Sheets of spiking neurons can perform Bayesian inference on distributed spiking input.

<p>(A) Local generative model with two competing hidden causes and five inputs. Each hidden cause stores a specific input pattern in the top-down parameters <i>π</i>_<i>ki</i>. (B) Corresponding local neural network. Top-down parameters <i>π</i>_<i>ki</i> translate to bottom-up synaptic weights <i>V</i>_<i>ki</i>, turning each network neuron into a probabilistic expert for a specific local input pattern. (C) Example network with six network neurons. Neighboring neurons with overlapping input inhibit each other (dashed line: range of lateral inhibition for red neuron). The spiking network is linked to a generative model <i>p</i> (<i><b>y</b></i>, <i><b>z</b></i> ∣ <i><b>θ</b></i>) according to Corollary 1. (D) The network in C performs sample-based inference of hidden causes <i><b>z</b></i> under time-varying input <i><b>y</b></i>(<i>t</i>) in the associated generative model. Comparison of posterior marginals <i>p</i> (<i>z</i>_<i>k</i> = 1 ∣ <i><b>y</b></i>(<i>t</i>), <i><b>θ</b></i>) between the analytically calculated exact posterior (top) and the average network response (bottom, estimated from 1000 simulation runs) under the time-varying input <i><b>y</b></i>(<i>t</i>) in panel E. All traces were smoothed with a 20ms box kernel for visual clarity. (E) Top: Network spike response in a single simulation run. Bottom: Input spike trains (colored: structured input, gray: background activity). The network response is an ongoing sampling process from the posterior <i>p</i> (<i><b>z</b></i> ∣ <i><b>y</b></i>(<i>t</i>), <i><b>θ</b></i>). Time points marked by a ‘*’ exemplify characteristic properties of sample-based Bayesian information processing. (F) Top: Bottom-up weights <i>V</i>_<i>ki</i> of the red neuron. Bottom: Average input activity while the matching pattern is presented (during the 300ms period marked in E).