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Message-Relevant Dimension Reduction of Neural Populations

Amanda Merkley, Alice Y. Nam, Y. Kate Hong, Pulkit Grover

TL;DR

This work presents Iterative Regression (IR), a linear, message-dependent dimension-reduction method that optimizes projections to maximize correlation with a known message $M$. By iteratively deflating prior components, IR yields a low-dimensional, interpretable basis that preserves $M$-relevance; the paper also defines $M$-forwarding to formalize how a message may be transmitted between neural populations. Applying IR to a whisker-detection network in mice (S1 and SC), the authors demonstrate robust, 1D representations that reveal an $M$-to-$A$ pathway in the 15–40 ms window, with less clear forwarding to SC, and show that IR outperforms or aligns with existing methods like dPCA and mTDR. The approach offers a practical framework for quantifying low-dimensional communication in neuroscience data and highlights the importance of choosing a relevance measure aligned with the scientific question. The findings support a low-dimensional organization of message transmission consistent with anatomical and functional evidence, while suggesting avenues for extending to nonlinear or alternative relevance metrics.

Abstract

Quantifying relevant interactions between neural populations is a prominent question in the analysis of high-dimensional neural recordings. However, existing dimension reduction methods often discuss communication in the absence of a formal framework, while frameworks proposed to address this gap are impractical in data analysis. This work bridges the formal framework of M-Information Flow with practical analysis of real neural data. To this end, we propose Iterative Regression, a message-dependent linear dimension reduction technique that iteratively finds an orthonormal basis such that each basis vector maximizes correlation between the projected data and the message. We then define 'M-forwarding' to formally capture the notion of a message being forwarded from one neural population to another. We apply our methodology to recordings we collected from two neural populations in a simplified model of whisker-based sensory detection in mice, and show that the low-dimensional M-forwarding structure we infer supports biological evidence of a similar structure between the two original, high-dimensional populations.

Message-Relevant Dimension Reduction of Neural Populations

TL;DR

This work presents Iterative Regression (IR), a linear, message-dependent dimension-reduction method that optimizes projections to maximize correlation with a known message . By iteratively deflating prior components, IR yields a low-dimensional, interpretable basis that preserves -relevance; the paper also defines -forwarding to formalize how a message may be transmitted between neural populations. Applying IR to a whisker-detection network in mice (S1 and SC), the authors demonstrate robust, 1D representations that reveal an -to- pathway in the 15–40 ms window, with less clear forwarding to SC, and show that IR outperforms or aligns with existing methods like dPCA and mTDR. The approach offers a practical framework for quantifying low-dimensional communication in neuroscience data and highlights the importance of choosing a relevance measure aligned with the scientific question. The findings support a low-dimensional organization of message transmission consistent with anatomical and functional evidence, while suggesting avenues for extending to nonlinear or alternative relevance metrics.

Abstract

Quantifying relevant interactions between neural populations is a prominent question in the analysis of high-dimensional neural recordings. However, existing dimension reduction methods often discuss communication in the absence of a formal framework, while frameworks proposed to address this gap are impractical in data analysis. This work bridges the formal framework of M-Information Flow with practical analysis of real neural data. To this end, we propose Iterative Regression, a message-dependent linear dimension reduction technique that iteratively finds an orthonormal basis such that each basis vector maximizes correlation between the projected data and the message. We then define 'M-forwarding' to formally capture the notion of a message being forwarded from one neural population to another. We apply our methodology to recordings we collected from two neural populations in a simplified model of whisker-based sensory detection in mice, and show that the low-dimensional M-forwarding structure we infer supports biological evidence of a similar structure between the two original, high-dimensional populations.
Paper Structure (14 sections, 2 theorems, 15 equations, 5 figures, 2 tables, 1 algorithm)

This paper contains 14 sections, 2 theorems, 15 equations, 5 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Linear Dimension Reduction
  3. A measure of $M$-relevance
  4. Iterative Regression
  5. Related methods: Linear dimension reduction
  6. Related methods: Dimension reduction in neuroscience
  7. $M$-Forwarding
  8. Experimental results
  9. Experiment design and data collection
  10. Marginal $M$-relevance in S1 and SC
  11. Inferring low-dimensional dependencies
  12. Discussion
  13. Experiment Methodology & Data Analysis
  14. Additional comparisons

Key Result

Theorem 1

Let $X \in \mathbb{R}^{n \times Q}$ be the mean-centered dataset and $M\in \mathbb{R}^Q$, the mean-centered message vector. Suppose $v = (XX^T)^{-1}X M$ is the regression vector and $\{p_i\}_{i=1}^n$ is the set of principal components of $\Sigma_X \propto XX^T$. Then, where $r(p_i^TX, M)$ is the sample correlation coefficient between $p_i^TX$ and $M$, $\lambda_i$ is the eigenvalue associated to $

Figures (5)

  • Figure 1: (Left) One whisker is deflected while population activity in S1 and SC is recorded. We infer the existence of the red and blue arrows from S1 to SC and SC to S1, respectively. (Right) Trial structure. The whisker is deflected at 0s and the response window opens at 0.3s. The blue shaded region depicts the window between 15-40ms after deflection in which communication is posited to occur, and where we test for $M$-forwarding.
  • Figure 2: $M$-correlations of low-dimensional representations of S1 for the top three dimensions, d1, d2, and d3. The solid vertical line at 0s marks the time of whisker deflection and the dashed line at 0.3s marks response start.
  • Figure 3: $M$-correlations of low-dimensional representations of SC for the top three dimensions. Arrows 1, 2, and 3 in IR mark three distinct peaks identified by IR.
  • Figure 4: PSTH for S1 (left) and SC (right) over all trials. The S1 PSTH exhibits two distinctive peaks, labeled A and B, while the SC PSTH only has one evident peak, labeled C.
  • Figure 5: $M$-correlations of low-dimensional representations of S1 and SC using PCA and PLS.

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Definition 1: $M$-forwarding
  • Theorem 2
  • proof
  • proof