Cortical-like dynamics in recurrent circuits optimized for sampling-based probabilistic inference

Sensory cortices display a suite of ubiquitous dynamical features, such as ongoing noise variability, transient overshoots, and oscillations, that have so far escaped a common, principled theoretical account. We developed a unifying model for these phenomena by training a recurrent excitatory–inhibitory neural circuit model of a visual cortical hypercolumn to perform sampling-based probabilistic inference. The optimized network displayed several key biological properties, including divisive normalization, as well as stimulus-modulated noise variability, inhibition-dominated transients at stimulus onset, and strong gamma oscillations. These dynamical features had distinct functional roles in speeding up inferences and made predictions that we confirmed in novel analyses of awake monkey recordings. Our results suggest that the basic motifs of cortical dynamics emerge as a consequence of the efficient implementation of the same computational function—fast sampling-based inference—and predict further properties of these motifs that can be tested in future experiments.

[1]  Guillaume Hennequin,et al.  Fast Sampling-Based Inference in Balanced Neuronal Networks , 2014, NIPS.

[2]  David Melcher,et al.  Trans-Saccadic Perception: “Object-otopy” across Space and Time , 2010 .

[3]  O. Schwartz,et al.  Flexible Gating of Contextual Influences in Natural Vision , 2015, Nature Neuroscience.

[4]  Christoph von der Malsburg,et al.  The Correlation Theory of Brain Function , 1994 .

[5]  Jascha Sohl-Dickstein,et al.  Hamiltonian Monte Carlo Without Detailed Balance , 2014, ICML.

[6]  Martin J. Wainwright,et al.  Scale Mixtures of Gaussians and the Statistics of Natural Images , 1999, NIPS.

[7]  Ha Hong,et al.  Performance-optimized hierarchical models predict neural responses in higher visual cortex , 2014, Proceedings of the National Academy of Sciences.

[8]  Haim Sompolinsky,et al.  Chaotic Balanced State in a Model of Cortical Circuits , 1998, Neural Computation.

[9]  György Buzsáki,et al.  What does gamma coherence tell us about inter-regional neural communication? , 2015, Nature Neuroscience.

[10]  J. Maunsell,et al.  Differences in Gamma Frequencies across Visual Cortex Restrict Their Possible Use in Computation , 2010, Neuron.

[11]  Guillaume Hennequin,et al.  Sampling-based probabilistic inference emerges from learning in neural circuits with a cost on reliability , 2018, 1807.08952.

[12]  Victor A. F. Lamme,et al.  Synchrony and covariation of firing rates in the primary visual cortex during contour grouping , 2004, Nature Neuroscience.

[13]  T. Sejnowski,et al.  Cortical Enlightenment: Are Attentional Gamma Oscillations Driven by ING or PING? , 2009, Neuron.

[14]  Devika Narain,et al.  Flexible sensorimotor computations through rapid reconfiguration of cortical dynamics , 2018 .

[15]  Andrew Gelman,et al.  Handbook of Markov Chain Monte Carlo , 2011 .

[16]  Laurence Aitchison,et al.  The Hamiltonian Brain: Efficient Probabilistic Inference with Excitatory-Inhibitory Neural Circuit Dynamics , 2014, PLoS Comput. Biol..

[17]  A. Pouget,et al.  Efficient computation and cue integration with noisy population codes , 2001, Nature Neuroscience.

[18]  Richard G. Baraniuk,et al.  A Probabilistic Theory of Deep Learning , 2015, ArXiv.

[19]  Wolf Singer,et al.  Stimulus complexity shapes response correlations in primary visual cortex , 2019, Proceedings of the National Academy of Sciences.

[20]  M. Carandini,et al.  Normalization as a canonical neural computation , 2011, Nature Reviews Neuroscience.

[21]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

[22]  L. F. Abbott,et al.  Generating Coherent Patterns of Activity from Chaotic Neural Networks , 2009, Neuron.

[23]  Martin Vinck,et al.  Surface color and predictability determine contextual modulation of V1 firing and gamma oscillations , 2018, bioRxiv.

