{"ID":2853050,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.00012","arxiv_id":"2511.00012","title":"Matrix Phylogeny: Compact Spectral Fingerprints for Trap-Robust Preconditioner Selection","abstract":"Matrix Phylogeny introduces compact spectral fingerprints (CSF/ASF) that characterize matrices at the family level. These fingerprints are low-dimensional, eigendecomposition-free descriptors built from Chebyshev trace moments estimated by Hutchinson sketches. A simple affine rescaling to [-1,1] makes them permutation/similarity invariant and robust to global scaling. Across synthetic and real tests, we observe phylogenetic compactness: only a few moments are needed. CSF with K=3-5 already yields perfect clustering (ARI=1.0; silhouettes ~0.89) on four synthetic families and a five-family set including BA vs ER, while ASF adapts the dimension on demand (median K*~9). On a SuiteSparse mini-benchmark (Hutchinson p~100), both CSF-H and ASF-H reach ARI=1.0. Against strong alternatives (eigenvalue histograms + Wasserstein, heat-kernel traces, WL-subtree), CSF-K=5 matches or exceeds accuracy while avoiding eigendecompositions and using far fewer features (K\u003c=10 vs 64/9153). The descriptors are stable to noise (log-log slope ~1.03, R^2~0.993) and support a practical trap-\u003erecommend pipeline for automated preconditioner selection. In an adversarial E6+ setting with a probe-and-switch mechanism, our physics-guided recommender attains near-oracle iteration counts (p90 regret=0), whereas a Frobenius 1-NN baseline exhibits large spikes (p90~34-60). CSF/ASF deliver compact (K\u003c=10), fast, invariant fingerprints that enable scalable, structure-aware search and recommendation over large matrix repositories. We recommend CSF with K=5 by default, and ASF when domain-specific adaptivity is desired.","short_abstract":"Matrix Phylogeny introduces compact spectral fingerprints (CSF/ASF) that characterize matrices at the family level. These fingerprints are low-dimensional, eigendecomposition-free descriptors built from Chebyshev trace moments estimated by Hutchinson sketches. A simple affine rescaling to [-1,1] makes them permutation/...","url_abs":"https://arxiv.org/abs/2511.00012","url_pdf":"https://arxiv.org/pdf/2511.00012v1","authors":"[\"Jinwoo Baek\"]","published":"2025-10-19T02:35:09Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.LG\"]","methods":"[]","has_code":false}