# P2: Geometry of Neural Representations and Dynamics

> **NIH NIH U19** · PRINCETON UNIVERSITY · 2024 · $324,363

## Abstract

Project Summary/Abstract: Project 2, Geometry of Neural Representations and Dynamics
In this project, we will measure and model the geometry of neural coding and dynamics during an
evidence-accumulation decision task. This work will advance the overall goal of this U19 program—elucidating
the circuit mechanisms that underlie working memory and decision-making and applying this information to
construct a multi-region, mechanistic circuit model. Neural population activity in the dorsal hippocampus of
mice is constrained to lie on a low-dimensional manifold during our task. Important behavioral variables like
position along the maze, and learned cognitive variables like evidence, are represented as gradients in
different directions along this latent space, giving rise to a geometric representation of knowledge. Observed
neural activity sequences correspond to trial-specific trajectories along the manifold.
 The first aim will characterize geometric representations in hippocampus and neocortex, to identify
general encoding principles of these representations and provide a richer dataset for comparison with our
mechanistic models. We will compare firing fields and manifold structure to predictions from several existing
statistical learning models to test the general idea that the manifolds capture task-specific statistical
regularities. We will also characterize geometric properties of neural coding and manifold structure across
these areas, starting with the prefrontal cortex, using simultaneous Neuropixels recordings from multiple
regions. We will identify what attributes, such as intrinsic dimensionality and variable encodings, are preserved
in the cortex compared to hippocampal representations.
 The second aim will evaluate the neural dynamics that govern state space flow along the manifold. So
far, we have focused on inferring the geometry of neural representations and have not directly examined
dynamics on the manifold. We developed a nonlinear method to simultaneously estimate manifold dimensions
and the dynamics on that manifold, based on neural spike data. We will extend this method for use with
calcium imaging data and then apply it to spiking and imaging data from other projects to infer manifold state
space flow. These data-driven inferences will be compared to the dynamics predicted by existing models.
 Finally, the third aim will causally probe manifold structure and the mechanisms of sequence generation
using optogenetic perturbation. With our new technology for simultaneous optogenetic perturbation and
imaging, we will measure changes in neural population activity during multi-neuron perturbations that will be
designed using sequence and manifold structure derived from population imaging data. Data, analyses, and
modeling from this project will provide key insights into the general properties of neural manifolds in a variety of
brain regions, along with the flow-field dynamics along manifolds that define neural trajectories on individu...

## Key facts

- **NIH application ID:** 10900683
- **Project number:** 5U19NS132720-02
- **Recipient organization:** PRINCETON UNIVERSITY
- **Principal Investigator:** Carlos D Brody
- **Activity code:** U19 (R01, R21, SBIR, etc.)
- **Funding institute:** NIH
- **Fiscal year:** 2024
- **Award amount:** $324,363
- **Award type:** 5
- **Project period:** 2023-08-08 → 2028-06-30

## Primary source

NIH RePORTER: https://reporter.nih.gov/project-details/10900683

## Citation

> US National Institutes of Health, RePORTER application 10900683, P2: Geometry of Neural Representations and Dynamics (5U19NS132720-02). Retrieved via AI Analytics 2026-05-23 from https://api.ai-analytics.org/grant/nih/10900683. Licensed CC0.

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