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Invited Symposia

The Geometry of Neural Representations of Tasks: What Does it Mean for Cognition and Behavior?

Invited Symposium 4: Tuesday, April 16, 2024, 10:00 am – 12:00 pm EDT, Ballroom Center + West

Chair: Tim Buschman¹; ¹Princeton University
Presenters: Tatiana Engel, Nikolaus Kriegeskorte, Tatyana Sharpee, Tim Buschman

A central goal of cognitive neuroscience is to understand how the brain represents and transforms information relevant to the current task. Previous work has shown sensory inputs, thoughts, and actions are all represented in the pattern of activity across large populations of neurons. Yet, it has been difficult to understand how these high-dimensional representations relate to cognition and behavior. Recent work suggests new insights may come from understanding the geometry of neural representations – that is, how representations relate to one another in neural space. This symposium brings together speakers using experimental and computational techniques to understand how the geometry of neural representations can capture semantic meaning, facilitate learning, influence cognitive computations, and support behavior.

Presentations

The dynamics and geometry of choice in premotor cortex

Tatiana Engel¹; ¹Princeton University

The brain represents sensory variables in the coordinated activity of neural populations, in which tuning curves of single neurons define the geometry of the population code. Whether the same coding principle holds for dynamic cognitive variables remains unknown because internal cognitive processes unfold with a unique time course on single trials observed only in the irregular spiking of heterogeneous neural populations. We show the existence of such a population code for the dynamics of choice formation in the primate premotor cortex. We developed an approach to simultaneously infer population dynamics and tuning functions of single neurons to the population state. Applied to spike data recorded during decision-making, our model revealed that populations of neurons encoded the same dynamic variable predicting choices, and heterogeneous firing rates resulted from the diverse tuning of single neurons to this decision variable. The inferred dynamics indicated an attractor mechanism for decision computation. Our results reveal a unifying geometric principle for neural encoding of sensory and dynamic cognitive variables.

Comparing task-performing models by their predictions of representational geometries and topologies

Nikolaus Kriegeskorte¹; ¹Columbia University

Understanding the brain-computational mechanisms underlying cognitive functions requires that we implement our theories in task-performing models and adjudicate among these models on the basis of their predictions of brain representations and behavioral responses. Previous studies have characterized brain representations by their representational geometry, which is defined by the representational dissimilarity matrix (RDM), a summary statistic that abstracts from the roles of individual neurons (or responses channels) and characterizes the discriminability of stimuli. The talk will cover (1) recent methodological advances implemented in Python in the open-source RSA3 toolbox that support unbiased estimation of representational distances and model-comparative statistical inference that generalizes simultaneously to the populations of subjects and stimuli from which the experimental subjects and stimuli have been sampled, (2) computational insights on recurrent and generative processes in visual recognition gained with these methods, and (3) topological representational similarity analysis (tRSA), an extension of representational similarity analysis (RSA) that uses a family of geo-topological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. Results show that topology-sensitive characterizations of population codes are robust to noise and interindividual variability and maintain excellent sensitivity to the unique representational signatures of different neural network layers and brain regions.

Hyperbolic geometry of neural responses expands in maximally informative way

Tatyana Sharpee¹; ¹Salk Institute

I will describe results showing that neural responses in the hippocampus have a low-dimensional hyperbolic geometry and that their hyperbolic size is optimized for the number of available neurons. It was also possible to analyze how neural representations change with experience. In particular, neural representations continued to be described by a low-dimensional hyperbolic geometry as the animal explored the environment but the radius increased logarithmically with time. This time dependence matches the maximal rate of information acquisition by a maximum entropy discrete Poisson process, further implying that neural representations continue to perform optimally as they change with experience.

The geometry of cognitive control

Tim Buschman¹; ¹Princeton University

Cognition is flexible – behavior can change on a moment-by-moment basis. Such flexibility is thought to rely on the brain’s ability to route information through different networks of brain regions in order to support different cognitive computations. However, the mechanisms that determine which network of brain regions is engaged are unknown. To address this, we combined cortex-wide calcium imaging with high-density electrophysiological recordings in eight cortical and subcortical regions of mice. This revealed different dimensions within the population activity of each brain region were functionally connected with different cortex-wide ‘subspace networks’ of regions. These subspace networks were multiplexed, allowing a brain region to simultaneously interact with multiple independent, yet overlapping, networks. Alignment of neural activity within a region to a specific subspace network dimension predicted how neural activity propagated between regions. Thus, changing the geometry of the neural representation within a brain region could be a mechanism to selectively engage different brain-wide networks to support cognitive flexibility.