The paper investigates how post‑softmax attention weights behave across different language models by marginalizing over query positions to create a joint token‑head space. Across more than 60 diverse LLMs, token‑wise marginal attention reveals a text‑intrinsic signal that is conserved across models, while head‑wise marginal attention yields a model‑private signature that is consistent across documents. This insight enables a practical method for estimating per‑head budgets for key‑value cache eviction, achieving competitive performance on standard benchmarks without per‑document recomputation or training.
By Valentino Maiorca, Walter Nelson, Francesco Locatello
arXiv:2602. 01893v2 Announce Type: replace-cross Abstract: We present a geometric framework for analysing multi-head attention in large language models (LLMs).
By Timur Mudarisov, Mikhal Burtsev, Tatiana Petrova, Radu State
arXiv:2608. 11427v1 Announce Type: new Abstract: Full attention exposes every token pair, whereas kernel attention compresses a sequence into a fixed-dimensional sketch.
By Vicente Opazo
arXiv:2608. 30417v2 Announce Type: replace Abstract: We give a complete characterization of equivariant multi-head self-attention (MHSA): if an MHSA layer is equivariant to a symmetry group $G$, then $G$ can only act by permuting head-clusters, with QK and OV matrices satisfying an equivariance constraint tied to the group action.
By T\=ikun \^Ong, Georg B\"okman
arXiv:2607. 07047v1 Announce Type: cross Abstract: Understanding the geometric structure of pre-trained language model embeddings matters for interpretability and safety.
By Szczepan Konior, Alexandre Quemy, Przemys{\l}aw Klocek, Gr\'egoire Cattan, Bart{\l}omiej Sobieski
arXiv:2509. 07963v2 Announce Type: replace Abstract: The core component of attention is the scoring function, which transforms the inputs into low-dimensional queries and keys and takes the dot product of each pair.
By Yilun Kuang, Noah Amsel, Sanae Lotfi, Shikai Qiu, Andres Potapczynski, Andrew Gordon Wilson
arXiv:2602.04852v3 Announce Type: replace
Abstract: Linear attention offers a computationally efficient yet expressive alternative to softmax attention. However, recent empirical results indicate tha...
By Philipp Nazari, T. Konstantin Rusch
Full attention exposes every token pair, whereas kernel attention compresses a sequence into a fixed-dimensional sketch. We show that this distinction becomes exponential at the first context length containing two competing candidates.
arXiv:2608.30417v1 Announce Type: new
Abstract: We give a complete characterization of equivariant multi-head self-attention (MHSA): if an MHSA layer is equivariant to a symmetry group $G$, then $G$...
By T\=ikun \^Ong
The paper investigates the training dynamics of attention mechanisms in high-dimensional settings, focusing on attention-indexed models that encompass multi-layer and multi-head architectures. It shows that while the loss landscape can be described by a finite set of trace order parameters, the online stochastic gradient descent dynamics involve an infinite hierarchy of matrix moments that can be accurately approximated by a finite truncated system. The study further reveals that the choice of attention parameterization acts as an implicit bias: untied attention can get trapped in uninformative states, whereas tied attention induces symmetry breaking and enables weak recovery with θ(d² log d) samples, and untied attention exhibits a fast-slow dynamic leading to weak recovery when symmetry is broken.
By Yizhou Xu, Margarita Sagitova, Lenka Zdeborov\'a, Florent Krzakala
arXiv:2602. 15029v3 Announce Type: replace Abstract: The internal representations learned by language models consistently exhibit striking geometric structure: calendar months organize into a circle, historical years form a smooth one-dimensional manifold, and cities' latitudes and longitudes can be decoded using a linear probe.
By Dhruva Karkada, Daniel J. Korchinski, Andres Nava, Matthieu Wyart, Yasaman Bahri
The paper introduces Outlier-Aware Attention Linearization (OAL), a method that improves linearized softmax attention by explicitly accounting for a few outlier dimensions that disproportionately affect query-key dot products. OAL builds on a second-order Taylor approximation, uses a Hadamard-product formulation to expose dimension-specific contributions, and groups dimensions with similar scales to share coefficients while treating outliers separately. Experiments on Qwen2.5-0.5B show an 8.9% reduction in frozen-attention output MSE, and fine-tuning with LoRA lowers WikiText-103 perplexity from 31.71 to 27.50 while boosting performance on PIQA, HellaSwag, and ARC-E.
By Weiqi Sun, Qianyue Wu, Wenjia Wang, Tianyang Hu