arXiv:2609. 20278v1 Announce Type: cross Abstract: Text, knowledge graphs, and hypergraphs all have elements that play distinct roles within relation instances, structure that is lost when data is flattened into token sequences.
arXiv:2606. 07205v1 Announce Type: cross Abstract: The attention mechanism is a cornerstone of modern transformer architectures.
arXiv:2606. 19411v3 Announce Type: replace Abstract: Selecting a fixed-size subset that maximizes the determinant of a positive semidefinite kernel is the MAP problem for a size-constrained determinantal point process and the classical maximum-entropy sampling problem.
arXiv:2608. 15466v1 Announce Type: new Abstract: Distributional changes can be invisible to means and covariances yet appear in skewness, asymmetric interactions, or other third-order structure.
arXiv:2601.01405v3 Announce Type: replace-cross Abstract: Ball Mapper summarizes a finite metric dataset by covering the sample with closed balls centered at selected landmarks and connecting landmar...
arXiv:2610. 41218v1 Announce Type: new Abstract: Why does length generalization (LG) depend so sharply on the positional encoding (PE)?
The paper investigates how a vanilla Transformer learns symmetries from finite data augmentation on point cloud datasets. It finds an ordering of learnability: non-angle-preserving symmetries are easiest, followed by angle-preserving symmetries, and finally base angle-preserving subgroups such as translation, rotation, and scale. The study also examines the Transformer's extrapolation behavior, performs a structural analysis of trained models to uncover interpretable mechanisms for invariance, and extends these findings to equivariant functions, suggesting that the identified mechanisms can serve as building blocks for learned equivariance.
arXiv:2610.03556v1 Announce Type: new Abstract: Empirical claims about the connection between over-squashing and long-range interactions in GNNs, can only be trusted if the benchmarks used to validat...
arXiv:2607. 03112v1 Announce Type: cross Abstract: We revisit random projections for reducing the dimension of high-dimensional polygonal curves.
This paper introduces the Sierpiński-Knopp (SK) Wasserstein distance, a fast metric between persistence diagrams. The SK-Wasserstein distance, denoted $d_{\mathrm{SK}}$, maps diagram points and their...
arXiv:2607. 22757v1 Announce Type: cross Abstract: We introduce Graded Large Language Models (GLLMs), an algebraic framework that equips the representation space of a transformer with a grading and propagates the induced weighted scalar action through embeddings, self-attention, and the training objective.
How many directions does a neural representation use to encode a concept? A common answer repeatedly erases probe directions and reports the stopping count or cumulative removed rank.