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.
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.
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).
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.
Scaled dot product attention conflates directional alignment and vector magnitude, limiting its effectiveness as a similarity metric in Transformer models. We introduce L1 augmented attention, a simple and computationally parallelizable modification that subtracts a learned, head specific L1 distance between queries and keys from the dot product score.
arXiv:2606. 07205v1 Announce Type: cross Abstract: The attention mechanism is a cornerstone of modern transformer architectures.
arXiv:2607. 20214v1 Announce Type: cross Abstract: The quadratic $N\times N$ attention score matrix remains a central obstacle to extending Transformers to longer input lengths.
arXiv:2607. 07047v1 Announce Type: cross Abstract: Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety.