### Abstract

The efficient coding hypothesis posits that sensory systems maximize information transmitted to the brain about the environment.We develop a precise and testable form of this hypothesis in the context of encoding a sensory variable with a population of noisy neurons, each characterized by a tuning curve. We parameterize the population with two continuous functions that control the density and amplitude of the tuning curves, assuming that the tuning widths vary inversely with the cell density. This parameterization allows us to solve, in closed form, for the informationmaximizing allocation of tuning curves as a function of the prior probability distribution of sensory variables. For the optimal population, the cell density is proportional to the prior, such that more cells with narrower tuning are allocated to encode higher-probability stimuli and that each cell transmits an equal portion of the stimulus probability mass.We also compute the stimulus discrimination capabilities of a perceptual system that relies on this neural representation and find that the best achievable discrimination thresholds are inversely proportional to the sensory prior. We examine how the prior information that is implicitly encoded in the tuning curves of the optimal population may be used for perceptual inference and derive a novel decoder, the Bayesian population vector, that closely approximates a Bayesian least-squares estimator that has explicit access to the prior. Finally, we generalize these results to sigmoidal tuning curves, correlated neural variability, and a broader class of objective functions. These results provide a principled embedding of sensory prior information in neural populations and yield predictions that are readily testable with environmental, physiological, and perceptual data.

Original language | English (US) |
---|---|

Pages (from-to) | 2103-2134 |

Number of pages | 32 |

Journal | Neural Computation |

Volume | 26 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1 2014 |

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### ASJC Scopus subject areas

- Cognitive Neuroscience
- Arts and Humanities (miscellaneous)

### Cite this

*Neural Computation*,

*26*(10), 2103-2134. https://doi.org/10.1162/NECO_a_00638

**Efficient sensory encoding and Bayesian inference with heterogeneous neural populations.** / Ganguli, Deep; Simoncelli, Eero.

Research output: Contribution to journal › Article

*Neural Computation*, vol. 26, no. 10, pp. 2103-2134. https://doi.org/10.1162/NECO_a_00638

}

TY - JOUR

T1 - Efficient sensory encoding and Bayesian inference with heterogeneous neural populations

AU - Ganguli, Deep

AU - Simoncelli, Eero

PY - 2014/10/1

Y1 - 2014/10/1

N2 - The efficient coding hypothesis posits that sensory systems maximize information transmitted to the brain about the environment.We develop a precise and testable form of this hypothesis in the context of encoding a sensory variable with a population of noisy neurons, each characterized by a tuning curve. We parameterize the population with two continuous functions that control the density and amplitude of the tuning curves, assuming that the tuning widths vary inversely with the cell density. This parameterization allows us to solve, in closed form, for the informationmaximizing allocation of tuning curves as a function of the prior probability distribution of sensory variables. For the optimal population, the cell density is proportional to the prior, such that more cells with narrower tuning are allocated to encode higher-probability stimuli and that each cell transmits an equal portion of the stimulus probability mass.We also compute the stimulus discrimination capabilities of a perceptual system that relies on this neural representation and find that the best achievable discrimination thresholds are inversely proportional to the sensory prior. We examine how the prior information that is implicitly encoded in the tuning curves of the optimal population may be used for perceptual inference and derive a novel decoder, the Bayesian population vector, that closely approximates a Bayesian least-squares estimator that has explicit access to the prior. Finally, we generalize these results to sigmoidal tuning curves, correlated neural variability, and a broader class of objective functions. These results provide a principled embedding of sensory prior information in neural populations and yield predictions that are readily testable with environmental, physiological, and perceptual data.

AB - The efficient coding hypothesis posits that sensory systems maximize information transmitted to the brain about the environment.We develop a precise and testable form of this hypothesis in the context of encoding a sensory variable with a population of noisy neurons, each characterized by a tuning curve. We parameterize the population with two continuous functions that control the density and amplitude of the tuning curves, assuming that the tuning widths vary inversely with the cell density. This parameterization allows us to solve, in closed form, for the informationmaximizing allocation of tuning curves as a function of the prior probability distribution of sensory variables. For the optimal population, the cell density is proportional to the prior, such that more cells with narrower tuning are allocated to encode higher-probability stimuli and that each cell transmits an equal portion of the stimulus probability mass.We also compute the stimulus discrimination capabilities of a perceptual system that relies on this neural representation and find that the best achievable discrimination thresholds are inversely proportional to the sensory prior. We examine how the prior information that is implicitly encoded in the tuning curves of the optimal population may be used for perceptual inference and derive a novel decoder, the Bayesian population vector, that closely approximates a Bayesian least-squares estimator that has explicit access to the prior. Finally, we generalize these results to sigmoidal tuning curves, correlated neural variability, and a broader class of objective functions. These results provide a principled embedding of sensory prior information in neural populations and yield predictions that are readily testable with environmental, physiological, and perceptual data.

UR - http://www.scopus.com/inward/record.url?scp=84907255039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84907255039&partnerID=8YFLogxK

U2 - 10.1162/NECO_a_00638

DO - 10.1162/NECO_a_00638

M3 - Article

C2 - 25058702

AN - SCOPUS:84907255039

VL - 26

SP - 2103

EP - 2134

JO - Neural Computation

JF - Neural Computation

SN - 0899-7667

IS - 10

ER -