[24]  Michael Okun,et al.  Instantaneous correlation of excitation and inhibition during ongoing and sensory-evoked activities , 2008, Nature Neuroscience.

[25]  P. Berkes,et al.  Statistically Optimal Perception and Learning: from Behavior to Neural Representations , 2022 .

[26]  Guillaume Hennequin,et al.  The Dynamical Regime of Sensory Cortex: Stable Dynamics around a Single Stimulus-Tuned Attractor Account for Patterns of Noise Variability , 2018, Neuron.

[27]  D. McCormick,et al.  Rapid Neocortical Dynamics: Cellular and Network Mechanisms , 2009, Neuron.

[28]  Daniel B. Rubin,et al.  The Stabilized Supralinear Network: A Unifying Circuit Motif Underlying Multi-Input Integration in Sensory Cortex , 2015, Neuron.

[29]  P. Fries,et al.  Robust Gamma Coherence between Macaque V1 and V2 by Dynamic Frequency Matching , 2013, Neuron.

[30]  Kenneth D Miller,et al.  How biological attention mechanisms improve task performance in a large-scale visual system model , 2017, bioRxiv.

[31]  G. Buzsáki,et al.  Mechanisms of gamma oscillations. , 2012, Annual review of neuroscience.

[32]  Cristina Savin,et al.  Spatio-temporal Representations of Uncertainty in Spiking Neural Networks , 2014, NIPS.

[33]  David J. Freedman,et al.  A hierarchy of intrinsic timescales across primate cortex , 2014, Nature Neuroscience.

[34]  Kenneth D. Miller,et al.  Analysis of the Stabilized Supralinear Network , 2012, Neural Computation.

[35]  Guillaume Hennequin,et al.  Asymptotic scaling properties of the posterior mean and variance in the Gaussian scale mixture model , 2017 .

[36]  Aapo Hyvärinen,et al.  Interpreting Neural Response Variability as Monte Carlo Sampling of the Posterior , 2002, NIPS.

[37]  József Fiser,et al.  Neural Variability and Sampling-Based Probabilistic Representations in the Visual Cortex , 2016, Neuron.

[38]  Andrew M. Clark,et al.  Stimulus onset quenches neural variability: a widespread cortical phenomenon , 2010, Nature Neuroscience.

[39]  Wei Ji Ma,et al.  Bayesian inference with probabilistic population codes , 2006, Nature Neuroscience.

[40]  Dimitri M. Kullmann,et al.  Oscillations and Filtering Networks Support Flexible Routing of Information , 2010, Neuron.

[41]  József Fiser,et al.  Perceptual Decision-Making as Probabilistic Inference by Neural Sampling , 2014, Neuron.

[42]  P J Webros BACKPROPAGATION THROUGH TIME: WHAT IT DOES AND HOW TO DO IT , 1990 .

[43]  Wei Ji Ma,et al.  Efficient Probabilistic Inference in Generic Neural Networks Trained with Non-Probabilistic Feedback , 2018 .

[44]  Nicholas J. Priebe,et al.  The Emergence of Contrast-Invariant Orientation Tuning in Simple Cells of Cat Visual Cortex , 2007, Neuron.

[45]  Rajesh P. N. Rao,et al.  Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. , 1999 .

[46]  Nicholas J. Priebe,et al.  Inhibition, Spike Threshold, and Stimulus Selectivity in Primary Visual Cortex , 2008, Neuron.

[47]  David J. C. MacKay,et al.  Information Theory, Inference, and Learning Algorithms , 2004, IEEE Transactions on Information Theory.

[48]  Peter Dayan,et al.  A Neural Substrate of Prediction and Reward , 1997, Science.

[49]  Paul J. Werbos,et al.  Backpropagation Through Time: What It Does and How to Do It , 1990, Proc. IEEE.

[50]  Karl J. Friston,et al.  Canonical Microcircuits for Predictive Coding , 2012, Neuron.

[51]  W. Wildman,et al.  Theoretical Neuroscience , 2014 .

[52]  P. Dayan,et al.  Perceptual organization in the tilt illusion. , 2009, Journal of vision.

