An Approximation of the Error Backpropagation Algorithm in a Predictive Coding Network with Local Hebbian Synaptic Plasticity

Abstract

To efficiently learn from feedback, cortical networks need to update synaptic weights on multiple levels of cortical hierarchy. An effective and well-known algorithm for computing such changes in synaptic weights is the error backpropagation algorithm. However, in this algorithm, the change in synaptic weights is a complex function of weights and activities of neurons not directly connected with the synapse being modified, whereas the changes in biological synapses are determined only by the activity of presynaptic and postsynaptic neurons. Several models have been proposed that approximate the backpropagation algorithm with local synaptic plasticity, but these models require complex external control over the network or relatively complex plasticity rules. Here we show that a network developed in the predictive coding framework can efficiently perform supervised learning fully autonomously, employing only simple local Hebbian plasticity. Furthermore, for certain parameters, the weight change in the predictive coding model converges to that of the backpropagation algorithm. This suggests that it is possible for cortical networks with simple Hebbian synaptic plasticity to implement efficient learning algorithms in which synapses in areas on multiple levels of hierarchy are modified to minimize the error on the output.

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References 53

1. 1.

   Ackley DH, Hinton GE, Sejnowski TJ. A learning algorithm for Boltzmann machines. Cognitive Science. 1985;9:147-169.

   Not in our library

2. 2.

   Balduzzi D, Vanchinathan H, Buhmann J. Kickback cuts backprop’s red-tape: Biologically plausible credit assignment in neural networks. arXiv:1411.6191v1. 2014.

   Not in our library

3. 3.

   Barto A, Jordan M. Gradient following without back-propagation in layered networks. 1987;2:629-636.

   Not in our library

4. 4.

   Bastos AM, Usrey WM, Adams RA, Mangun GR, Fries P, Friston KJ. Canonical microcircuits for predictive coding. Neuron. 2012;76:695-711.

   Not in our library10.1016/j.neuron.2012.10.038

5. 5.

   Bell AH, Summerfield C, Morin EL, Malecek NJ, Ungerleider LG. Encoding of stimulus probability in macaque inferior temporal cortex. Current Biology. 2016;26(17):2280.

   Not in our library10.1016/j.cub.2016.07.007

6. 6.

   Bengio Y. How auto-encoders could provide credit assignment in deep networks via target propagation. arXiv:1407.7906. 2014.

   Not in our library

7. 7.

   Bengio Y, Fischer A. Early inference in energy-based models approximates back-propagation. arXiv:1510.02777. 2015.

   Not in our library

8. 8.

   Bengio Y, Lee D-H, Bornschein J, Lin Z. Towards biologically plausible deep learning. arXiv:1502.04156. 2015.

   Not in our library

9. 9.
   A tutorial on the free-energy framework for modelling perception and learning · 2017

   No notice
10. 10.

    Bogacz R, Markowska-Kaczmar U, Kozik A. Blinking artefact recognition in EEG signal using artificial neural network. 1999;502-507.

    Not in our library

11. 11.

    Bogacz R, Moraud EM, Abdi A, Magill PJ, Baufreton J. Properties of neurons in external globus pallidus can support optimal action selection. PLoS Comput Biol. 2016;12(7):e1005004.

    Not in our library10.1371/journal.pcbi.1005004

12. 12.

    Brown MW, Aggleton JP. Recognition memory: What are the roles of the perirhinal cortex and hippocampus? Nature Reviews Neuroscience. 2001;2(1):51-61.

    Not in our library10.1038/35049064

13. 13.

    Chauvin Y, Rumelhart DE. Backpropagation: Theory, architectures, and applications. 1995.

    Not in our library

14. 14.

    Crick F. The recent excitement about neural networks. Nature. 1989;337:129-132.

    Not in our library10.1038/337129a0

15. 15.

    Dayan P, Hinton GE, Neal RM, Zemel RS. The Helmholtz machine. Neural Computation. 1995;7(5):889-904.

