Implicit encoding of prior probabilities in optimal neural populations.

Area of Science:

• Computational neuroscience
• Neural coding theory
• Sensory processing

Background:

• Optimal coding principles guide understanding of neural representations.
• Prior probability distributions significantly influence neural population activity and information encoding.
• Neural responses are often modeled using tuning curves and Poisson processes.

Purpose of the Study:

• To investigate how prior probability distributions of sensory variables affect optimal neural population coding.
• To derive theoretical predictions for neural resource allocation (neuron density, spike rates) based on sensory priors.
• To establish a link between stimulus priors, neural properties, and perceptual discriminability.

Main Methods:

• Modeling neural spikes as Poisson processes with rate governed by tuning curves.
• Approximating Fisher information considering tuning curve density, amplitude, and width.
• Analyzing objective functions based on expected Fisher information over sensory priors.
• Deriving closed-form solutions for optimal neural allocation.

Main Results:

• Neural population density and gain follow power law functions of the stimulus prior.
• A power law relationship is established between stimulus priors and perceptual discriminability.
• Theoretical predictions align with empirical data on stimulus priors, neural properties, and discrimination thresholds.

Conclusions:

• Sensory prior probabilities fundamentally shape optimal neural coding strategies.
• The derived power law relationships provide a predictive framework for neural and perceptual systems.
• This work bridges theoretical optimal coding with empirical observations in neural and behavioral data.