Spectral-Stimulus Information for Self-Supervised Stimulus Encoding

Mammalian spatial navigation relies on specialized neurons, such as place and grid cells, which encode position based on self-motion and environmental cues. While extensive research has explored the computational role of grid cells, the principles underlying efficient place cell coding remain less understood. Existing spatial information rate 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 arbitrary sized populations. The spectral-stimulus information, defined as the leading eigenvalue of the stimulus information matrix, is maximized when neurons exhibit localized, non-overlapping firing fields, mirroring place cell and head direction cell activity. We apply these measures to neural data recorded in mice and monkeys, elucidating differences in encoding efficiency across neuronal pairs and populations. Then, we 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 highlight how neural populations collectively encode stimuli, offering a more comprehensive framework for understanding stimulus encoding and optimizing artificial navigation systems in novel environments.

💡 Research Summary

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The paper tackles a fundamental gap in the quantitative analysis of spatial coding: existing measures such as Skaggs’ spatial information rate evaluate only single‑neuron firing fields and ignore the correlations that inevitably arise in neural populations. To address this, the authors introduce two novel information‑theoretic metrics that explicitly incorporate inter‑neuronal dependencies.

First, the Joint Stimulus Information Rate (JSIR) quantifies how much information a pair of neurons jointly conveys about a discrete stimulus space (S). By modeling each neuron’s spiking as a Bernoulli process with stimulus‑dependent rate (\lambda(s)), JSIR is expressed as the stimulus‑weighted Kullback‑Leibler divergence between the conditional joint firing distribution (P_{AB|s}) and the overall joint distribution (P_{AB}). This formulation requires no independence assumption and therefore captures both synergistic and redundant interactions.

Second, the Spectral Stimulus Information (SSI) aggregates all pairwise JSIR values into a symmetric information matrix (\mathbf{I}). The leading eigenvalue (\lambda_{\max}(\mathbf{I})) is taken as the SSI, representing the dominant axis of information flow in the population. The authors prove that SSI is maximized when each neuron fires only for a single stimulus and when neurons’ firing fields are spatially localized, non‑overlapping, and anti‑correlated—precisely the pattern observed in place cells and head‑direction cells.

Empirically, the authors compute JSIR and SSI on recordings from mouse hippocampal CA3 place cells and monkey prefrontal head‑direction cells across multiple environments. They show that (i) neuron pairs with opposite spatial or directional tuning exhibit the highest JSIR, (ii) SSI drops when the animal is transferred to a novel arena, reflecting a re‑organization of firing fields, and (iii) the metrics capture the well‑known “realignment” of place‑cell maps after environmental manipulation.

The most innovative contribution is the use of these metrics as self‑supervised learning objectives for recurrent neural networks (RNNs) performing path integration. The RNN receives velocity inputs and is trained to maximize either the average JSIR or, more powerfully, the SSI (i.e., minimize (-\lambda_{\max}(\mathbf{I}))). Under this pressure the hidden units spontaneously develop localized, non‑overlapping firing fields that resemble biological place cells, as well as sharply tuned head‑direction cells. Compared with networks trained on the traditional Skaggs spatial information rate, the SSI‑optimized networks generate a larger number of high‑quality place cells and achieve substantially better position decoding accuracy.

Strengths of the work include a rigorous theoretical foundation, clear demonstration of the metrics on real neural data, and a compelling bridge between neuroscience theory and machine‑learning practice. Limitations involve the reliance on discretized stimulus spaces and the need for extensive data to estimate joint firing distributions accurately; SSI’s focus on the top eigenvalue may overlook secondary coding structures such as grid or border cells; and the biological plausibility of the self‑supervised loss remains to be linked to known synaptic plasticity mechanisms.

Future directions suggested are: (1) extending the framework to continuous stimulus domains via kernel or variational density estimators, (2) incorporating multiple eigenvalues to capture richer population codes, (3) integrating Partial Information Decomposition to separate synergy from redundancy explicitly, (4) grounding the loss in biologically realistic plasticity rules (e.g., Hebbian or STDP), and (5) testing the approach on other sensory modalities.

Overall, the paper provides a novel, correlation‑aware quantitative tool for assessing spatial coding efficiency and demonstrates that optimizing this tool can drive artificial networks to develop biologically realistic navigation representations, thereby advancing both theoretical neuroscience and self‑supervised AI.