    Not in our library10.1162/neco.1995.7.5.889

16. 16.

    de Sa VR, Ballard DH. Perceptual learning from cross-modal feedback. Psychology of Learning and Motivation. 1998;36:309-351.

    Not in our library

17. 17.

    Feldman H, Friston K. Attention, uncertainty, and free-energy. Frontiers in Human Neuroscience. 2010;4:215.

    Not in our library10.3389/fnhum.2010.00215

18. 18.

    Fiser A, Mahringer D, Oyibo HK, Petersen AV, Leinweber M, Keller GB. Experience-dependent spatial expectations in mouse visual cortex. Nature Neuroscience. 2016;19:1658-1664.

    Not in our library10.1038/nn.4385

19. 19.

    Friston K. Learning and inference in the brain. Neural Networks. 2003;16:1325-1352.

    Not in our library10.1016/j.neunet.2003.06.005

20. 20.

    Friston K. A theory of cortical responses. Philosophical Transactions of the Royal Society B. 2005;360:815-836.

    Not in our library10.1098/rstb.2005.1622

21. 21.

    Friston K. The free-energy principle: A unified brain theory? Nature Reviews Neuroscience. 2010;11:127-138.

    Not in our library10.1038/nrn2787

22. 22.

    Friston KJ, Daunizeau J, Kilner J, Kiebel SJ. Action and behavior: A free-energy formulation. Biological Cybernetics. 2010;102(3):227-260.

    Not in our library10.1007/s00422-010-0364-z

23. 23.

    Hinton G, Deng L, Yu D, Dahl G, Mohamed A, Jaitly N, Kingsbury B, et al. Deep neural networks for acoustic modeling in speech recognition: The shared views of four research groups. IEEE Signal Processing Magazine. 2012;29:82-97.

    Not in our library

24. 24.

    Hinton GE, McClelland JL, Anderson DZ. Learning representations by recirculation. Neural information processing systems. 1988;358-366.

    Not in our library

25. 25.

    Hinton GE, Osindero S, Teh Y-W. A fast learning algorithm for deep belief nets. Neural Computation. 2006;18(7):1527-1554.

    Not in our library10.1162/neco.2006.18.7.1527

26. 26.

    Hyvarinen A. Regression using independent component analysis, and its connection to multi-layer perceptrons. 1999;491-496.

    Not in our library

27. 27.

    Kingma D, Ba J. Adam: A method for stochastic optimization. arXiv:1412.6980. 2014.

    Not in our library

28. 28.

    Krizhevsky A, Sutskever I, Hinton GE, Pereira F, Burges C, Bottou L, Weinberger K. Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems. 2012;25:1097-1105.

    Not in our library

29. 29.

    Larochelle H, Bengio Y. Towards biologically plausible deep learning. 2008;536-543.

    Not in our library

30. 30.

    LeCun Y, Boser B, Denker JS, Henderson D, Howard RE, Hubbard W, Jackel LD. Backpropagation applied to handwritten zip code recognition. Neural Computation. 1989;1:541-551.

    Not in our library

31. 31.
    Random synaptic feedback weights support error backpropagation for deep learning · 2016

    No notice
32. 32.

    Mazzoni P, Andersen RA, Jordan MI. A more biologically plausibile learning rule for neural networks. Proc Natl Acad Sci USA. 1991;88:4433-4437.

    Not in our library10.1073/pnas.88.10.4433

33. 33.

    McClelland JL, McNaughton BL, O’Reilly RC. Why there are complementary learning systems in the hippocampus and neocortex: Insights from the successes and failures of connectionist models of learning and memory. Psychological Review. 1995;102:419-457.

    Not in our library10.1037/0033-295x.102.3.419

34. 34.

    Miller LL, Desimone R. The representation of stimulus familiarity in anterior inferior temporal cortex. Journal of Neurophysiology. 1993;69(6):1918-1929.

