One nose but two nostrils: interaction between two hemispheres aligns bilateral responses*

Odors are detected by olfactory receptor neurons in the nose, which project to the ipsilateral olfactory bulb (OB). Each olfactory cortex on one hemisphere receives olfactory information from ipsilateral OB, plus contralateral information from the other hemisphere cortex. Since the projection from OB to cortex is largely random, odor representations in two cortices are presumably independent. Surprisingly, experiments in mice showed that the two representations are aligned, suggesting the inter-hemispheric projections must be structured. But how such structure emerges remains an enigma. 

We hypothesized that the inter-hemispheric projections are plastic and are shaped by constant experience of different environmental odors. Then we modeled this online learning process with local Hebb's rule, and found that: bilateral alignment of odor representations can be achieved; with larger OB to cortex expansion ratio, the projection can be sparser. Further, we found a power law with exponent 1/2 between alignment quality and projection sparsity. A theory was developed for the (unique) Hebbian solution, and explained two scalings.

To explore the landscape in larger parameter space, we optimized an alignment loss function over projection matrices, with global stochastic gradient descent (SGD) update rule. We showed that SGD outperforms Hebb’s rule and may find perfect alignment solutions. This difference between local Hebbian and global SGD rules, and their connections, may be understood analytically.