The spectral weak-recovery threshold for linearized AMP in the multi-view spiked Wigner model is SNR(λ,B)=1, where SNR is the largest eigenvalue of Diag(√λ)(B⊙B)Diag(√λ), and this coincides with the information-theoretic threshold for a broad class of spike priors.
Proceedings of the forty-seventh annual ACM symposium on Theory of computing , pages=
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An efficient algorithm recovers phylogenetic trees from Θ(n) noisy quartets under random classification noise, matching the information-theoretic lower bound and achieving near-optimal quartet distance.
Triplet constraints realizable in D-dimensional Euclidean space cannot be preserved above 50% accuracy by any embedding of dimension at most cD for constant c<1, with UGC-hardness preventing better polynomial-time solutions in any dimension.
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Sharp Spectral Thresholds for Multi-View Spiked Wigner Models
The spectral weak-recovery threshold for linearized AMP in the multi-view spiked Wigner model is SNR(λ,B)=1, where SNR is the largest eigenvalue of Diag(√λ)(B⊙B)Diag(√λ), and this coincides with the information-theoretic threshold for a broad class of spike priors.
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Optimal Phylogenetic Reconstruction from Sampled Quartets
An efficient algorithm recovers phylogenetic trees from Θ(n) noisy quartets under random classification noise, matching the information-theoretic lower bound and achieving near-optimal quartet distance.
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Provable Accuracy Collapse in Embedding-Based Representations under Dimensionality Mismatch
Triplet constraints realizable in D-dimensional Euclidean space cannot be preserved above 50% accuracy by any embedding of dimension at most cD for constant c<1, with UGC-hardness preventing better polynomial-time solutions in any dimension.