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Abstract Sensory data about most natural task-relevant variables are entangled with task-irrelevant nuisance variables. The neurons that encode these relevant signals typically constitute a nonlinear population code. Here we present a theoretical framework for quantifying how the brain uses or decodes its nonlinear information. Our theory obeys fundamental mathematical limitations on information content inherited from the sensory periphery, describing redundant codes when there are many more cortical neurons than primary sensory neurons. The theory predicts that if the brain uses its nonlinear population codes optimally, then more informative patterns should be more correlated with choices. More specifically, the theory predicts a simple, easily computed quantitative relationship between fluctuating neural activity and behavioral choices that reveals the decoding efficiency. This relationship holds for optimal feedforward networks of modest complexity, when experiments are performed under natural nuisance variation. We analyze recordings from primary visual cortex of monkeys discriminating the distribution from which oriented stimuli were drawn, and find these data are consistent with the hypothesis of near-optimal nonlinear decoding. 

Abstract Understanding the brain requires understanding neurons’ functional responses to the circuit architecture shaping them. Here we introduce the MICrONS functional connectomics dataset with dense calcium imaging of around 75,000 neurons in primary visual cortex (VISp) and higher visual areas (VISrl, VISal and VISlm) in an awake mouse that is viewing natural and synthetic stimuli. These data are co-registered with an electron microscopy reconstruction containing more than 200,000 cells and 0.5 billion synapses. Proofreading of a subset of neurons yielded reconstructions that include complete dendritic trees as well the local and inter-areal axonal projections that map up to thousands of cell-to-cell connections per neuron. Released as an open-access resource, this dataset includes the tools for data retrieval and analysis^1,2. Accompanying studies describe its use for comprehensive characterization of cell types^3–6, a synaptic level connectivity diagram of a cortical column⁴, and uncovering cell-type-specific inhibitory connectivity that can be linked to gene expression data^4,7. Functionally, we identify new computational principles of how information is integrated across visual space⁸, characterize novel types of neuronal invariances⁹and bring structure and function together to uncover a general principle for connectivity between excitatory neurons within and across areas^10,11.