Supplementary Information: A sampling-based circuit for optimal decision making

The generative model for our observations is defined as s = Ax + ε. We therefore set β to K φ, where φ is the average magnitude of the kernel functions. For all of our simulations, the kernels were a set of 20 Gaussians with σ = 0.06, centered such that they evenly tile the range from 1 to 1, and β = 9.45. Briefly, this framework proposes a way of embedding a linear dynamical system defined by (3) in the spiking activity of a network of N neurons. The network's estimate of the desired dynamics, ĉ Specifically, each neuron's conditional intensity function is a sigmoidal function of its membrane potential: λ Figure 1 shows a simple demonstration of the decision circuit using samples from a 2D posterior generated by the inference circuit. In this case, the inference circuit is sampling from the posterior of a linear Gaussian model.