High-dimensional geometry of population responses in visual cortex

Abstract

A neuronal population encodes information most efficiently when its stimulus responses are highdimensional and uncorrelated, and most robustly when they are correlated and lower-dimensional. Here, we analyzed the dimensionality of the encoding of natural images by large visual cortical populations recorded from awake mice. Evoked population activity was high dimensional, with correlations obeying an unexpected power-law: the n th principal component variance scaled as 1/n. This scaling was not inherited from the 1/f spectrum of natural images, because it persisted after stimulus whitening. We proved mathematically that if the variance spectrum decayed any slower, the population code could not be smooth, allowing small changes in input to dominate population activity. The theory also predicts larger power-law exponents for lower-dimensional stimulus ensembles, which we validated experimentally. These results suggest that coding smoothness may represent a fundamental constraint governing correlations in neural population codes.

Natural images are reliably represented by sparse and variable populations of neurons in visual cortex

“…Together, any natural image could be represented by a combination of responsive neurons. These findings also suggest that the representation of multiple natural images is high dimensional, consistent with a report about highdimensional representation in mouse V1 50 . Thus, a single natural image can be low dimensionally represented in a highdimensional representation space for a large number of natural scenes.…”

Simultaneous Electrophysiology and Fiber Photometry in Freely Behaving Mice

“…Genetically encoded indicators offer complementary advantages over in vivo electrophysiological approaches (Lin and Schnitzer, 2016;Deo and Lavis, 2018;Wang et al, 2019). Over the last two decades, genetically encoded calcium indicators (GECIs) have been widely used to interrogate not only neuronal ensemble dynamics, but also activity of non-neuronal cells, such as astrocytes in vivo (Nakai et al, 2001;Chen et al, 2013;Stobart et al, 2018;Dana et al, 2019;Inoue et al, 2019;Stringer et al, 2019). For example, GECIs enable cell-type-specific targeting and long-term monitoring of neuronal activity in vivo.…”

Explainable Artificial Intelligence for Neuroscience: Behavioral Neurostimulation

“…Importantly, XAI needs to be able to effectively handle multi-modal data (e.g., visual, auditory, clinical). It should provide inherently non-linear computational algorithms that will be able to combine large datasets such as those provided by modern calcium imaging techniques [>1000 of neurons recorded simultaneously (Soltanian-Zadeh et al, 2019;Stringer et al, 2019)] and voltage sensitive dye techniques (Grinvald et al, 2016;Chemla et al, 2017) with smaller but highly meaningful datasets such as those describing behavior. These improvements would result, in turn, in better ways to 'close the loop' and devise effective algorithms for neurostimulation.…”