Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

A deep learning framework for neuroscience


Systems neuroscience seeks explanations for how the brain implements a wide variety of perceptual, cognitive and motor tasks. Conversely, artificial intelligence attempts to design computational systems based on the tasks they will have to solve. In artificial neural networks, the three components specified by design are the objective functions, the learning rules and the architectures. With the growing success of deep learning, which utilizes brain-inspired architectures, these three designed components have increasingly become central to how we model, engineer and optimize complex artificial learning systems. Here we argue that a greater focus on these components would also benefit systems neuroscience. We give examples of how this optimization-based framework can drive theoretical and experimental progress in neuroscience. We contend that this principled perspective on systems neuroscience will help to generate more rapid progress.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: The three core components of ANN design.
Fig. 2: Bias and variance in learning rules.
Fig. 3: Learning rules that don’t follow gradients.
Fig. 4: Comparing deep ANN models and the brain.
Fig. 5: Biological models of credit assignment.


  1. 1.

    Mathis, A. et al. DeepLabCut: markerless pose estimation of user-defined body parts with deep learning. Nat. Neurosci. 21, 1281–1289 (2018).

    CAS  PubMed  Google Scholar 

  2. 2.

    Steinmetz, N. A., Koch, C., Harris, K. D. & Carandini, M. Challenges and opportunities for large-scale electrophysiology with Neuropixels probes. Curr. Opin. Neurobiol. 50, 92–100 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  3. 3.

    Marder, E. & Bucher, D. Central pattern generators and the control of rhythmic movements. Curr. Biol. 11, R986–R996 (2001).

    CAS  PubMed  Google Scholar 

  4. 4.

    Cullen, K. E. The vestibular system: multimodal integration and encoding of self-motion for motor control. Trends Neurosci. 35, 185–196 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  5. 5.

    Kim, J. S. et al. Space-time wiring specificity supports direction selectivity in the retina. Nature 509, 331–336 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  6. 6.

    Olshausen, B.A. & Field, D.J. What is the other 85 percent of V1 doing? in 23 Problems in Systems Neuroscience (eds van Hemmen, J. L. & Sejnowski, T. J.) 182–211 (Oxford Univ. Press, 2006).

  7. 7.

    Thompson, L. T. & Best, P. J. Place cells and silent cells in the hippocampus of freely-behaving rats. J. Neurosci. 9, 2382–2390 (1989).

    CAS  PubMed  Google Scholar 

  8. 8.

    Yamins, D. L. K. & DiCarlo, J. J. Using goal-driven deep learning models to understand sensory cortex. Nat. Neurosci. 19, 356–365 (2016).

    CAS  PubMed  Google Scholar 

  9. 9.

    Botvinick, M. et al. Reinforcement learning, fast and slow. Trends Cogn. Sci. 23, 408–422 (2019).

    PubMed  Google Scholar 

  10. 10.

    Kriegeskorte, N. & Douglas, P. K. Cognitive computational neuroscience. Nat. Neurosci. 21, 1148–1160 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  11. 11.

    Rumelhart, D. E., McClelland, J. L. & PDP Research Group. Parallel Distributed Processing (MIT Press, 1988).

  12. 12.

    Sacramento, J., Costa, R. P., Bengio, Y. & Senn, W. Dendritic cortical microcircuits approximate the backpropagation algorithm. Adv. Neural Inf. Proc. Sys. 31, 8735–8746 (2018).

    Google Scholar 

  13. 13.

    Poirazi, P., Brannon, T. & Mel, B. W. Pyramidal neuron as two-layer neural network. Neuron 37, 989–999 (2003).

    CAS  PubMed  Google Scholar 

  14. 14.

    Guerguiev, J., Lillicrap, T. P. & Richards, B. A. Towards deep learning with segregated dendrites. eLife 6, e22901 (2017).

    PubMed  PubMed Central  Google Scholar 

  15. 15.

    Goodfellow, I., Bengio, Y. & Courville, A. Deep Learning (MIT Press, 2016).

  16. 16.

    Cichy, R. M., Khosla, A., Pantazis, D., Torralba, A. & Oliva, A. Comparison of deep neural networks to spatio-temporal cortical dynamics of human visual object recognition reveals hierarchical correspondence. Sci. Rep. 6, 27755 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  17. 17.

    Kell, A. J. E., Yamins, D. L. K., Shook, E. N., Norman-Haignere, S. V. & McDermott, J. H. A task-optimized neural network replicates human auditory behavior, predicts brain responses, and reveals a cortical processing hierarchy. Neuron 98, 630–644.e16 (2018).