[53]  Peter E. Latham,et al.  Demixing odors - fast inference in olfaction , 2013, NIPS.

[54]  Timothy D. Hanks,et al.  Probabilistic Population Codes for Bayesian Decision Making , 2008, Neuron.

[55]  Georg B. Keller,et al.  Mismatch Receptive Fields in Mouse Visual Cortex , 2016, Neuron.

[56]  M. Carandini,et al.  Inhibition dominates sensory responses in awake cortex , 2012, Nature.

[57]  Wolfgang Maass,et al.  Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons , 2011, PLoS Comput. Biol..

[58]  Geoffrey E. Hinton,et al.  Bayesian Learning for Neural Networks , 1995 .

[59]  Tatjana Tchumatchenko,et al.  Stabilized supralinear network can give rise to bistable, oscillatory, and persistent activity , 2018, Proceedings of the National Academy of Sciences.

[60]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[61]  Laurence Aitchison,et al.  With or without you: predictive coding and Bayesian inference in the brain , 2017, Current Opinion in Neurobiology.

[62]  József Fiser,et al.  Spontaneous Cortical Activity Reveals Hallmarks of an Optimal Internal Model of the Environment , 2011, Science.

[63]  Alexander S. Ecker,et al.  Decorrelated Neuronal Firing in Cortical Microcircuits , 2010, Science.

[64]  Michael W. Spratling Predictive Coding as a Model of Response Properties in Cortical Area V1 , 2010, The Journal of Neuroscience.

[65]  Georg B. Keller,et al.  Predictive Processing: A Canonical Cortical Computation , 2018, Neuron.

[66]  M. Landy,et al.  Bayesian Modelling of Visual Perception , 2002 .

[67]  A. Thiele,et al.  Neuronal synchrony does not correlate with motion coherence in cortical area MT , 2003, Nature.

[68]  Michael N. Shadlen,et al.  Synchrony Unbound A Critical Evaluation of the Temporal Binding Hypothesis , 1999, Neuron.

[69]  W. Newsome,et al.  The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding , 1998, The Journal of Neuroscience.

[70]  Martin Vinck,et al.  More Gamma More Predictions: Gamma-Synchronization as a Key Mechanism for Efficient Integration of Classical Receptive Field Inputs with Surround Predictions , 2016, Front. Syst. Neurosci..

[71]  Gustavo Deco,et al.  Stimulus-dependent variability and noise correlations in cortical MT neurons , 2013, Proceedings of the National Academy of Sciences.

[72]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[73]  W. Newsome,et al.  Context-dependent computation by recurrent dynamics in prefrontal cortex , 2013, Nature.

[74]  Alexander S. Ecker,et al.  State Dependence of Noise Correlations in Macaque Primary Visual Cortex , 2014, Neuron.

[75]  Gustavo Deco,et al.  Oscillations, Phase-of-Firing Coding, and Spike Timing-Dependent Plasticity: An Efficient Learning Scheme , 2009, The Journal of Neuroscience.

[76]  Yuhong Yang,et al.  Information Theory, Inference, and Learning Algorithms , 2005 .

[77]  D Hermes,et al.  Stimulus Dependence of Gamma Oscillations in Human Visual Cortex. , 2015, Cerebral cortex.

[78]  Adam Binch,et al.  Perception as Bayesian Inference , 2014 .

[79]  H. Sompolinsky,et al.  Theory of orientation tuning in visual cortex. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[80]  S. Morad,et al.  Ceramide-orchestrated signalling in cancer cells , 2012, Nature Reviews Cancer.

[81]  Guangyu R. Yang,et al.  Training Excitatory-Inhibitory Recurrent Neural Networks for Cognitive Tasks: A Simple and Flexible Framework , 2016, PLoS Comput. Biol..

[82]  W. Gerstner,et al.  Optimal Control of Transient Dynamics in Balanced Networks Supports Generation of Complex Movements , 2014, Neuron.

[83]  Guillaume Hennequin,et al.  Analog Memories in a Balanced Rate-Based Network of E-I Neurons , 2014, NIPS.