Extended Data Fig. 1: Neural Circuits for Random Walk Algorithm.

(A) Neural Circuits for Buffering and Counting on Loihi. Red input lines (from left) represent inputs from supervisor neuron. Circle ends represent inhibitory connections (weight =-1), arrows represent excitatory connections (weight = 1). For buffer circuit, outputs (to right) go to counter circuit count neuron; for counter circuit, outputs go to probability neurons. (B) Illustration of computing probabilistic circuit with a decision tree to compute probabilities with example output probabilities in red. (C) Same decision tree compressed into a single layer, with source input driving probabilistic choice. The dotted line is an excitatory connection with a delay to correspond to skipping the probabilistic layer. From source neuron, weights from source neuron (green) to probability neurons (blue) are set to tune probabilities neurons fire, per equation M.1. Outputs of probability neurons with arrows are excitatory (weight = 1) and with circles are inhibitory (weight = −1). (D) Binary tree representing the stochastic walk through a TrueNorth mesh node. Probability neurons are 𝑟₀, 𝑟₁, and 𝑟₂. Black edges are excitatory, red edges are inhibitory. Blue edges indicate a delay of 1, and bold blue and red dashed edges indicate a delay of 2. The four leaf nodes, 𝑜₀, 𝑜₁, 𝑜₂, and 𝑜₃, are the directional nodes with derived exit probabilities. (E) A near complete specification of the TrueNorth mesh node model for a random walk algorithm. This is a more defined representation of the binary tree from panel D. Neurons are represented by triangles, neuron inputs are on the left edge of the square and a synapse to a neuron is defined by a circle on the cross bar. Green circles are excitatory connections and yellow circles are inhibitory connections. The red number 2 above neurons 6, 7, and 8 indicate that they fire as a result of 2 or more incoming spikes, all other neurons fire as a result of 1 or more incoming spikes.