arXiv:2608. 01283v1 Announce Type: new Abstract: All Transformer-based large language models compute attention via the Euclidean inner product, an architectural choice that Dong et al.
Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direction is equally meaningful, but there is no reason...
arXiv:2609.27988v1 Announce Type: cross Abstract: Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direc...
arXiv:2605. 18848v3 Announce Type: replace Abstract: This paper introduces Exact Linear Attention (ELA), a mechanism that achieves linear computational complexity for Transformer attention by exploiting the exact decomposition property of kernel functions, thereby eliminating approximation error.
arXiv:2607. 10677v1 Announce Type: new Abstract: Self-attention is a ubiquitous primitive in modern sequence models, yet its operator-level geometry is only partially understood.
The paper studies matrices built from block‑diagonal factors interleaved with fixed permutations, a structured family useful in deep learning for balancing expressivity and efficiency. By applying Riemannian geometry, the authors determine when this class forms a smooth manifold and develop Riemannian tools for the orthogonal two‑factor case. They propose efficient algorithms that use automatic differentiation, allow parameter sharing, and avoid dense matrix construction, testing them on matrix approximation and fine‑tuning large language models, while also exploring properties of factorizations with more factors.
arXiv:2608. 10416v1 Announce Type: cross Abstract: We present a theoretical foundation for inverse-distance attention, from its Euclidean prototype (Resolver) to its non-Euclidean realization (Riemann GeoResolver).
arXiv:2605. 24942v2 Announce Type: replace-cross Abstract: Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention transformations without learning an explicit geometry over paths in activation space.
arXiv:2606. 13276v1 Announce Type: cross Abstract: Weight-space geometry plays a central role in neural network optimization, yet manifold constraints are often applied uniformly across all weight matrices.
arXiv:2601. 11618v2 Announce Type: replace-cross Abstract: Geometric Attention (GA) specifies an attention layer by four independent inputs: a finite carrier (what indices are addressable), an evidence-kernel rule (how masked proto-scores and a link induce nonnegative weights), a probe family (which observables are treated as admissible), and an anchor/update rule (which representative kernel is selected and how it is applied).
arXiv:2609.10305v1 Announce Type: new Abstract: Language models under one million parameters matter for edge deployment, domain adaptation, and reproducible research, yet a two-layer LSTM or Transfor...
Weight-space geometry plays a central role in neural network optimization, yet manifold constraints are often applied uniformly across all weight matrices. In this work, we ask whether different transformer modules prefer different manifold geometries.
arXiv:2607. 18027v1 Announce Type: new Abstract: Scaled dot product attention conflates directional alignment and vector magnitude, limiting its effectiveness as a similarity metric in Transformer models.