A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classification
arXiv:2605.02836v2 Announce Type: replace Abstract: We introduce PLACE (Persistence-Landmark Analytic Classification Engine), a closed-form pipeline for classifying point clouds and graphs through their persistent-homology signatures. Three quantitative guarantees -- a margin-based excess-risk rate, a closed-form descriptor-selection rule, and a per-prediction certificate -- are derived from training labels alone, with no learned weights or held-out calibration. The embedding sums Mitra-Virk single-point coordinate functions over a sparse landmark grid; the closed-form weight rule $w_k^2 \prop
The increasing complexity and opacity of AI models necessitate new methods for verifiable robustness and certification, especially for critical applications.
This development offers a potential pathway to more transparent, certifiable, and robust AI systems, which is crucial for trust and widespread adoption in sensitive domains.
The ability to classify complex data like point clouds and graphs with closed-form, certifiable guarantees shifts the paradigm from purely statistical confidence to mathematical assurance in certain AI tasks.
- · AI certification bodies
- · High-stakes AI applications (defense, medical, autonomous driving)
- · Topological data analysis researchers
- · AI models without explainability or certification
Increased trust and adoption of AI in industries requiring high assurance and interpretability.
Development of new industry standards and regulatory frameworks for certifiable AI components.
Shift in AI research priorities towards explainability, robustness, and formal verification methodologies over purely performance-driven metrics.
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Read at arXiv cs.LG