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

COMPLEX is a closed‑form, training‑free embedding for multiparameter persistence modules that provides both an upper and a lower Lipschitz bound, enabling faithful feature representations. By slicing modules along a near‑diagonal net and embedding each slice with the certified PLACE/PALACE landmark map, the method guarantees that separated modules remain separated in the embedding. On Orbit benchmarks and molecular graph tasks, COMPLEX achieves state‑of‑the‑art accuracy, outperforming existing landmark, transformer, and graph‑based approaches.

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• llms
• rag
• benchmarks