    CAS  PubMed  Google Scholar 

  18. 18.

    Richards, B. A. & Lillicrap, T. P. Dendritic solutions to the credit assignment problem. Curr. Opin. Neurobiol. 54, 28–36 (2019).

    CAS  PubMed  Google Scholar 

  19. 19.

    Roelfsema, P. R. & Holtmaat, A. Control of synaptic plasticity in deep cortical networks. Nat. Rev. Neurosci. 19, 166–180 (2018).

    CAS  PubMed  Google Scholar 

  20. 20.

    Krizhevsky, A., Sutskever, I. & Hinton, G. E. ImageNet classification with deep convolutional neural networks. Adv. Neural Inf. Proc. Sys. 25, 1097–1105 (2012).

    Google Scholar 

  21. 21.

    Hannun, A. et al. Deep speech: scaling up end-to-end speech recognition. Preprint at arXiv (2014).

  22. 22.

    Radford, A. et al. Better language models and their implications. OpenAI Blog (2019).

  23. 23.

    Gao, Y., Hendricks, L.A., Kuchenbecker, K.J. & Darrell, T. Deep learning for tactile understanding from visual and haptic data. in IEEE International Conference on Robotics and Automation (ICRA) 536–543 (2016).

  24. 24.

    Banino, A. et al. Vector-based navigation using grid-like representations in artificial agents. Nature 557, 429–433 (2018).

    CAS  PubMed  Google Scholar 

  25. 25.

    Finn, C., Goodfellow, I. & Levine, S. Unsupervised learning for physical interaction through video prediction. Adv. Neural Inf. Proc. Sys. 29, 64–72 (2016).

    Google Scholar 

  26. 26.

    Silver, D. et al. Mastering the game of Go without human knowledge. Nature 550, 354–359 (2017).

    CAS  PubMed  Google Scholar 

  27. 27.

    Santoro, A. et al. A simple neural network module for relational reasoning. Adv. Neural Inf. Proc. Sys. 30, 4967–4976 (2017).

    Google Scholar 

  28. 28.

    Khaligh-Razavi, S.-M. & Kriegeskorte, N. Deep supervised, but not unsupervised, models may explain IT cortical representation. PLoS Comput. Biol. 10, e1003915 (2014).

    PubMed  PubMed Central  Google Scholar 

  29. 29.

    Bashivan, P., Kar, K. & DiCarlo, J. J. Neural population control via deep image synthesis. Science 364, eaav9436 (2019).

    PubMed  Google Scholar 

  30. 30.

    Pospisil, D. A., Pasupathy, A. & Bair, W. ‘Artiphysiology’ reveals V4-like shape tuning in a deep network trained for image classification. eLife 7, e38242 (2018).

    PubMed  PubMed Central  Google Scholar 

  31. 31.

    Singer, Y. et al. Sensory cortex is optimized for prediction of future input. eLife 7, e31557 (2018).

    PubMed  PubMed Central  Google Scholar 

  32. 32.

    Watanabe, E., Kitaoka, A., Sakamoto, K., Yasugi, M. & Tanaka, K. Illusory motion reproduced by deep neural networks trained for prediction. Front. Psychol. 9, 345 (2018).

    PubMed  PubMed Central  Google Scholar 

  33. 33.

    Wang, J. X. et al. Prefrontal cortex as a meta-reinforcement learning system. Nat. Neurosci. 21, 860–868 (2018).

    CAS  PubMed  Google Scholar 

  34. 34.

    Scellier, B. & Bengio, Y. Equilibrium propagation: bridging the gap between energy-based models and backpropagation. Front. Comput. Neurosci. 11, 24 (2017).

    PubMed  PubMed Central  Google Scholar 

  35. 35.

    Whittington, J. C. R. & Bogacz, R. An approximation of the error backpropagation algorithm in a predictive coding network with local hebbian synaptic plasticity. Neural Comput. 29, 1229–1262 (2017).

    PubMed  PubMed Central  Google Scholar 

  36. 36.

    Lillicrap, T. P., Cownden, D., Tweed, D. B. & Akerman, C. J. Random synaptic feedback weights support error backpropagation for deep learning. Nat. Commun. 7, 13276 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  37. 37.

    Roelfsema, P. R. & van Ooyen, A. Attention-gated reinforcement learning of internal representations for classification. Neural Comput. 17, 2176–2214 (2005).

    PubMed  Google Scholar 

  38. 38.

    Pozzi, I., Bohté, S. & Roelfsema, P. A biologically plausible learning rule for deep learning in the brain. Preprint at arXiv (2018).

  39. 39.

