Transformers can learn broad families of tasks during pretraining and adapt to unseen tasks from a short prompt, but a rigorous understanding of this capability is limited. This paper studies how shared cross‑task structure influences the sample complexity of in‑context learning (ICL) by characterizing task‑space complexity through covering numbers, yielding a set of anchor functions that localize unseen tasks and predict responses. The authors construct a Transformer with Softmax attention to approximate this procedure and derive an error bound that separates the effects of pretraining tasks and prompt length, showing that once enough tasks are available the dependence on prompt length becomes dimension‑free.
By Zhongjie Shi, Rongjie Lai, Alexander Cloninger, Wenjing Liao
arXiv:2606. 29256v1 Announce Type: cross Abstract: In recent years, models based on the Transformer architecture have seen widespread applications and have become one of the core tools in the field of deep 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. 03660v1 Announce Type: cross Abstract: Modern sequence models have a striking capacity for in-context learning (ICL); they can perform new tasks based only on examples given in the prompt.
By Mary Letey, Yue M. Lu, Cengiz Pehlevan, Jacob Zavatone-Veth
arXiv:2512. 11784v2 Announce Type: replace Abstract: Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis.
By Etienne Boursier, Claire Boyer
arXiv:2606. 16694v1 Announce Type: cross Abstract: Transformers are widely used as a general-purpose substrate for learning complex correlations between a large collection of coupled variables, but their internal mechanisms have remained mysterious.
By Ravin Raj, Gautam Reddy
arXiv:2606. 27748v1 Announce Type: cross Abstract: Transformer models rely on attention mechanism to capture long-range dependencies but suffer from quadratic complexity, limiting their scalability to long sequences.
By Haoran Zhang, Feng Zhou
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
arXiv:2609.08981v1 Announce Type: cross
Abstract: A growing body of work establishes that large language models are not mere statistical memorizers, but are capable of in-context learning: performing...
By Arman Adibi, Alireza Jafari, Mohammad Ghavamzadeh, Hadi Daneshmand
arXiv:2606. 25010v1 Announce Type: new Abstract: Neural scaling laws for transformer language models predict smooth improvements in pretraining loss with increasing parameters, but downstream capabilities such as in-context learning are known to emerge abruptly past a certain model scale.
By Vatsal Baherwani, Zixi Chen, Shikai Qiu, Andrew Gordon Wilson, Pavel Izmailov
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:2605. 08475v3 Announce Type: replace-cross Abstract: In this paper, we study in-context kernel ridge regression (KRR) with Gaussian kernels and show, both theoretically and empirically, that a standard softmax-attention transformer can approximate the KRR predictor during its forward pass.
By Mingsong Yan, Dongyang Li, Charles Kulick, Sui Tang