Neural computation with non-uniform population codes

A central goal of neuroscience is to understand how the responses of populations of neurons and the connectivity patterns between groups of neurons allow brains to perform computations. The Neural Engineering Framework (NEF) is a promising approach to designing neural models that perform a wide range of computations. Emerging principles of efficient coding and divisive normalization from neuroscience constrain models of neural computation, but their role in the NEF has not been described. Here, we show how efficient coding and divisive normalization are important in this approach to modeling neural computation. We show that divisive normalization in networks of neurons that encode the statistics of the environment in their tuning properties allows networks to perform Bayes-optimal computations across multiple layers in a network. The result is to incorporate several emerging principles of neural computation in an already successful modeling framework.

[1]  Herman P. Snippe,et al.  Parameter Extraction from Population Codes: A Critical Assessment , 1996, Neural Computation.

[2]  M. Carandini,et al.  Normalization as a canonical neural computation , 2013, Nature Reviews Neuroscience.

[3]  Eero P. Simoncelli,et al.  Natural image statistics and neural representation. , 2001, Annual review of neuroscience.

[4]  Emilio Salinas,et al.  Vector reconstruction from firing rates , 1994, Journal of Computational Neuroscience.

[5]  Eero P. Simoncelli,et al.  Implicit encoding of prior probabilities in optimal neural populations , 2010, NIPS.

[6]  A P Georgopoulos,et al.  On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex , 1982, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[7]  Brian J. Fischer,et al.  Owl's behavior and neural representation predicted by Bayesian inference , 2011, Nature Neuroscience.

[8]  H. B. Barlow,et al.  Possible Principles Underlying the Transformations of Sensory Messages , 2012 .

[9]  Thomas L. Griffiths,et al.  Neural Implementation of Hierarchical Bayesian Inference by Importance Sampling , 2009, NIPS.

[10]  M. Meister,et al.  Fast and Slow Contrast Adaptation in Retinal Circuitry , 2002, Neuron.

[11]  Trevor Bekolay,et al.  A Large-Scale Model of the Functioning Brain , 2012, Science.

[12]  Chris Eliasmith,et al.  Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems , 2004, IEEE Transactions on Neural Networks.

[13]  Brian J. Fischer,et al.  Bayesian estimates from heterogeneous population codes , 2010, The 2010 International Joint Conference on Neural Networks (IJCNN).

[14]  E. Pitman,et al.  Sufficient statistics and intrinsic accuracy , 1936, Mathematical Proceedings of the Cambridge Philosophical Society.

[15]  Sophie Denève,et al.  Spike-Based Population Coding and Working Memory , 2011, PLoS Comput. Biol..

[16]  I. Dean,et al.  Rapid Neural Adaptation to Sound Level Statistics , 2008, The Journal of Neuroscience.

[17]  Fanny Cazettes,et al.  Cue Reliability Represented in the Shape of Tuning Curves in the Owl's Sound Localization System , 2016, The Journal of Neuroscience.