Bayesian Encoding and Decoding as Distinct Perspectives on Neural Coding

The Bayesian Brain hypothesis, according to which the brain implements statistically optimal algorithms, is one of the leading theoretical frameworks in neuroscience. There are two distinct underlying philosophies: one in which the brain recovers experimenter-defined structures in the world from sensory neural activity (decoding), and another in which it represents latent quantities in an internal model (encoding). We argue that an implicit disagreement on this point underlies some of the debate surrounding the neural implementation of statistical algorithms, in particular the difference between sampling-based and parametric distributional codes. To demonstrate the complementary nature of the two approaches, we have shown mathematically that encoding by sampling can be equivalently interpreted as decoding task variables in a manner consistent with linear probabilistic population codes (PPCs), a popular decoding approach. Awareness of these differences in perspective helps misunderstandings and false dichotomies, and future research will benefit from an explicit discussion of the relative advantages and disadvantages of either approach to constructing models.

[1]  David J. Field,et al.  Sparse coding with an overcomplete basis set: A strategy employed by V1? , 1997, Vision Research.

[2]  Max Welling,et al.  Markov Chain Monte Carlo and Variational Inference: Bridging the Gap , 2014, ICML.

[3]  Wolfgang Maass,et al.  Probabilistic Inference in General Graphical Models through Sampling in Stochastic Networks of Spiking Neurons , 2011, PLoS Comput. Biol..

[4]  Konrad Paul Kording,et al.  Decision Theory: What "Should" the Nervous System Do? , 2007, Science.

[5]  D. Burr,et al.  The Ventriloquist Effect Results from Near-Optimal Bimodal Integration , 2004, Current Biology.

[6]  Xaq Pitkow,et al.  Inference by Reparameterization in Neural Population Codes , 2016, NIPS.

[7]  David J. Field,et al.  Emergence of simple-cell receptive field properties by learning a sparse code for natural images , 1996, Nature.

[8]  M. Tribus,et al.  Probability theory: the logic of science , 2003 .

[9]  Jörg Lücke,et al.  Are V1 Simple Cells Optimized for Visual Occlusions? A Comparative Study , 2013, PLoS Comput. Biol..

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

[11]  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.

[12]  Christopher R Fetsch,et al.  Neural correlates of reliability-based cue weighting during multisensory integration , 2011, Nature Neuroscience.

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

[14]  D. Knill,et al.  The Bayesian brain: the role of uncertainty in neural coding and computation , 2004, Trends in Neurosciences.

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

[16]  A. Pouget,et al.  Marginalization in Neural Circuits with Divisive Normalization , 2011, The Journal of Neuroscience.

[17]  Chong Wang,et al.  Stochastic variational inference , 2012, J. Mach. Learn. Res..

[18]  Karl J. Friston,et al.  A theory of cortical responses , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

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

[20]  Thomas L. Griffiths,et al.  One and Done? Optimal Decisions From Very Few Samples , 2014, Cogn. Sci..

[21]  Guillaume Hennequin,et al.  Cortical-like dynamics in recurrent circuits optimized for sampling-based probabilistic inference , 2019, Nature Neuroscience.

[22]  Alexandre Pouget,et al.  Neural Correlates of Optimal Multisensory Decision Making under Time-Varying Reliabilities with an Invariant Linear Probabilistic Population Code , 2019, Neuron.

[23]  Peter Dayan,et al.  Doubly Distributional Population Codes: Simultaneous Representation of Uncertainty and Multiplicity , 2003, Neural Computation.

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

[25]  Eero P. Simoncelli,et al.  Natural signal statistics and sensory gain control , 2001, Nature Neuroscience.

[26]  Adam N. Sanborn,et al.  Bayesian Brains without Probabilities , 2016, Trends in Cognitive Sciences.

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

[28]  A. Pouget,et al.  Probabilistic brains: knowns and unknowns , 2013, Nature Neuroscience.

[29]  Samuel J. Gershman,et al.  Complex Probabilistic Inference , 2017 .

[30]  Thomas L. Griffiths,et al.  "Burn-in, bias, and the rationality of anchoring" , 2012, NIPS.

[31]  Peter Dayan,et al.  Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems , 2001 .

[32]  Adam N. Sanborn.  Types of approximation for probabilistic cognition: Sampling and variational , 2017, Brain and Cognition.

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

[34]  Radford M. Neal.  Pattern Recognition and Machine Learning , 2007, Technometrics.

[35]  Richard D. Lange,et al.  A probabilistic population code based on neural samples , 2018, NeurIPS.

[36]  Gregory C. DeAngelis,et al.  Bridging the gap between theories of sensory cue integration and the physiology of multisensory neurons , 2013, Nature Reviews Neuroscience.

[37]  Ned Block,et al.  If perception is probabilistic, why does it not seem probabilistic? , 2018, Philosophical Transactions of the Royal Society B: Biological Sciences.

[38]  Hideyuki Suzuki,et al.  Population Code Dynamics in Categorical Perception , 2016, Scientific Reports.

[39]  Alexandre Pouget,et al.  Probabilistic Interpretation of Population Codes , 1996, Neural Computation.

[40]  Noah D. Goodman,et al.  Empirical evidence for resource-rational anchoring and adjustment , 2017, Psychonomic Bulletin & Review.

[41]  Hermann von Helmholtz,et al.  Treatise on Physiological Optics , 1962 .

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

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

[44]  Joshua B. Tenenbaum,et al.  Multistability and Perceptual Inference , 2012, Neural Computation.

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

[46]  Richard D. Lange,et al.  Task-induced neural covariability as a signature of approximate Bayesian learning and inference , 2016, PLoS Comput. Biol..

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

[48]  Wei Ji Ma,et al.  A neural basis of probabilistic computation in visual cortex , 2019, Nature Neuroscience.

[49]  Guillaume Hennequin,et al.  Cortical-like dynamics in recurrent circuits optimized for sampling-based probabilistic inference , 2020, Nature Neuroscience.

[50]  Maneesh Sahani,et al.  Flexible and accurate inference and learning for deep generative models , 2018, NeurIPS.

[51]  M. Ernst,et al.  Humans integrate visual and haptic information in a statistically optimal fashion , 2002, Nature.

[52]  Rachel N. Denison,et al.  Is Perception Probabilistic , 2020 .

[53]  Kevin P. Murphy,et al.  Machine learning - a probabilistic perspective , 2012, Adaptive computation and machine learning series.

[54]  H B Barlow,et al.  PATTERN RECOGNITION AND THE RESPONSES OF SENSORY NEURONS * , 1969, Annals of the New York Academy of Sciences.