Primacy coding in dual olfactory networks

In the olfactory system, odor percepts retain their identity despite substantial variations in concentration, timing, and background. We propose a novel strategy for encoding intensity-invariant stimuli identity based on representing relative rather than absolute stimulus features. In this scheme, dependence on relative amplitudes of stimulus features makes identity invariant to intensity and monotonous non-linearities of neuronal responses. We propose that the olfactory system represents stimulus identity using the information that a subset of odorant receptor types responds more strongly than all receptor types in the complement set. We show that this information is sufficient to ensure the robust recovery of a sparse stimulus (odorant) via elastic net loss minimization. This minimization is performed under the constraints imposed by the relationships between these two receptor sets. We formulate this problem using its dual Lagrangian. We show that the dual problem can be solved by a neural network whose Lyapunov function represents the dual Lagrangian. We thus propose that networks in the piriform cortex compute odorant identity and implement dual computations with the sparse activities of individual neurons representing Lagrange multipliers.