arXiv:2603. 02238v2 Announce Type: replace Abstract: Length generalization is a key property of a learning algorithm that enables it to make correct predictions on inputs of any length, given finite training data.
By Andy Yang, Pascal Bergstr\"a{\ss}er, Georg Zetzsche, David Chiang, Anthony W. Lin
arXiv:2609.08851v1 Announce Type: new
Abstract: Recent advancements in transformer length generalization theory enable us to reliably predict when a transformer can learn to solve a task. In particul...
By Georg Zetzsche, Hongjian Jiang, Andy Yang, Pascal Bergstr\"a{\ss}er, Marco S\"alzer, David Chiang, Anthony W. Lin
arXiv:2605. 22223v2 Announce Type: replace Abstract: We study how we can leverage only a handful of characteristics of a transformer's architecture to closely predict the number of different sequences it can output, both qualitatively and quantitatively.
By Maxime Meyer, Mario Michelessa, Caroline Chaux, Vincent Y. F. Tan
arXiv:2606. 09731v1 Announce Type: new Abstract: We tightly characterize the VC dimension of depth-$L$ Transformers with a total of $W$ parameters, mapping an input sequence of length $T$ to a single output, establishing an upper bound of $O(L W \log (T W))$ and a nearly matching lower bound of $\Omega(L W \log (T W / L))$.
By Chenxiao Yang, Nathan Srebro, Zhiyuan Li
arXiv:2606. 07205v1 Announce Type: cross Abstract: The attention mechanism is a cornerstone of modern transformer architectures.
By Justin Y. Chen, Ying Feng, Piotr Indyk, Michael Kapralov, Ekaterina Kochetkova, Boris Prokhorov
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