The animal body is bilaterally symmetric, and most sense organs (eyes, ears and nose) occur in pairs. These paired sensory organs provide independent measurements of the environment in a way that can aid behavior. For example, two eyes allow organisms to perceive depth. For the eyes or ears, spatially organized wiring (referred to as topographic mapping) makes it obvious that both organs contribute towards creating a consistent internal representation. Further, interactions between the two topographically organized streams of information (e.g. sound from left ear and right ear) are used by the brain to perform computations that make sense of the world (e.g. sound localization).
In the olfactory system, information from each nostril is thought to be mapped in a distributed and fragmented manner in the cortex. Therefore the same odor environment may be represented differently on the two sides of the brain. How can we create a consistent internal representation from these differing pieces of evidence? In any logical processing scheme, these two differing representations should be aligned to create a consistent view of the external world. We therefore asked the question: ‘Are the two olfactory cortices connected in a structured manner in order to coordinate each hemisphere’s differing representation of the same odor?’
From neuronal recordings in the olfactory cortex in mice, we found that the representations of odors presented selectively to each nostril are highly correlated in one side of the brain, and this correlation is not simply inherited from the ipsilateral olfactory bulb. Such aligned representations mean that a population of cortical neurons will have very similar responses whether the animal smells the odor through one nostril or the other.
(top left to bottom right) Venki Murthy, Will Dorrell, Cengiz Pehlevan, Siddharth Jayakumar, and Julien Grimaud
With a simple mathematical model, we showed that a random intercortical connectivity leads to uncorrelated representations. Hence the mapping must be structured in some way. This analysis also showed that such matched odor representation can readily arise from conventional correlation-based, Hebbian synaptic plasticity (“neurons that fire together wire together”) of initially unstructured connectivity. Our work, published in eNeuro (PDF) recently, revealed that, despite the distributed and fragmented nature of sensory representation in the olfactory cortex, odor information across hemispheres is highly coordinated.
Our first study points to structured, non-random connections linking the two olfactory cortices, but it is unclear whether this alignment can arise from plausible biological mechanisms involving continual correlation-based synaptic plasticity. It was also uncertain whether the experimentally observed sparsity of inter-hemispheric connections (when compared to much denser ipsilateral projections from the olfactory bulb) can support the observed alignment.
(top left to bottom right) Venki Murthy, Bo Liu. Shanshan Qin, and Yuhai Tu
Therefore, in a theoretically framed study published in PRX Life (PDF), we hypothesized that continuous exposure to environmental odors shapes these projections through online learning with a local Hebbian rule. We found that Hebbian learning with sparse connections can achieve bilateral alignment with a small number of training samples. Furthermore, we identified an inverse scaling relationship between the number of cortical neurons and the inter-hemispheric projection density required for
. Thus, more cortical neurons (estimated at ~500,000 in mouse) allow sparser inter-hemispheric projections, which was explained analytically.
Another goal of our theory paper was to understand the difference and similarity between the local Hebb’s learning rule and gradient-based global learning rules, such as stochastic gradient descend (SGD). SGD has been the predominant machine learning algorithm for training deep-learning neural networks. Here, 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 synaptic 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 leads to nearly as good an alignment of bilateral responses as an optimal machine learning method.
In addition to the specific insights for the olfactory system, our work can offer a general framework to study representational alignment in other sensory or cognitive systems with a broad range of realistic stimulus statistics and neural network architectures.
