arXiv AI August 6, 2026 By Alokendu Mazumder, Arnab Roy, Punit Rathore

On Hamming-Lipschitz Type Stability of the Subdominant (Minmax) Ultrametric: Theory and Simple Proofs

arXiv:2608. 04014v1 Announce Type: cross Abstract: The subdominant (minmax) ultrametric is a canonical tree-structured summary of a dissimilarity matrix, arising equivalently as the ultrametric induced by single-linkage clustering.

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arXiv Machine Learning

Sep 23

Intrinsic Interaction Geometry Controls the Low-Rank Complexity of Softmax Attention

arXiv:2608.28150v2 Announce Type: replace Abstract: How much matrix rank is required to preserve every bounded value output of normalized softmax attention? We study the unrestricted maximum-row-\(\e...

By Yuhe Sui, Jianing Zhang, Yingzhi Tang

llms

arXiv Machine Learning

Aug 31

The Approximation Rank of Softmax Attention: Sharp Geometric Laws and Robust Interaction Dimension

arXiv:2608. 28150v1 Announce Type: new Abstract: Which geometry controls the rank complexity of normalized softmax attention?

By Yuhe Sui, Jianing Zhang

arXiv Machine Learning

Aug 10

Sub-Quadratic Bisimulation Metrics via Approximate Nearest Neighbors: Coverage-Augmented Guarantees and Computable Two-Sided Certificates

arXiv:2608. 06762v1 Announce Type: new Abstract: Bisimulation metrics quantify behavioral similarity in Markov decision processes, but their Wasserstein fixed-point operator updates every state pair and incurs quadratic pairwise work.

By Ibne Farabi Shihab, Joyanta Jyoti Mondal

rag reinforcement-learning benchmarks

arXiv Machine Learning

Aug 17

High-dimensional nonparametric changepoint detection via low-rank degree-two density projection

arXiv:2608. 13922v1 Announce Type: new Abstract: Detecting distributional changes in high dimension is difficult when neither the pre-change nor post-change density is parametrically specified.

By Guoqing Zhang, Zhaixin Chen

efficiency benchmarks

Hugging Face Trending Papers

Aug 25

Hyperbolic Latent Geometry for Tree-Structured Prototype Networks: A Local-vs-Global Trade-off

We study a tree-structured regularizer over class-prototype layouts in a hierarchical-classification model and ask whether the choice of latent manifold for the prototypes (Euclidean R^d vs. the Poinc...

rag diffusion

arXiv Machine Learning

Jul 27

Encoding orders and trees in real-valued functions

arXiv:2607. 21761v1 Announce Type: cross Abstract: We prove function-theoretic analogues of a quantitative result of Hodges on extracting the order property from a sufficiently large 2-tree coded in a binary relation.

By G Conant, C Terry

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Intrinsic Interaction Geometry Controls the Low-Rank Complexity of Softmax Attention

The Approximation Rank of Softmax Attention: Sharp Geometric Laws and Robust Interaction Dimension

Sub-Quadratic Bisimulation Metrics via Approximate Nearest Neighbors: Coverage-Augmented Guarantees and Computable Two-Sided Certificates

High-dimensional nonparametric changepoint detection via low-rank degree-two density projection

Hyperbolic Latent Geometry for Tree-Structured Prototype Networks: A Local-vs-Global Trade-off

Encoding orders and trees in real-valued functions