Causal Geometric Structure in Neural Populations

This project applies differential geometry and causal inference to Neuropixels recordings from mouse visual decision-making. The core question: when standard analysis tools disagree about neural population structure, can geometry tell you why?

Standard similarity metrics (CKA, Procrustes) give opposite answers about which brain regions are "similar" --- the anti-correlation is strong and replicates across datasets. Dimensionality mediates it: CKA measures kernel alignment (sensitive to variance), Procrustes measures subspace orientation (sensitive to geometry), and they diverge predictably in high-dimensional regions. Linear subspace methods systematically fail in the highest-dimensional brain regions where causal signals are strongest.

Slides

Main talk — Causal Geometric Structure in Neural Populations (source) --- 69 slides covering geometric dissociation, causal subspace interventions, structured VAE, optogenetic validation, cross-region patching, and six independent lines of evidence.

Differential geometry of neural population codes (source) --- 47 pages covering spectral universality, evidence-choice alignment, dimensionality as computational strategy, and IBL cross-dataset replication.

IIA vacuity investigation (source) --- IIA interchange interventions, structured VAE subspaces, Sutter et al. vacuity replication, engagement separation, and external validation.

To compile:

cd docs/slides
pdflatex main_v6.tex

Paper

Neural Geometry Is Not Metric-Neutral: Dimensionality, Dissociation, and Causal Subspaces in Brain-Wide Neuropixels Recordings --- working draft (TMLR format). Includes 16 appendix sections with full experimental details.

Key findings

1. CKA and Procrustes anti-correlate across brain regions (Steinmetz: rho = -0.90, n = 50 regions; IBL replication: rho = -0.94, n = 11 regions, p < 0.0001)
2. Dimensionality mediates the dissociation: partial correlation controlling for power-law exponent reverses the sign (partial r = +0.44)
3. A structured VAE finds causal subspaces 3.4x stronger than LDA (73/73 regions, p = 5.7e-14)
4. LDA is anti-correlated with optogenetic causal importance (rho = -0.73, p = 0.01)
5. IIA is vacuous for nonlinear methods (Sutter et al. 2025) --- external validation is essential

Data

Source	Loader	Description
Steinmetz et al. 2019	data/steinmetz.py	Neuropixels recordings (73 regions, 39 sessions, 10 mice)
IBL Brain-Wide Map	data/ibl.py	Cross-dataset replication (139 mice, 12 labs)
Allen Institute	data/allen.py	Mouse Brain Atlas structural connectivity
Modal GPU	results/exp*/	All experiment results (JSON, JSONL)

Experiments

81 experiments in experiments/ and batch2_reviewer_fixes/, run on Modal GPUs. Key ones:

Experiment	What it tests
exp42	Core CKA-Procrustes anti-correlation across 73 regions
exp46	IBL cross-dataset replication (11 matched regions)
exp47b	Optogenetic silencing validation (n=16 regions)
exp51	Confound control (neuron count, firing rate, temporal shuffle)
exp53	Dose-response: progressive dimension ablation
exp57	Structured VAE for nonlinear causal subspaces
exp62	Shuffled-label control (p = 6e-8)
exp67	Potent/null space decomposition
exp70	Cross-region activation patching (1,438 directed pairs)
exp71	VAE causal circuits (2.73x choice effect size)
exp74	Debiased CKA (reviewer fix)
exp76	UMAP stochasticity robustness
exp78	Optogenetic power analysis
exp80	iVAE identifiability verification
exp81	CD-NOD causal discovery over brain regions

Library

Module	Description
geometry/distances.py	Grassmannian distance, CKA, Procrustes, subspace angles
geometry/subspace.py	Subspace extraction (PCA, LDA, VAE latent)
geometry/holonomy.py	Parallel transport and holonomy on the Grassmannian
geometry/sheaf.py	Sheaf cohomology for inter-region consistency

Scripts

Script	What it does
modal_run.py	Run experiments on Modal GPUs
docs/slides/generate_figures.py	Generate slide figures from exp42 results
docs/slides/generate_exp46_figures_v2.py	Generate IBL cross-dataset figures
paper/generate_figures.py	Generate paper figures

Setup

uv sync

# Configure GCS credentials (for data caching)
cp .env.example .env
# Edit .env with your GCS_BUCKET and GCS_SA_KEY_PATH

Reproducing

# Run an experiment locally (CPU, small subset)
uv run python -m experiments.exp42_real_iia

# Run on Modal GPU
uv run modal run --detach modal_run.py --experiment exp42

Pre-computed results for all experiments are in results/.

License

MIT

Citation

Tower, E. (2026). Causal Geometric Structure in Neural Populations. Zenodo.