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COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modules

arXiv · AI, language, vision and robotics · article · Sep 18, 2026 · UTC

Every multiparameter persistence vectorization we know of carries a one-sided Lipschitz upper bound and nothing below it: without a lower gauge there is no sense in which the features are faithful, and no per-prediction guarantee can be built on them. This paper supplies the missing side. COMPLEX is a closed-form, training-free embedding of multiparameter modules -- slice the module along a fixed near-diagonal net, embed each slice barcode by the certified PLACE/PALACE landmark map, concatenate. Under a checkable witnessing-slice coherence condition, holding on 100% of audited pairs on Orbit5k

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Evidence & attribution

arXiv · AI, language, vision and robotics · 2026-09-18T17:08:41.000Z

First collected: 2026-09-23T13:51:27.104Z. This is not the publication date.