Neural Comput - Insights from a simple expression for linear fisher information in a recurrently connected population of spiking neurons.

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Resumo

A simple expression for a lower bound of Fisher information is derived for a network of recurrently connected spiking neurons that have been driven to a noise-perturbed steady state. We call this lower bound linear Fisher information, as it corresponds to the Fisher information that can be recovered by a locally optimal linear estimator. Unlike recent similar calculations, the approach used here includes the effects of nonlinear gain functions and correlated input noise and yields a surprisingly simple and intuitive expression that offers substantial insight into the sources of information degradation across successive layers of a neural network. Here, this expression is used to (1) compute the optimal (i.e., information-maximizing) firing rate of a neuron, (2) demonstrate why sharpening tuning curves by either thresholding or the action of recurrent connectivity is generally a bad idea, (3) show how a single cortical expansion is sufficient to instantiate a redundant population code that can propagate across multiple cortical layers with minimal information loss, and (4) show that optimal recurrent connectivity strongly depends on the covariance structure of the inputs to the network.

Resumo Limpo

simpl express lower bound fisher inform deriv network recurr connect spike neuron driven noiseperturb steadi state call lower bound linear fisher inform correspond fisher inform can recov local optim linear estim unlik recent similar calcul approach use includ effect nonlinear gain function correl input nois yield surpris simpl intuit express offer substanti insight sourc inform degrad across success layer neural network express use comput optim ie informationmaxim fire rate neuron demonstr sharpen tune curv either threshold action recurr connect general bad idea show singl cortic expans suffici instanti redund popul code can propag across multipl cortic layer minim inform loss show optim recurr connect strong depend covari structur input network

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