
2632:
2573:
2499:
2473:
2413:
2383:
2353:
2316:(9): 586–595.
2293:
2268:
2266:
2265:
2203:(9): 969–973.
2182:
2148:
2127:
2068:
2033:
1972:
1953:(4): 115–133.
1933:
1926:
1908:
1901:
1883:
1814:
1799:
1770:
1769:
1767:
1764:
1763:
1762:
1757:
1755:Binding neuron
1750:
1747:
1736:false
1623:
1605:
1602:
1573:
1568:
1560:
1558:
1555:
1552:
1551:
1548:
1545:
1542:
1539:
1531:
1529:
1526:
1525:
1523:
1518:
1515:
1512:
1509:
1506:
1453:
1452:
1441:
1438:
1435:
1432:
1429:
1426:
1423:
1420:
1415:
1411:
1407:
1404:
1401:
1398:
1395:
1358:
1355:
1327:
1324:
1275:
1272:
1256:
1255:
1242:
1237:
1234:
1231:
1223:
1221:
1218:
1217:
1214:
1211:
1208:
1200:
1198:
1195:
1194:
1192:
1187:
1184:
1161:
1158:
1142:
1141:
1128:
1124:
1118:
1114:
1108:
1103:
1100:
1097:
1093:
1089:
1086:
1045:Main article:
1042:
1039:
1013:in 1960 – see
1011:Bernard Widrow
963:
960:
894:
891:
877:
874:
869:
868:
860:
852:
823:Main article:
820:
817:
813:Turing machine
782:
779:
776:
773:
770:
767:
764:
761:
737:
734:
731:
728:
725:
722:
719:
716:
696:
693:
690:
670:
667:
664:
661:
658:
655:
652:
649:
646:
643:
640:
637:
634:
611:
608:
605:
602:
599:
596:
593:
590:
587:
584:
581:
578:
575:
539:
517:
513:
509:
506:
503:
500:
497:
492:
488:
469:
466:
432:
421:
420:
408:
402:
398:
392:
389:
385:
379:
374:
371:
368:
364:
359:
355:
352:
347:
343:
330:th neuron is:
318:
311:
298:
288:
277:
268:
264:
258:
254:
246:
239:
228:
225:
160:logic circuits
148:differentiable
136:step functions
56:neural network
50:of biological
26:
9:
6:
4:
3:
2:
3083:
3072:
3069:
3067:
3064:
3062:
3059:
3058:
3056:
3047:
3044:
3042:
3040:
3035:
3034:
3023:
3019:
3015:
3011:
3007:
3003:
2999:
2995:
2991:
2987:
2983:
2978:
2974:
2970:
2966:
2962:
2958:
2957:Pitts, Walter
2954:
2950:
2949:
2936:
2930:
2922:
2915:
2911:
2907:
2903:
2897:
2886:
2885:
2880:
2879:Yoshua Bengio
2873:
2865:
2858:
2850:
2846:
2842:
2838:
2834:
2830:
2826:
2822:
2818:
2814:
2810:
2806:
2798:
2790:
2786:
2782:
2778:
2774:
2770:
2766:
2762:
2758:
2754:
2748:
2741:
2736:
2728:
2722:
2718:
2717:
2709:
2701:
2695:
2691:
2690:
2682:
2674:
2670:
2666:
2662:
2658:
2654:
2650:
2646:
2642:
2636:
2628:
2624:
2620:
2616:
2611:
2606:
2601:
2596:
2592:
2588:
2584:
2577:
2569:
2565:
2561:
2557:
2552:
2547:
2543:
2539:
2535:
2531:
2527:
2523:
2519:
2515:
2511:
2503:
2488:
2484:
2477:
2469:
2465:
2460:
2455:
2450:
2445:
2441:
2437:
2433:
2429:
2425:
2417:
2401:
2397:
2393:
2387:
2371:
2367:
2363:
2357:
2349:
2345:
2341:
2337:
2332:
2327:
2323:
2319:
2315:
2311:
2306:
2297:
2282:
2281:New Scientist
2278:
2272:
2255:
2251:
2246:
2245:
2242:
2238:
2234:
2230:
2226:
2222:
2218:
2214:
2210:
2206:
2202:
2198:
2194:
2186:
2171:
2167:
2163:
2159:
2152:
2143:
2138:
2131:
2123:
2119:
2114:
2109:
2104:
2099:
2095:
2091:
2087:
2083:
2079:
2072:
2057:on 2015-04-12
2053:
2046:
2045:
2037:
2029:
2025:
2021:
2017:
2012:
2007:
2003:
1999:
1995:
1991:
1987:
1983:
1976:
1968:
1964:
1960:
1956:
1952:
1948:
1944:
1937:
1929:
1923:
1919:
1912:
1904:
1898:
1894:
1887:
1879:
1875:
1871:
1867:
1863:
1859:
1855:
1851:
1847:
1843:
1838:
1833:
1829:
1825:
1818:
1810:
1806:
1802:
1796:
1791:
1786:
1782:
1775:
1771:
1761:
1760:Connectionism
1758:
1756:
1753:
1752:
1745:
1742:
1739:
1735:
1732:
1729:true
1728:
1725:
1721:
1718:
1715:
1711:
1707:
1703:
1699:
1696:
1692:
1688:
1684:
1680:
1676:
1672:
1669:
1665:
1661:
1657:
1653:
1649:
1645:
1641:
1637:
1633:
1630:
1626:
1622:
1619:
1615:
1611:
1601:
1599:
1595:
1591:
1586:
1566:
1556:
1553:
1546:
1543:
1540:
1537:
1527:
1521:
1516:
1510:
1504:
1496:
1493:
1491:
1487:
1483:
1479:
1474:
1470:
1466:
1462:
1461:ramp function
1458:
1439:
1433:
1430:
1427:
1418:
1413:
1409:
1405:
1399:
1393:
1386:
1385:
1384:
1382:
1378:
1374:
1370:
1364:
1354:
1352:
1348:
1344:
1339:
1333:
1323:
1321:
1320:Deconvolution
1317:
1313:
1309:
1305:
1304:Linear filter
1301:
1297:
1292:
1291:to the data.
