P130 Manifold Inference by Maximising Information: Hypothesis-driven extraction of CA1 neural manifolds via information theory
Michael G. Kareithi*1, Mary Ann Go 1, Pier Luigi Dragotti 2 Simon R. Schultz1
1 Department of Bioengineering, Imperial College London, London, United Kingdom 2Department of Electrical and Electronic Engineering, Imperial College London, London, United Kingdom
*Email: m.kareithi21@imperial.ac.uk
Introduction Neural manifolds have been a useful concept for understanding cognition, with recent work showing the importance of "hypothesis-driven" analyses: linking behaviour with manifolds via supervised manifold learning [1]. Linear dimensionality reduction methods are easier to interpret than their nonlinear counterparts, but often can only detect linear correlations in neural activity. From an information-theory perspective, a natural approach to supervised manifolds is to maximise Mutual Information between the embedding and the target variable. We use simple linear embeddings with an information-theoretic objective function: Quadratic Mutual Information [2], and apply it as a tool for hypothesis-driven manifold learning in mouse hippocampus. Methods Quadratic Mutual Information (QMI) is derived from Renyi entropy and divergence, a broader family of measures than Shannon entropy and mutual information (MI), the latter being a special case of the former. Like MI, QMI has the desirable property of being zero if and only if the variables are independent. Its advantage is that it can be estimated with high-dimensional data, and is differentiable. We fit a linear projection from activity to a lower-dimensional subspace by maximising QMI between the projection and a target variable. We call our framework Manifold Inference by Maximising Information (MIMI). We apply MIMI to two-photon calcium recordings in mouse CA1 during a 1D running task. Results In our dataset, mice run continuously along a circular track [3]. We fit MIMI on calcium fluorescence activity, with the animal's angular position as target variable, cross-validating with a 75%-25% train-test split. In four out of eight mice we find the majority of position-information in a 2-3 dimensional subspace (Fig 1.a). In the sessions without informative subspaces, the linear decodability of position is low even from the full population activity, indicating the absence of a population code (Fig 1.e). The informative subspaces contain ring-shaped manifolds mapping continuously onto the animal's physical coordinates (Fig 1.f). Discussion Combining information-theoretic measures with linear embeddings is a useful idea for analysing populations, where our aim is not only to find manifold structure, but to understand how cell assemblies coordinate to sculpt it. MIMI shows that we can find behaviourally-informative manifolds without nonlinear embeddings: only a nonlinear measure of dependence. Downstream analysis can then pose questions about representation by examining the linear transformation weights: for example, asking if two variables are represented orthogonally. We believe MIMI will be a useful framework for interpretable, hypothesis-driven manifold analysis.
Figure 1. A) Explained position variance (R-squared of ridge-regressor, left) and Mutual Information (right) between position and MIMI projection at different dimensionalities. Each line is an individual mouse. B) Position-variance explained by full population vs by MIMI subspace. C) Activity in MIMI subspace for four mice with informative subspaces, coloured by associated position of mouse. Acknowledgements- References 1.https://doi.org/10.1038/s41586-023-06031-6 2.https://doi.org/10.1007/978-1-4419-1570-2_2 3.https://doi.org/10.3389/fncel.2021.618658
