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Life sciences · Preprint
arXiv · September 8, 2026
Early or partial results. Treat as a signal, not a conclusion.
This unrefereed computational study proposes the Intersection Euler Characteristic Profile as a certified topological measure of class disentanglement in neural networks and reports that pairwise class interactions dominate triple-class overlaps in 97–99.5% of cells examined across vision and language models. The unnormalized profile mass correlates strongly with test accuracy (R²=0.94), but the work is primarily descriptive and methodological, identifying regularities in network behaviour rather than establishing causal mechanisms or practical improvements to model training or interpretation.
Computational study: large-scale empirical analysis across 111 trained neural networks with factorial design. Neural networks: vision encoders and frozen language models; networks trained under varying conditions (depth, width, data augmentation, weight decay). Intervention: Intersection Euler Characteristic Profile applied to measure topological interaction between labeled point clouds in neural representations. Compared with: Cheap separability statistics and linear probe baseline for predictive performance. n = 111.
Interaction quotients rank class pairs by confusability with Spearman rho=0.83, on par with cheap separability statistics Pairwise dominance: joint entanglement of a class triple sits below its strongest pair in 97% of triple-layer cells and 99.5% of deep cells Unnormalized profile mass predicts test accuracy with R²=0.94; augmentation is the only training choice that separates classes relative to chance
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A methodological study introducing a novel topological measurement framework (Intersection Euler Characteristic Profile) applied across 111 networks and 52,650 measurements, with findings about pairwise class disentanglement; the work is unrefereed, lacks clinical application, and reports descriptive and correlational results rather than establishing causation or practical utility.
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Class disentanglement (the separation of a representation's class-conditional point clouds along depth and over training) is usually read off descriptive curves. We measure it as certified topological interaction between labeled point clouds, using the recently introduced Intersection Euler Characteristic Profile: the Euler characteristic of the overlap of the clouds' ball unions as a function of scale, computed by one Alpha-complex sweep with no boundary-matrix reduction. Every number carries a test: exact permutation tests in both directions, a guarded separation certificate, and a paired test for the comparative claims applications make. Across 111 trained networks and 52,650 certified measurements, disentanglement is depth-graded and concentrated in the first epochs, and interaction quotients rank class pairs by confusability (Spearman rho=0.83), on par with cheap separability statistics. In a 96-model factorial population, augmentation is the one training choice that separates classes relative to chance; weight decay compresses the overlap without separating, and depth and width do nothing. The structural finding is one only a k-fold statistic can pose: the joint entanglement of a class triple sits below that of its strongest pair in 97% of triple-layer cells and 99.5% of deep cells, far below a measured null floor, in vision encoders and frozen language models alike. This pairwise dominance is a regularity, not a law: expected from the nesting of overlaps but not forced by geometry, present at initialization and in raw pixels, and manufactured in the last stage alone when a network memorizes random labels. The unnormalized profile mass predicts test accuracy (R^2=0.94), the quotient does not, and neither beats a linear probe. One lesson is reported in full: the paired test must use a scale-free statistic, or it certifies feature-norm dynamics as disentanglement.
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