    Körding, K. P. & König, P. Supervised and unsupervised learning with two sites of synaptic integration. J. Comput. Neurosci. 11, 207–215 (2001).

    PubMed  Google Scholar 

  40. 40.

    Marblestone, A. H., Wayne, G. & Kording, K. P. Toward an integration of deep learning and neuroscience. Front. Comput. Neurosci. 10, 94 (2016).

    PubMed  PubMed Central  Google Scholar 

  41. 41.

    Raman, D. V., Rotondo, A. P. & O’Leary, T. Fundamental bounds on learning performance in neural circuits. Proc. Natl Acad. Sci. USA 116, 10537–10546 (2019).

    CAS  PubMed  Google Scholar 

  42. 42.

    Neyshabur, B., Li, Z., Bhojanapalli, S., LeCun, Y. & Srebro, N. The role of over-parametrization in generalization of neural networks. in International Conference on Learning Representations (ICLR) 2019 (2019).

  43. 43.

    Wolpert, D. H. & Macready, W. G. No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1, 67–82 (1997).

    Google Scholar 

  44. 44.

    Bengio, Y. & LeCun, Y. Scaling learning algorithms towards AI. in Large-Scale Kernel Machines (eds Bottou, L., Chapelle, O., DeCoste, D. & Weston, J.) chapter 14 (MIT Press, 2007).

  45. 45.

    Neyshabur, B., Tomioka, R. & Srebro, N. In search of the real inductive bias: on the role of implicit regularization in deep learning. Preprint at arXiv (2014).

  46. 46.

    Snell, J., Swersky, K. & Zemel, R. Prototypical networks for few-shot learning. Adv. Neural Inf. Proc. Sys. 30, 4077–4087 (2017).

    Google Scholar 

  47. 47.

    Ravi, S. & Larochelle, H. Optimization as a model for few-shot International Conference on Learning Representations (ICLR) 2017 (2017).

  48. 48.

    Zador, A. M. A critique of pure learning and what artificial neural networks can learn from animal brains. Nat. Commun. 10, 3770 (2019).

    PubMed  PubMed Central  Google Scholar 

  49. 49.

    Bellec, G., Salaj, D., Subramoney, A., Legenstein, R. & Maass, W. Long short-term memory and learning-to-learn in networks of spiking neurons. Adv. Neural Inf. Proc. Sys. 31, 787–797 (2018).

    Google Scholar 

  50. 50.

    Huang, Y. & Rao, R. P. N. Predictive coding. Wiley Interdiscip. Rev. Cogn. Sci. 2, 580–593 (2011).

    PubMed  Google Scholar 

  51. 51.

    Williams, R. J. Simple statistical gradient-following algorithms for connectionist reinforcement learning. Mach. Learn. 8, 229–256 (1992).

    Google Scholar 

  52. 52.

    Klyubin, A.S., Polani, D. & Nehaniv, C.L. Empowerment: A universal agent-centric measure of control. in 2005 IEEE Congress on Evolutionary Computation 128–135 (IEEE, 2005).

  53. 53.

    Salge, C., Glackin, C. & Polani, D. Empowerment–an introduction. in Guided Self-Organization: Inception (ed. Prokopenko, M.) 67–114 (Springer, 2014).

  54. 54.

    Newell, A. & Simon, H.A. GPS, a Program that Simulates Human Thought. (RAND Corp., 1961).

  55. 55.

    Nguyen, A., Yosinski, J. & Clune, J. Understanding neural networks via feature visualization: a survey. Preprint at arXiv (2019).

  56. 56.

    Kebschull, J. M. et al. High-throughput mapping of single-neuron projections by sequencing of barcoded RNA. Neuron 91, 975–987 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  57. 57.

    Kornfeld, J. & Denk, W. Progress and remaining challenges in high-throughput volume electron microscopy. Curr. Opin. Neurobiol. 50, 261–267 (2018).

    CAS  PubMed  Google Scholar 

  58. 58.

    Lillicrap, T. P. & Kording, K. P. What does it mean to understand a neural network? Preprint at arXiv (2019).

  59. 59.

    Olshausen, B. A. & Field, D. J. Natural image statistics and efficient coding. Network 7, 333–339 (1996).

    CAS  PubMed  Google Scholar 

  60. 60.

    Hyvärinen, A. & Oja, E. Simple neuron models for independent component analysis. Int. J. Neural Syst. 7, 671–687 (1996).

    PubMed  Google Scholar 

  61. 61.

    Oja, E. A simplified neuron model as a principal component analyzer. J. Math. Biol. 15, 267–273 (1982).

