Predictive versus Correlational Coarse-Graining in the Brain

In complex systems with many degrees of freedom, e.g. neural systems, we learn a great deal by studying their coarse-grained, or simplified, representations. Here, we study the effect of adding a cost function to simplification by comparing computation-explicit and computation-agnostic coarse-grainings. We use retinal data, which displays a variety of nonlinear processes associated with prediction, near-optimally. The activity of a group of 𝑁 neurons is modeled as a binary pattern σ_t, where σ_tⁱ represents the activity of cell 𝑖 at time 𝑡 with a 1 if the cell spiked and 0 if not. To study computation downstream of the retina, we coarse-grain 𝑁 cells into one meta neuron, 𝑀(𝑡), whose 2 response states depend probabilistically on the original activity σ_t, then test how well the meta neuron retains information about future input activity: 𝐼(𝑀_t; σ_t+Δt) = 𝐻(𝑀_t) + 𝐻(σ_t+Δt) − 𝐻(𝑀_t, σ_t+Δt), where 𝐻 denotes entropy. The benefits of a predictive coarse-graining (PCG) far outweigh the costs: a prediction-agnostic correlational coarse-graining (CCG) that simply aims to reduce redundancy in the data by combining highly correlated neurons can, surprisingly, preserve predictive information in natural scenes, but it is sub-optimal and does not generalize across scenes. In contrast, PCG preserves near-optimal predictive information, and can generalize across natural scenes. While CCG might seem more computationally simple, it may not be as efficient as solving just one generalized optimization problem.