Form and Function of Drifting Olfactory Representations in the Piriform Cortex

Abstract: Cognition and behavior are generated by patterns of neural activity. This has led many to equate brain functions with specific neural activity patterns, also called representations. However, recent data suggest that the mapping between neural representations, cognition, and behavior is more complicated. For instance, the set of neurons representing an odor’s identity in the olfactory (piriform) cortex changes over time. Such shifts in neural representations are termed “representational drift,” because they are devoid of discernible learning, forgetting, or behavioral alterations. Recent work has modeled representational drift in neural networks as the random exploration of representations that correctly produce a memorized set of input-output associations. This revealed that representational drift can benefit memory by finding sparse representations that make the system more robust to noise and continual learning. However, current models do not produce realistic representational drift, and it is unclear if this theoretical benefit occurs for biological systems. Here we will assess whether this robustness benefit applies to realistic models of representational drift in the piriform cortex. First, we will use data from the Fink Lab to quantify the geometry of representational drift and its statistics of change. Previous findings suggest that there is no linear stable subspace, so we will specifically search for nonlinear representational features that are invariant to drift. Second, we will generalize the Fitzgerald Lab’s analyses of neural network solution spaces from linear readouts to nonlinear readouts that better match the empirically stable dimensions. Finally, we will combine these results to build and analyze a representational drift model that realistically mimics the piriform cortex. This work will advance both biology and mathematics, as representational drift is a fundamental biological mechanism, and new mathematics will be needed to quantify representational geometry and neural network solution spaces.