    Not in our library10.1152/jn.1993.69.6.1918

35. 35.

    Mizuseki K, Buzsáki G. Preconfigured, skewed distribution of firing rates in the hippocampus and entorhinal cortex. Cell Reports. 2013;4(5):1010-1021.

    Not in our library10.1016/j.celrep.2013.07.039

36. 36.

    O’Reilly RC. Biologically plausible error-driven learning using local activation differences: The generalized recirculation algorithm. Neural Computation. 1998;8:895-938.

    Not in our library

37. 37.

    O’Reilly RC, Munakata Y. Computational explorations in cognitive neuroscience. 2000.

    Not in our library

38. 38.

    Plaut DC, McClelland JL, Seidenberg MS, Patterson K. Understanding normal and impaired word reading: Computational principles in quasi-regular domains. Psychological Review. 1996;103:56-115.

    Not in our library10.1037/0033-295x.103.1.56

39. 39.

    Rao RPN, Ballard DH. Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience. 1999;2:79-87.

    Not in our library10.1038/4580

40. 40.

    Rumelhart DE, Durbin R, Golden R, Chauvin Y, Chauvin Y, Rumelhart DE. Backpropagation: The basic theory. Backpropagation: Theory, architectures and applications. 1995;1-34.

    Not in our library

41. 41.

    Rumelhart DE, Hinton GE, Williams RJ. Learning representations by back-propagating errors. Nature. 1986;323:533-536.

    Not in our library

42. 42.

    Scellier B, Bengio Y. Towards a biologically plausible backprop. arXiv:1602.05179. 2016.

    Not in our library

43. 43.

    Seidenberg MS, McClelland JL. A distributed, developmental model of word recognition and naming. Psychological Review. 1989;96:523-568.

    Not in our library10.1037/0033-295x.96.4.523

44. 44.

    Seung HS. Learning in spiking neural networks by reinforcement of stochastic synaptic transmission. Neuron. 2003;40:1063-1073.

    Not in our library10.1016/s0896-6273(03)00761-x

45. 45.

    Spratling MW. Reconciling predictive coding and biased competition models of cortical function. Frontiers in Computational Neuroscience. 2008;2:4.

    Not in our library10.3389/neuro.10.004.2008

46. 46.

    Srivastava N, Salakhutdinov R, Pereira F, Burges CJC, Bottou L, Weinberger KQ. Multimodal learning with deep boltzmann machines. Advances in neural information processing systems. 2012;25:2222-2230.

    Not in our library

47. 47.

    Summerfield C, Egner T, Greene M, Koechlin E, Mangels J, Hirsch J. Predictive codes for forthcoming perception in the frontal cortex. Science. 2006;314:1311-1314.

    Not in our library10.1126/science.1132028

48. 48.

    Summerfield C, Trittschuh EH, Monti JM, Mesulam M-M, Egner T. Neural repetition suppression reflects fulfilled perceptual expectations. Nature Neuroscience. 2008;11(9):1004-1006.

    Not in our library10.1038/nn.2163

49. 49.

    Unnikrishnan K, Venugopal K. Alopex: A correlation-based learning algorithm for feedforward and recurrent neural networks. Neural Computation. 1994;6:469-490.

    Not in our library

50. 50.

    Werfel J, Xiew X, Seung HS. Learning curves for stochastic gradient descent in linear feedforward networks. Neural Computation. 2005;17:2699-2718.

    Not in our library10.1162/089976605774320539

51. 51.

    Whittington JC, Bogacz R. Learning in cortical networks through error back-propagation. bioRxiv. 2015;035451.

    Not in our library

52. 52.

    Williams RJ. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Machine Learning. 1992;8:229-256.

    Not in our library

53. 53.

    Zmarz P, Keller GB. Mismatch receptive fields in mouse visual cortex. Neuron. 2016;92(4):766-772.

    Not in our library10.1016/j.neuron.2016.09.057

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• Theories of Error Back-Propagation in the Brain · 2019
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