Fig. 1: A network with structured recurrent connections limits the linear Fisher Information (LFI) about external stimuli.
From: Sampling-based Bayesian inference in recurrent circuits of stochastic spiking neurons
a A schematic diagram showing how a stimulus, s, is encoded in neuronal response, rt. A stimulus estimate, \({\hat{s}}_{t},\) can be obtained from rt.. b A recurrent ring model (top) where the connections between excitatory neurons are dependent on their distance along the ring. Blue arrows: excitatory synapses with line width denoting connection strength; red arrows: inhibitory synapses. c The population activity of excitatory neurons in the ring model, rt, dependent on a stimulus, s. The blue curve shows the population activity in response to s = 0, and gray curves the activities in response to stimuli with values at the peak locations of the curves. d For finite size networks (colored lines; ratio of excitatory to inhibitory neurons kept constant) LFI decreases as wE increases. In the limit of infinite network size LFI does not depend on wE (dashed line). Since neural responses are variable, LFI in the neuronal response converges to only half of the LFI in the feedforward input. Error bars denote one standard deviation (SD), which were estimated from N = 50 independent samples generated by using Bootstrap.
