Describing the collective activity of neural populations is a daunting task. Recent empirical studies in retina, however, suggest a vast simplification in how multi-neuron spiking occurs: the activity patterns of retinal ganglion cell (RGC) populations under some conditions are nearly completely captured by pairwise interactions among neurons. In other circumstances, higher-order statistics are required and appear to be shaped by input statistics and intrinsic circuit mechanisms. Here, we study the emergence of higher-order interactions in a model of the RGC circuit in which correlations are generated by common input. We quantify the impact of higher-order interactions by comparing the responses of mechanistic circuit models vs. “null” descriptions in which all higher-than-pairwise correlations have been accounted for by lower order statistics; these are known as pairwise maximum entropy (PME) models. We find that over a broad range of stimuli, output spiking patterns are surprisingly well captured by the pairwise model. To understand this finding, we study an analytically tractable simplification of the RGC model. We find that in the simplified model, bimodal input signals produce larger deviations from pairwise predictions than unimodal inputs. The characteristic light filtering properties of the upstream RGC circuitry suppress bimodality in light stimuli, thus removing a powerful source of higher-order interactions. This provides a novel explanation for the surprising empirical success of pairwise models.


  • Information in neural circuits is often encoded in the activity of large, highly interconnected neural populations

  • Our findings provide insight into why some previously measured activity patterns are well captured by pairwise maximum entropy (PME) descriptions, and provide predictions for the mechanisms that allow for higher-order spike correlations to emerge

  • One strategy to identify higher-order interactions is to compare multi-neuron spike data against a description in which any higher-order interactions have been removed in a principled way—that is, a description in which all higher-order correlations are completely described by lower-order statistics

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Information in neural circuits is often encoded in the activity of large, highly interconnected neural populations. The combinatoric explosion of possible responses of such circuits poses major conceptual, experimental, and computational challenges. How much of this potential complexity is realized? Maximum entropy approaches from statistical physics have provided a powerful approach to distinguish genuine higher-order synchrony (correlations) from that explainable by pairwise statistical interactions among neurons (Martignon et al, 2000; Amari, 2001; Schneidman et al, 2003). The diversity of empirical results highlights the need to understand the network and input features that control the statistical complexity of synchronous activity patterns


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