One nose but two nostrils: Learning to align with sparse connections between two olfactory cortices

Abstract

The integration of neural representations in the two brain hemispheres has been studied extensively in vision, audition, and somatosensation, but less so in olfaction. Recent experiments have revealed that odor responses in cortical neurons driven by separate stimulation of the two nostrils are highly correlated. This bilateral alignment points to structured, nonrandom interhemispheric connections, but how this structure leads to alignment is unclear. Here, 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, exhibiting a linear tradeoff between speed and accuracy (lower learning rate leads to higher alignment level but slower convergence). Furthermore, we identified an inverse scaling relationship between the number of cortical neurons and the interhemispheric projection density required for desired alignment accuracy. Thus, more cortical neurons allow sparser interhemispheric projections, which was explained analytically. We next compared the alignment performance of local Hebbian rule and the global stochastic gradient descent (SGD) learning rule used in artificial neural networks. 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 correlated bilateral responses. The quantitative comparison between the local Hebbian rule and the global SGD rule may inspire efficient sparse local learning algorithms for more complex problems. Published by the American Physical Society 2024