cs.DS · 2026-08-12 · No. 82

Data Structures and Algorithms, 2026-08-12.

2 new papers in cs.DS. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

2 entries
  1. 01

    Improving TensorSketch Using Complex Random Variables

    Amit Sharma, Mohammad Azhar Khan, Rameshwar Pratap, Keegan Kang

    cs.DS · cs.AI · stat.ML

    \texttt{TensorSketch} by~\cite{pham2013fast,kar2012random} provides efficient sketching algorithms for high-dimensional polynomial kernels $\vec{x}^{\otimes p} \in \R^{d^p}$. \cite{kar2012random} uses dense Johnson-Lindenstrauss (JL)-type projections with computational cost $O(pDd)$, where $D$ denotes the sketch dimension, whereas~\cite{pham2013fast} extends the sparse \texttt{CountSketch}~\citep{count_sketch} algorithm, yielding a faster...

    arxiv.org/abs/2608.10523 · PDF

  2. 02

    Riemann GeoResolver: A Non-Euclidean Attention Framework from Euclidean Resolver to Hyperbolic-Spherical Geometry

    Liangchen Ge

    cs.DS · cs.AI · cs.CL · cs.LG

    We present a theoretical foundation for inverse-distance attention, from its Euclidean prototype (Resolver) to its non-Euclidean realization (Riemann GeoResolver). The Euclidean part establishes three core theorems: (1) circuit separation---IDA achieves exact retrieval with $\mathcal{O}(1)$ resources while softmax requires $Ω((\log n)^2)$ width; (2) a Polyak--Lojasiewicz inequality with $Ω(e^{Δ^2/\sqrt{d}}/Δ^2)$ stronger constant than...

    arxiv.org/abs/2608.10416 · PDF

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