Spectral-stimulus information for self-supervised stimulus encoding

Understanding how neural populations efficiently encode stimuli is a fundamental challenge in computational neuroscience. Existing rate-based information measures primarily assess single-neuron encoding, limiting insights into population-level representations, while the role of correlation in neural coding remains a subject of considerable debate. To address this, we introduce novel, correlation-aware information-theoretic measures that quantify the encoding efficiency of multiple neurons, including the joint stimulus information rate for neuron pairs and the spectral-stimulus information for arbitrarily sized populations. The spectral-stimulus information, defined as the leading eigenvalue of the stimulus information matrix, is maximized when neurons exhibit localized, nonoverlapping firing fields. We apply these measures to the domain of spatial navigation, where specialized neurons, such as place cells, grid cells, and head direction cells, encode position and orientation from self-motion and environmental cues. Analyzing neural recordings from mice and monkeys, we elucidate differences in encoding efficiency across neuronal pairs and populations. We then demonstrate that these measures can be used to train recurrent neural networks (RNNs) via self-supervised learning, leading to the emergence of place cells and head direction cells. Our findings provide a principled population-level framework for understanding stimulus encoding, with broad implications for neuroscience and the optimization of artificial navigation systems.