    CAS  PubMed  Google Scholar 

  62. 62.

    Intrator, N. & Cooper, L. N. Objective function formulation of the BCM theory of visual cortical plasticity: Statistical connections, stability conditions. Neural Netw. 5, 3–17 (1992).

    Google Scholar 

  63. 63.

    Fiser, A. et al. Experience-dependent spatial expectations in mouse visual cortex. Nat. Neurosci. 19, 1658–1664 (2016).

    CAS  PubMed  Google Scholar 

  64. 64.

    Schultz, W., Dayan, P. & Montague, P. R. A neural substrate of prediction and reward. Science 275, 1593–1599 (1997).

    CAS  PubMed  PubMed Central  Google Scholar 

  65. 65.

    Momennejad, I. et al. The successor representation in human reinforcement learning. Nat. Hum. Behav. 1, 680–692 (2017).

    CAS  PubMed  Google Scholar 

  66. 66.

    Nayebi, A. et al. Task-driven convolutional recurrent models of the visual system. Adv. Neural Inf. Proc. Sys. 31, 5290–5301 (2018).

    Google Scholar 

  67. 67.

    Schrimpf, M. et al. Brain-Score: which artificial neural network for object recognition is most brain-like? Preprint at bioRxiv (2018).

  68. 68.

    Kepecs, A. & Fishell, G. Interneuron cell types are fit to function. Nature 505, 318–326 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  69. 69.

    Van Essen, D.C. & Anderson, C.H. Information processing strategies and pathways in the primate visual system. in Neural Networks: Foundations to Applications. An Introduction to Neural and Electronic Networks (eds Zornetzer, S. F., Davis, J. L., Lau, C. & McKenna, T.) 45–76 (Academic Press, 1995).

  70. 70.

    Lindsey, J., Ocko, S. A., Ganguli, S. & Deny, S. A unified theory of early visual representations from retina to cortex through anatomically constrained deep CNNs. in International Conference on Learning Representations (ICLR) Blind Submissions (2019).

  71. 71.

    Güçlü, U. & van Gerven, M. A. Deep neural networks reveal a gradient in the complexity of neural representations across the ventral stream. J. Neurosci. 35, 10005–10014 (2015).

    PubMed  PubMed Central  Google Scholar 

  72. 72.

    Kwag, J. & Paulsen, O. The timing of external input controls the sign of plasticity at local synapses. Nat. Neurosci. 12, 1219–1221 (2009).

    CAS  PubMed  Google Scholar 

  73. 73.

    Bittner, K. C., Milstein, A. D., Grienberger, C., Romani, S. & Magee, J. C. Behavioral time scale synaptic plasticity underlies CA1 place fields. Science 357, 1033–1036 (2017).

    CAS  PubMed  Google Scholar 

  74. 74.

    Lacefield, C. O., Pnevmatikakis, E. A., Paninski, L. & Bruno, R. M. Reinforcement learning recruits somata and apical dendrites across layers of primary sensory cortex. Cell Rep. 26, 2000–2008.e2 (2019).

    CAS  PubMed  Google Scholar 

  75. 75.

    Williams, L. E. & Holtmaat, A. Higher-order thalamocortical inputs gate synaptic long-term potentiation via disinhibition. Neuron 101, 91–102.e4 (2019).

    CAS  PubMed  Google Scholar 

  76. 76.

    Yagishita, S. et al. A critical time window for dopamine actions on the structural plasticity of dendritic spines. Science 345, 1616–1620 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  77. 77.

    Lim, S. et al. Inferring learning rules from distributions of firing rates in cortical neurons. Nat. Neurosci. 18, 1804–1810 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  78. 78.

    Costa, R. P. et al. Synaptic transmission optimization predicts expression loci of long-term plasticity. Neuron 96, 177–189.e7 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  79. 79.

    Zolnik, T. A. et al. All-optical functional synaptic connectivity mapping in acute brain slices using the calcium integrator CaMPARI. J. Physiol. (Lond.) 595, 1465–1477 (2017).

    CAS  Google Scholar 

  80. 80.

    Scott, S. H. Optimal feedback control and the neural basis of volitional motor control. Nat. Rev. Neurosci. 5, 532–546 (2004).

    CAS  Google Scholar 

  81. 81.

    Krakauer, J. W., Ghazanfar, A. A., Gomez-Marin, A., MacIver, M. A. & Poeppel, D. Neuroscience needs behavior: correcting a reductionist bias. Neuron 93, 480–490 (2017).

    CAS  PubMed  PubMed Central  Google Scholar 

  82. 82.

