Title: One nose but two nostrils, local vs global learning rules: Learn to align with sparse connections between two olfactory cortices
Abstract: Bilateral integration of cortical representations is a general problem in neuroscience that has been mainly studied in vision and audition but less explored in olfaction. Recent studies have revealed that odor representations in two olfactory cortices can be aligned, presumably through structured inter-hemispheric projections, but how this structure forms is unclear. We hypothesized that continuous exposure to environmental odors shapes these projections and modeled it as online learning with a local Hebbian rule. We found that Hebbian learning with sparse connections achieves bilateral alignment and exhibits a linear trade-off between speed and accuracy. Furthermore, we identified an inverse scaling relationship between the number of cortical neurons and the inter-hemispheric projection density (sparsity) required for desired alignment accuracy. Thus, more cortical neurons allow sparser inter-hemispheric projections, which was explained analytically. As a comparison to the local Hebbian rule, we also studied the global stochastic gradient descent (SGD) learning rule for alignment. We found that although SGD leads to the same alignment accuracy with a slightly reduced sparsity, the same inverse scaling relation holds. Our analysis showed that their similar performance originates from the fact that the update vectors of the two learning rules align with each other throughout the entire learning process. Our work suggests that a biologically plausible mechanism with sparse connections suffices for bilateral alignment. The quantitative comparison between the local Hebbian rule and the global SGD rule may also inspire more efficient sparse local learning algorithms for more complex problems.