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arXiv:2605. 13768v2 Announce Type: replace-cross Abstract: This is the second part of the work investigating quantized matrix multiplication (MatMul).
The paper introduces TORQUE, a framework that enhances quantization by jointly optimizing which coordinates to keep at high precision before and after applying uniform random rotations, all within a fixed bit budget. By preserving large input coordinates before rotation and the largest-magnitude coordinates after rotation, TORQUE reduces quantization error and allows efficient use of offline-optimized codebooks. The authors provide an error upper bound, prove that top‑k pre‑rotation retention is optimal for each k, and demonstrate improved accuracy‑storage tradeoffs in Gaussian models and practical tasks such as nearest‑neighbor retrieval, KV‑cache compression, and activation compression.
arXiv:2609. 02155v1 Announce Type: new Abstract: The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of $n$ points to $m=O(\varepsilon^{-2}\log n)$ dimensions preserves pairwise squared distances within relative error $\varepsilon$ with high probability, and this dimension order is asymptotically optimal.
arXiv:2606. 11255v1 Announce Type: new Abstract: Bernstein--Schur kernels are products of a finite-feature kernel (one with an explicit finite-dimensional feature map) and a completely monotone shift-invariant kernel: nonstationary kernels that fall between the shift-invariant and dot-product templates random features usually exploit, so in general neither Bochner sampling nor polynomial sketching applies to the full kernel directly.
arXiv:2606. 10458v1 Announce Type: cross Abstract: We derive the optimal quantizer of a real-valued random variable $W$ with distribution $P_W$ such that 1) the distribution of the quantization output $X$ that can take $k$ values follows any specified distribution $P_X$ over $\{1,\ldots,k\}$, and 2) the minimum mean squared error (MMSE) of estimating $W$ from $X$ is minimized.
DANCo (Dimensionality from Angle and Norm Concentration) jointly calibrates nearest-neighbor distance and angular statistics and consistently reaches state-of-the-art accuracy on clean intrinsic-dimen...