    Zylberberg, J., Murphy, J. T. & DeWeese, M. R. A sparse coding model with synaptically local plasticity and spiking neurons can account for the diverse shapes of V1 simple cell receptive fields. PLoS Comput. Biol. 7, e1002250 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  83. 83.

    Chalk, M., Tkačik, G. & Marre, O. Inferring the function performed by a recurrent neural network. Preprint at bioRxiv (2019).

  84. 84.

    Cadieu, C. F. et al. Deep neural networks rival the representation of primate IT cortex for core visual object recognition. PLoS Comput. Biol. 10, e1003963 (2014).

    PubMed  PubMed Central  Google Scholar 

  85. 85.

    Golub, M. D. et al. Learning by neural reassociation. Nat. Neurosci. 21, 607–616 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  86. 86.

    Fukushima, K. Neocognitron: a self organizing neural network model for a mechanism of pattern recognition unaffected by shift in position. Biol. Cybern. 36, 193–202 (1980).

    CAS  PubMed  PubMed Central  Google Scholar 

  87. 87.

    Vogels, T. P., Rajan, K. & Abbott, L. F. Neural network dynamics. Annu. Rev. Neurosci. 28, 357–376 (2005).

    CAS  PubMed  Google Scholar 

  88. 88.

    Koren, V. & Denève, S. Computational account of spontaneous activity as a signature of predictive coding. PLoS Comput. Biol. 13, e1005355 (2017).

    PubMed  PubMed Central  Google Scholar 

  89. 89.

    Advani, M. S. & Saxe, A. M. High-dimensional dynamics of generalization error in neural networks. Preprint at arXiv (2017).

  90. 90.

    Amit, Y. Deep learning with asymmetric connections and Hebbian updates. Front. Comput. Neurosci. 13, 18 (2019).

    PubMed  PubMed Central  Google Scholar 

  91. 91.

    Lansdell, B. & Kording, K. Spiking allows neurons to estimate their causal effect. Preprint at bioRxiv (2018).

  92. 92.

    Werfel, J., Xie, X. & Seung, H. S. Learning curves for stochastic gradient descent in linear feedforward networks. Adv. Neural Inf. Proc. Sys. 16, 1197–1204 (2004).

    Google Scholar 

  93. 93.

    Samadi, A., Lillicrap, T. P. & Tweed, D. B. Deep learning with dynamic spiking neurons and fixed feedback weights. Neural Comput. 29, 578–602 (2017).

    PubMed  Google Scholar 

  94. 94.

    Akrout, M., Wilson, C., Humphreys, P. C., Lillicrap, T. & Tweed, D. Using weight mirrors to improve feedback alignment. Preprint at arXiv (2019).

  95. 95.

    Bartunov, S. et al. Assessing the scalability of biologically-motivated deep learning algorithms and architectures. Adv. Neural Inf. Proc. Sys. 31, 9368–9378 (2018).

    Google Scholar 

  96. 96.

    MacKay, D.J. Information Theory, Inference and Learning Algorithms (Cambridge University Press, 2003).

  97. 97.

    Goel, V., Weng, J. & Poupart, P. Unsupervised video object segmentation for deep reinforcement learning. Adv. Neural Inf. Proc. Sys. 31, 5683–5694 (2018).

    Google Scholar 

  98. 98.

    LeCun, Y. & Bengio, Y. Convolutional networks for images, speech, and time series. in The Handbook of Brain Theory and Neural Networks (ed. Arbib, M. A.) 276–279 (MIT Press, 1995).

  99. 99.

    Chorowski, J. K., Bahdanau, D., Serdyuk, D., Cho, K. & Bengio, Y. Attention-based models for speech recognition. Adv. Neural Inf. Proc. Sys. 28, 577–585 (2015).

    Google Scholar 

  100. 100.

    Houthooft, R. et al. Vime: variational information maximizing exploration. Adv. Neural Inf. Proc. Sys. 29, 1109–1117 (2016).

    Google Scholar 

Download references


This article emerged from a workshop on optimization in the brain that took place February 24–28, 2019 at the Bellairs Research Institute of McGill University. We thank Element AI and Bellairs Research Institute for their critical support in organizing this workshop. This work was also supported by the Canadian Institute for Advanced Research Learning in Machines and Brains Program.

Author information



Corresponding author

Correspondence to Blake A. Richards.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer Review Information Nature Neuroscience thanks Gabriel Kreiman and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Richards, B.A., Lillicrap, T.P., Beaudoin, P. et al. A deep learning framework for neuroscience. Nat Neurosci 22, 1761–1770 (2019).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing