Error-Based Analysis of Optimal Tuning Functions Explains Phenomena Observed in Sensory Neurons

Biological systems display impressive capabilities in effectively responding to environmental signals in real time. There is increasing evidence that organisms may indeed be employing near optimal Bayesian calculations in their decision-making. An intriguing question relates to the properties of optimal encoding methods, namely determining the properties of neural populations in sensory layers that optimize performance, subject to physiological constraints. Within an ecological theory of neural encoding/decoding, we show that optimal Bayesian performance requires neural adaptation which reflects environmental changes. Specifically, we predict that neuronal tuning functions possess an optimal width, which increases with prior uncertainty and environmental noise, and decreases with the decoding time window. Furthermore, even for static stimuli, we demonstrate that dynamic sensory tuning functions, acting at relatively short time scales, lead to improved performance. Interestingly, the narrowing of tuning functions as a function of time was recently observed in several biological systems. Such results set the stage for a functional theory which may explain the high reliability of sensory systems, and the utility of neuronal adaptation occurring at multiple time scales.

[1]  William Bialek,et al.  Adaptive Rescaling Maximizes Information Transmission , 2000, Neuron.

[2]  J. P. Rauschecker,et al.  Auditory compensation of the effects of visual deprivation in the cat's superior colliculus , 2004, Experimental Brain Research.

[3]  Shlomo Shamai,et al.  Mutual information and minimum mean-square error in Gaussian channels , 2004, IEEE Transactions on Information Theory.

[4]  M. Meister,et al.  Dynamic predictive coding by the retina , 2005, Nature.

[5]  A. Pouget,et al.  Tuning curve sharpening for orientation selectivity: coding efficiency and the impact of correlations , 2004, Nature Neuroscience.

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

[7]  J. Rauschecker,et al.  A Positron Emission Tomographic Study of Auditory Localization in the Congenitally Blind , 2000, The Journal of Neuroscience.

[8]  H. V. Trees,et al.  Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking , 2007 .

[9]  Roger W. Brockett,et al.  Trajectory estimation from place cell data , 2001, Neural Networks.

[10]  Alexandre Pouget,et al.  A computational perspective on the neural basis of multisensory spatial representations , 2002, Nature Reviews Neuroscience.

[11]  Don H. Johnson,et al.  Optimal Stimulus Coding by Neural Populations Using Rate Codes , 2004, Journal of Computational Neuroscience.

[12]  M. Pettet,et al.  Dynamic changes in receptive-field size in cat primary visual cortex. , 1992, Proceedings of the National Academy of Sciences of the United States of America.

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

[14]  A. Pouget,et al.  Neural correlations, population coding and computation , 2006, Nature Reviews Neuroscience.

[15]  H. White.  Maximum Likelihood Estimation of Misspecified Models , 1982 .

[16]  Matthew A. Wilson,et al.  Dynamic Analyses of Information Encoding in Neural Ensembles , 2004, Neural Computation.

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

[18]  Terrence J. Sejnowski,et al.  Neuronal Tuning: To Sharpen or Broaden? , 1999, Neural Computation.

[19]  Ron Meir,et al.  Frontiers in Computational Neuroscience Computational Neuroscience Perspective Article on the Precarious Path of Reverse Neuro-engineering , 2022 .

[20]  Eric I. Knudsen,et al.  Gated Visual Input to the Central Auditory System , 2002, Science.

[21]  Emery N. Brown,et al.  Dynamic Analysis of Neural Encoding by Point Process Adaptive Filtering , 2004, Neural Computation.

[22]  Matteo Carandini,et al.  Coding of stimulus sequences by population responses in visual cortex , 2009, Nature Neuroscience.

[23]  Tim Gollisch,et al.  Eye Smarter than Scientists Believed: Neural Computations in Circuits of the Retina , 2010, Neuron.

[24]  M. Bethge,et al.  Optimal neural rate coding leads to bimodal firing rate distributions. , 2003, Network.

[25]  Peter E. Latham,et al.  Narrow Versus Wide Tuning Curves: What's Best for a Population Code? , 1999, Neural Computation.

