Sparse connectivity for MAP inference in linear models using sister mitral cells

Sensory processing is hard because the variables of interest are encoded in spike trains in a relatively complex way. A major goal in studies of sensory processing is to understand how the brain extracts those variables. Here we revisit a common encoding model in which variables are encoded linearly. Although there are typically more variables than neurons, this problem is still solvable because only a small number of variables appear at any one time (sparse prior). However, previous solutions require all-to-all connectivity, inconsistent with the sparse connectivity seen in the brain. Here we propose an algorithm that provably reaches the MAP (maximum a posteriori) inference solution, but does so using sparse connectivity. Our algorithm is inspired by the circuit of the mouse olfactory bulb, but our approach is general enough to apply to other modalities. In addition, it should be possible to extend it to nonlinear encoding models.SummarySensory systems must infer latent variables from noisy and ambiguous input. MAP inference – choosing the most likely latent variable given the sensory input – is one of the simplest methods for doing that, but its neural implementation often requires all-to-all connectivity between the neurons involved. In common sensory contexts this can require a single neuron to connect to hundreds of thousands of others, which is biologically implausible. In this work we take inspiration from the ‘sister’ mitral cells of the olfactory system – groups of neurons associated with the same input channel – to derive a method for performing MAP inference using sparse connectivity. We do so by assigning sister cells to random subsets of the latent variables and using additional cells to ensure that sisters correctly share information. We then derive the circuitry and dynamics required for the sister cells to compute the original MAP inference solution. Our work yields a biologically plausible circuit that provably solves the MAP inference problem and provides experimentally testable predictions. While inspired by the olfactory system, our method is quite general, and is likely to apply to other sensory modalities.