Certified Topological Interaction in Neural Representations: Exact Tests and the Statistic They Require

arXiv:2609.08561 · cs.LG, math.AT · Submitted 2026-09-08 · Read on arXiv

cs.LG, math.AT

Submitted: 2026-09-08

Updated: 2026-09-18

Comments: 35 pages, 9 figures, 3 tables. Code and measurement records: https://github.com/sushovan4/disentanglement

Code: https://github.com/sushovan4/disentanglement

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 29× in this paper · explained in 1 episode
• Entanglement — 19× in this paper · explained in 3 episodes
• Generalization — 15× in this paper · explained in 13 episodes
• alpha — 14× in this paper · explained in 1 episode
• Calibration — 8× in this paper · explained in 7 episodes
• In International Conference on Learning Representations — 8× in this paper
• Intrinsic Dimension — 7× in this paper · explained in 2 episodes
• Point Clouds — 7× in this paper · explained in 2 episodes
• Robustness — 7× in this paper · explained in 5 episodes
• Transformer — 6× in this paper · explained in 2 episodes
• Linear probe — 5× in this paper · explained in 2 episodes
• In International Conference on Machine Learning — 4× in this paper
• Persistent Homology — 4× in this paper · explained in 3 episodes
• Conference on Computer Vision and Pattern Recognition — 2× in this paper
• Consistency — 2× in this paper · explained in 3 episodes
• Ablation — 1× in this paper · explained in 1 episode
• Adversarial Search — 1× in this paper · explained in 1 episode
• Ambient Dimension — 1× in this paper · explained in 1 episode
• Contrastive Learning — 1× in this paper · explained in 5 episodes
• Corruption Robustness — 1× in this paper · explained in 2 episodes
• Exchangeability — 1× in this paper · explained in 2 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Ontology — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Steering — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes

Sources

• Understanding intermediate layers using linear classifier probes
• Chromatic Topological Data Analysis
• The Intersection Euler Characteristic Profile: Euler Calculus and Stability for Topological Interaction of Ball Unions
• Detecting Regime Transitions in Dynamical Systems via the Mixup Euler Characteristic Profile
• A Closed-Form Adaptive-Landmark Kernel for Certified Point-Cloud and Graph Classification
• Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets
• Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds

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