Matrix Bernstein
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Kikuchi Graphs of Random Hypergraphs are Approximately Johnson
arXiv:2606.08597v1 Announce Type: new Abstract: We prove that level-$\ell$ Kikuchi graphs of random $2r$-uniform hypergraphs spectrally approximate the Kikuchi graph of the complete $2r$-uniform hypergraph at a sampling rate that is sharp up to a logarithmic factor, in the regime $r\leq \ell \leq n/2$. Our proof is based on the matrix Bernstein inequality, but, unlike prior works, we apply it to an appropriate collection of blocks of Johnson eigenspaces. Our analysis relies on a new, simple...
Adjacency Spectral Radius Under Laplacian Sparsification: Deterministic and Probabilistic Bounds
arXiv:2606.07459v1 Announce Type: cross Abstract: Spielman-Srivastava spectral sparsification preserves Laplacian quadratic forms to within (1 +/- epsilon), but does not directly control the adjacency spectral radius lambda_1, which governs the NIMFA epidemic threshold and arises in spectral clustering. We prove |lambda_1(A_H) - lambda_1(A_G)| <= epsilon(2 Delta - lambda_1) deterministically, with a sharp epsilon*lambda_1 bound for reweighting sparsifiers via Perron-Frobenius monotonicity....
Col-Bandit: Query-Time Top-$K$ Estimation for Late-Interaction Retrieval
Announce Type: replace Abstract: Multi-vector late-interaction retrievers such as ColBERT achieve state-of-the-art quality, but their query-time cost is dominated by exhaustively computing token-level MaxSim interactions for every candidate document. The MaxSim scores of $N$ candidates against $T$ query tokens form an $N\times T$ matrix whose row-sums are the late-interaction scores, and identifying the top-$K$ rarely requires every entry. We introduce Col-Bandit, a query-time estimator of...
Upstart chipmakers keep challenging Nvidia. This time it's Microsoft-backed D-Matrix
In the increasingly competitive AI chip market, there's another startup in production that claims an advantage over Nvidia, the world's most valuable company. D-Matrix, located three miles away from Nvidia's Silicon Valley headquarters, says its chips can run inference workloads 10 times faster and using five times less energy than a standalone graphics processing unit from the market leader — as long as the workloads are small. The new inference chip, called Corsair, takes a novel approach...