1290:
1286:
1281:
1271:
1269:
1265:
1261:
1235:
1232:
1229:
1219:
1212:
1209:
1206:
1196:
1190:
1185:
1182:
1175:
1174:
1173:
1171:
1167:
1160:Step function
1157:
1155:
1151:
1147:
1126:
1122:
1116:
1112:
1106:
1101:
1098:
1095:
1091:
1087:
1084:
1077:
1076:
1075:
1073:
1069:
1064:
1062:
1058:
1054:
1048:
1038:
1036:
1032:
1028:
1024:
1018:
1016:
1012:
1008:
1004:
999:
997:
993:
989:
985:
981:
977:
973:
969:
959:
957:
953:
948:
946:
942:
938:
934:
930:
925:
923:
919:
915:
911:
907:
903:
898:
890:
887:
883:
873:
866:
865:
861:
858:
857:
853:
850:
849:
845:
844:
843:
841:
831:
826:
816:
814:
810:
805:
802:
799:
794:
780:
777:
771:
768:
765:
759:
751:
735:
732:
726:
723:
720:
714:
694:
691:
688:
668:
665:
662:
659:
656:
653:
650:
647:
644:
641:
638:
635:
632:
623:
606:
603:
600:
597:
594:
591:
588:
585:
582:
576:
573:
565:
561:
557:
553:
537:
515:
511:
507:
504:
501:
498:
495:
490:
486:
475:
465:
462:
460:
456:
451:
449:
444:
430:
406:
400:
396:
390:
387:
383:
377:
372:
369:
366:
362:
357:
353:
350:
345:
341:
333:
332:
331:
329:
324:
321:
317:
310:
306:
301:
297:
294: =
291:
287:
283:
276:
271:
267:
257:
249:
245:
238:
234:
224:
221:
215:
211:
205:
203:
199:
195:
191:
187:
186:binary neuron
183:
179:
174:
172:
167:
165:
161:
157:
153:
149:
145:
141:
137:
133:
129:
128:sigmoid shape
125:
121:
117:
113:
109:
105:
100:
98:
94:
90:
80:
76:
72:
68:
63:
61:
57:
53:
49:
45:
41:
32:
19:
3038:
2989:
2985:
2964:
2960:
2929:
2920:
2896:
2883:
2872:
2866:. NIPS 2001.
2863:
2857:
2808:
2804:
2797:
2764:
2760:
2753:Werbos, P.J.
2747:
2735:
2715:
2708:
2688:
2681:
2648:
2644:
2635:
2610:10754/686016
2590:
2586:
2576:
2542:10754/673986
2517:
2513:
2502:
2490:. Retrieved
2486:
2476:
2431:
2427:
2416:
2404:. Retrieved
2395:
2386:
2374:. Retrieved
2365:
2356:
2331:10356/163240
2313:
2309:
2296:
2286:16 September
2284:. Retrieved
2280:
2271:
2259:23 September
2257:. Retrieved
2253:
2200:
2196:
2185:
2175:23 September
2173:. Retrieved
2161:
2151:
2130:
2085:
2081:
2071:
2059:. Retrieved
2052:the original
2043:
2036:
1993:
1989:
1975:
1950:
1946:
1936:
1917:
1911:
1892:
1886:
1827:
1823:
1817:
1780:
1774:
1743:
1741:end function
1740:
1737:
1733:
1730:
1726:
1723:
1719:
1717:end for each
1716:
1713:
1709:
1705:
1701:
1697:
1694:
1690:
1686:
1682:
1678:
1674:
1670:
1667:
1663:
1659:
1655:
1654:fire(inputs
1651:
1647:
1643:
1639:
1635:
1631:
1628:
1624:
1607:
1597:
1593:
1589:
1587:
1497:
1494:
1456:
1454:
1376:
1372:
1366:
1335:
1293:
1279:
1277:
1257:
1169:
1165:
1163:
1153:
1149:
1145:
1143:
1071:
1067:
1065:
1060:
1050:
1019:
1000:
972:Walter Pitts
965:
956:real neurons
949:
926:
899:
896:
882:unary coding
879:
870:
862:
854:
846:
840:XOR function
836:
806:
803:
797:
795:
749:
624:
563:
559:
555:
551:
477:
463:
452:
445:
422:
327:
325:
319:
315:
308:
304:
299:
295:
289:
285:
281:
274:
269:
262:
252:
251:and weights
247:
243:
236:
232:
230:
206:
201:
197:
193:
189:
185:
181:
177:
175:
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2906:Leon Bottou
2740:Paul Werbos
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1668:defined as:
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793:otherwise.
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2902:Yann LeCun
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