The paper investigates the theoretical expressive power of Transformers in modeling contextual relations. By framing a text as a distribution of representations and attention as a probabilistic relation, it connects attention normalization to optimal transport: softmax yields conditional relations, while Sinkhorn yields joint relations with fixed marginals. The authors prove universal approximation results, showing that Transformers with Sinkhorn normalization can represent any joint probability relation, whereas standard softmax Transformers can represent any conditional probability relation.
By Demi\'an Fraiman
arXiv:2608.30720v1 Announce Type: new
Abstract: Representational similarity is foundational to analyses of deep networks, yet distances between point-valued representations are not intrinsically tied...
By Kieran Murphy
arXiv:2607. 17060v1 Announce Type: new Abstract: A Bayes-filtered transformer (BFT) is a transformer trained on sequences that are generated in two steps: first a latent task is drawn from a prior, then observations are drawn conditional on that task.
By Afiq Abdillah Effiezal Aswadi, Haotong Ma, Susan Wei
arXiv:2607. 02800v1 Announce Type: new Abstract: Induction heads are attention circuits believed to underlie in-context learning in transformers, yet a precise characterization of the estimators they implement remains elusive.
By Francesco D'Angelo, Oguz Kaan Yuksel, Swathi Shree Narashiman, Nicolas Flammarion
arXiv:2602. 10743v2 Announce Type: replace Abstract: State-space language models such as Mamba and gated linear attention (GLA) offer linear-complexity, parallelisable alternatives to transformers, but their linear state updates limit expressivity and robust state tracking.
By Vaisakh Shaj, Cameron Barker, Aidan Scannell, Andras Szecsenyi, Elliot J. Crowley, Amos Storkey
arXiv:2605. 18079v2 Announce Type: replace Abstract: Existing expressivity results for transformers typically rely on hardmax attention, high precision, and other architectural modifications that disconnect them from the models used in practice.
By Moritz Br\"osamle, Stephan Eckstein
arXiv:2501. 18322v2 Announce Type: replace Abstract: Transformers, which are state-of-the-art in most machine learning tasks, represent the data as sequences of vectors called tokens.
By Val\'erie Castin, Pierre Ablin, Jos\'e Antonio Carrillo, Gabriel Peyr\'e
arXiv:2607. 00479v1 Announce Type: new Abstract: Transformer-based large models have demonstrated remarkable generalization abilities across different tasks by leveraging a context-aware attention module for in-context learning.
By Peilin Liu, Ding-Xuan Zhou
arXiv:2608. 09558v1 Announce Type: new Abstract: How expressive is prompting a transformer?
By Alexander Hsu, Rongjie Lai
arXiv:2607. 18804v1 Announce Type: new Abstract: In the \emph{latent posterior model} of transformer behavior, the next-token distribution arises from a posterior over latent predictive models conditioned on the context, mixed to generate continuations.
By Garrett Baker, Vinayak Pathak, Daniel Murfet, Susan Wei
arXiv:2510. 25013v2 Announce Type: replace-cross Abstract: Mechanistic interpretability aims to reverse-engineer large language models (LLMs) into human-understandable computational circuits.
By Rabin Adhikari
The paper examines how to allocate attention heads and head dimensions across Transformer layers to balance expressivity and efficiency. It provides a mathematical analysis of early layers’ role in information extraction and characterizes the trade‑off between head count and dimension under a fixed parameter budget. The authors prove a saturation effect of softmax activations, showing that increasing head dimensions yields diminishing returns, especially for long sequences, and propose strategies for efficient parameter allocation across layers.
By Ruoxi Yu, Haotian Jiang, Jingpu Cheng, Penghao Yu, Qianxiao Li, Zhong Li