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

[27]  Alexandre Pouget,et al.  Exact Inferences in a Neural Implementation of a Hidden Markov Model , 2007, Neural Computation.

[28]  Xiaoqin Wang,et al.  Sustained firing in auditory cortex evoked by preferred stimuli , 2005, Nature.

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

[30]  Mark D McDonnell,et al.  Neural population coding is optimized by discrete tuning curves. , 2008, Physical review letters.

[31]  T. Sharpee,et al.  Predictable irregularities in retinal receptive fields , 2009, Proceedings of the National Academy of Sciences.

[32]  P. Latham,et al.  Ruling out and ruling in neural codes , 2009, Proceedings of the National Academy of Sciences.

[33]  Sophie Denève,et al.  Bayesian Spiking Neurons I: Inference , 2008, Neural Computation.

[34]  H. Sompolinsky,et al.  A Neural Computation for Visual Acuity in the Presence of Eye Movements , 2007, PLoS biology.

[35]  Matthias Bethge,et al.  Optimal Short-Term Population Coding: When Fisher Information Fails , 2002, Neural Computation.

[36]  Stefano Panzeri,et al.  On Decoding the Responses of a Population of Neurons from Short Time Windows , 1999, Neural Computation.

[37]  R. Jacobs,et al.  Optimal integration of texture and motion cues to depth , 1999, Vision Research.

[38]  David McAlpine,et al.  Optimal neural population coding of an auditory spatial cue , 2004, Nature.

[39]  Ione Fine,et al.  Visual stimuli activate auditory cortex in the deaf , 2001, Nature Neuroscience.

[40]  I. Dean,et al.  Neural population coding of sound level adapts to stimulus statistics , 2005, Nature Neuroscience.

[41]  Helmut Schwegler,et al.  Neural Representation of Multi-Dimensional Stimuli , 1999, NIPS.

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

[43]  Peter Dayan,et al.  Fast Population Coding , 2007, Neural Computation.

[44]  J. Rauschecker,et al.  Auditory spatial tuning of cortical neurons is sharpened in cats with early blindness. , 1993, Journal of neurophysiology.

[45]  Abel M. Rodrigues.  Matrix Algebra Useful for Statistics , 2007 .

[46]  Rajesh P. N. Rao.  Bayesian Computation in Recurrent Neural Circuits , 2004, Neural Computation.

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

[48]  M. Sur,et al.  Adaptation-Induced Plasticity of Orientation Tuning in Adult Visual Cortex , 2000, Neuron.

[49]  Jiri Najemnik,et al.  Optimal stimulus encoders for natural tasks. , 2009, Journal of vision.

[50]  Yonina C. Eldar,et al.  Bayesian Filtering in Spiking Neural Networks: Noise, Adaptation, and Multisensory Integration , 2009, Neural Computation.

[51]  H Sompolinsky,et al.  Simple models for reading neuronal population codes. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[52]  Harry L. Van Trees,et al.  Detection, Estimation, and Modulation Theory, Part I , 1968 .

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

[54]  Nicolas Brunel,et al.  Mutual Information, Fisher Information, and Population Coding , 1998, Neural Computation.

[55]  M. McDonnell,et al.  Maximally informative stimuli and tuning curves for sigmoidal rate-coding neurons and populations. , 2008, Physical review letters.

[56]  S. Treue,et al.  Feature-Based Attention Increases the Selectivity of Population Responses in Primate Visual Cortex , 2004, Current Biology.

[57]  Petr Lánský,et al.  Optimal Signal Estimation in Neuronal Models , 2005, Neural Computation.

[58]  Nicolas J. Kerscher,et al.  State-dependent receptive-field restructuring in the visual cortex , 1998, Nature.

[59]  Kazuyuki Aihara,et al.  Fisher information for spike-based population decoding. , 2006, Physical review letters.

[60]  T. Duncan.  ON THE CALCULATION OF MUTUAL INFORMATION , 1970 .

[61]  D. Ferster,et al.  The contribution of noise to contrast invariance of orientation tuning in cat visual cortex. , 2000, Science.