Neural Population Coding is Optimized by Discrete Tuning Curves

Adaptation Properties Allow Identification of Optimized Neural Codes

The adaptation of neural codes to the statistics of their environment is well captured by efficient coding approaches. Here we solve an inverse problem: characterizing the objective and constraint functions that efficient codes appear to be optimal for, on the basis of how they adapt to different stimulus distributions. We formulate a general efficient coding problem, with flexible objective and constraint functions and minimal parametric assumptions. Solving special cases of this model, we provide solutions to broad classes of Fisher information-based efficient coding problems, generalizing a…

Maximally Informative Stimuli and Tuning Curves for Sigmoidal Rate-Coding Neurons and Populations

A general method for deriving maximally informative sigmoidal tuning curves for neural systems with small normalized variability is presented. The optimal tuning curve is a nonlinear function of the cumulative distribution function of the stimulus and depends on the mean-variance relationship of the neural system. The derivation is based on a known relationship between Shannon's mutual information and Fisher information, and the optimality of Jeffrey's prior. It relies on the existence of closed-form solutions to the converse problem of optimizing the stimulus distribution for a given tuning c…

The sign rule and beyond: Boundary effects, flexibility, and noise correlations in neural population codes

Over repeat presentations of the same stimulus, sensory neurons show variable responses. This "noise" is typically correlated between pairs of cells, and a question with rich history in neuroscience is how these noise correlations impact the population's ability to encode the stimulus. Here, we consider a very general setting for population coding, investigating how information varies as a function of noise correlations, with all other aspects of the problem - neural tuning curves, etc. - held fixed. This work yields unifying insights into the role of noise correlations. These are summarized i…

Understanding Neural Coding on Latent Manifolds by Sharing Features and Dividing Ensembles

Systems neuroscience relies on two complementary views of neural data, characterized by single neuron tuning curves and analysis of population activity. These two perspectives combine elegantly in neural latent variable models that constrain the relationship between latent variables and neural activity, modeled by simple tuning curve functions. This has recently been demonstrated using Gaussian processes, with applications to realistic and topologically relevant latent manifolds. Those and previous models, however, missed crucial shared coding properties of neural populations. We propose featu…

Lateral predictive coding revisited: Internal model, symmetry breaking, and response time

Predictive coding is a promising theoretical framework in neuroscience for understanding information transmission and perception. It posits that the brain perceives the external world through internal models and updates these models under the guidance of prediction errors. Previous studies on predictive coding emphasized top-down feedback interactions in hierarchical multi-layered networks but largely ignored lateral recurrent interactions. We perform analytical and numerical investigations in this work on the effects of single-layer lateral interactions. We consider a simple predictive respon…

相位码在为模运算优化的递归神经网络中出现

Phase codes emerge in recurrent neural networks optimized for modular arithmetic

研究发现，在无振荡偏置的条件下，RNNs可通过任务优化自然产生相位码解，并揭示了RNNs在模运算任务中存在多种不同动态机制的解。