Scaling of sensory information in large neural populations shows signatures of information-limiting correlations

Abstract

How is information distributed across large neuronal populations within a given brain area? Information may be distributed roughly evenly across neuronal populations, so that total information scales linearly with the number of recorded neurons. Alternatively, the neural code might be highly redundant, meaning that total information saturates. Here we investigate how sensory information about the direction of a moving visual stimulus is distributed across hundreds of simultaneously recorded neurons in mouse primary visual cortex. We show that information scales sublinearly due to correlated noise in these populations. We compartmentalized noise correlations into information-limiting and nonlimiting components, then extrapolate to predict how information grows with even larger neural populations. We predict that tens of thousands of neurons encode 95% of the information about visual stimulus direction, much less than the number of neurons in primary visual cortex. These findings suggest that the brain uses a widely distributed, but nonetheless redundant code that supports recovering most sensory information from smaller subpopulations.

Modelling the neural code in large populations of correlated neurons

“…We also consider widely used alternative measures of decoding performance, namely the Fisher information (FI), which is an upper bound on the average precision (inverse variance) of the posterior ( Brunel and Nadal, 1998 ), as well as the linear Fisher information (LFI), which is a linear approximation of the FI ( Seriès et al, 2004 ) corresponding to the accuracy of the optimal, unbiased linear decoder of the stimulus ( Kanitscheider et al, 2015a ). The FI is especially helpful when the posterior cannot be evaluated directly (such as when it is continuous), and is widely adopted in theoretical ( Abbott and Dayan, 1999 ; Beck et al, 2011b ; Ecker et al, 2014 ; Moreno-Bote et al, 2014 ; Kohn et al, 2016 ) and experimental ( Ecker et al, 2011 ; Kafashan et al, 2021 ; Rumyantsev et al, 2020 ) studies of neural coding. As with other models based on exponential family theory ( Ma et al, 2006 ; Beck et al, 2011b ; Ecker et al, 2016 ), the FI of a minimal CM may be expressed in closed-form, and is equal to its LFI (see Materials and methods), and therefore minimal CMs can be used to study FI analytically and obtain model-based estimates of FI from data.…”

“…However, when validated as Bayesian decoders, statistical models of neural encoding are often outperformed by models trained to decode stimulus-information directly, indicating that the encoding models miss key statistics of the neural code ( Graf et al, 2011 ; Walker et al, 2020 ). In particular, the correlations between neurons’ responses to repeated presentations of a given stimulus (noise correlations), and how these noise correlations are modulated by stimuli, can strongly impact coding in neural circuits ( Zohary et al, 1994 ; Abbott and Dayan, 1999 ; Sompolinsky et al, 2001 ; Ecker et al, 2016 ; Kohn et al, 2016 ; Schneidman, 2016 ), especially in large populations of neurons ( Moreno-Bote et al, 2014 ; Montijn et al, 2019 ; Bartolo et al, 2020 ; Kafashan et al, 2021 ; Rumyantsev et al, 2020 ).…”

“…Importantly, the resulting encoding model affords closed-form expressions for both its Fisher information and probability density function, and thereby a rigorous quantification of the coding properties of a modelled neural population ( Dayan and Abbott, 2005 ). Moreover, the model learns low-dimensional representations of stimulus-driven neural activity, and we show how it captures a fundamental property of population codes known as information-limiting correlations ( Moreno-Bote et al, 2014 ; Montijn et al, 2019 ; Bartolo et al, 2020 ; Kafashan et al, 2021 ; Rumyantsev et al, 2020 ).…”

Rational inattention in mice

“…However, these theories generally ignore the normative foundation that organisms must optimize behavioral processes in light of biological restrictions on information processing (98). Thus, the growing battery of molecular and imaging tools that is becoming available for use in rodents will enable a deeper un-derstanding of the neurobiological underpinnings of limited cognition and apparently irrational decision behavior (45)(46)(47)99). Thus, the corroboration of our theory using mice as a model organism opens the door to new directions that might be instrumental in the refinement and translation of these theories to applied settings in medicine, economics, and related social sciences.…”

Modelling the neural code in large populations of correlated neurons

“…However, when validated as Bayesian decoders, statistical models of neural encoding are often outperformed by models trained to decode stimulus-information directly, indicating that the encoding models miss key statistics of the neural code (Graf et al, 2011;Walker et al, 2020). In particular, the correlations between neurons' responses to repeated presentations of a given stimulus (noise correlations), and how these noise correlations are modulated by stimuli, can strongly impact coding in neural circuits (Zohary et al, 1994;Abbott and Dayan, 1999;Sompolinsky et al, 2001;Ecker et al, 2016;Kohn et al, 2016;Schneidman, 2016), especially in large populations of neurons (Moreno-Bote et al, 2014;Montijn et al, 2019;Bartolo et al, 2020;Kafashan et al, 2021;Rumyantsev et al, 2020).…”