arXiv Machine Learning By Michael Rizvi-Martel, Satwik Bhattamishra, Guillaume Rabusseau, Michael Hahn

From Expressivity to Sample Complexity: Narrow Teachers for Transformers via C-RASP

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arXiv:2607. 11760v1 Announce Type: new Abstract: A theoretical understanding of Transformers is crucial to better understand the capacities and limitations of large language models (LLMs).

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arXiv Machine Learning
Sep 10

Length Generalization for Transformers via Compression

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 Machine Learning
Jun 2

Length Generalization Bounds for Transformers

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 AI
Jul 7

On the Ability of Transformers to Verify Plans

arXiv:2603. 19954v2 Announce Type: replace Abstract: Transformers have shown inconsistent success in AI planning tasks, and theoretical understanding of when generalization should be expected has been limited.

By Yash Sarrof, Yupei Du, Katharina Stein, Alexander Koller, Sylvie Thi\'ebaux, Michael Hahn
arXiv Machine Learning
Jun 9

Tight Sample Complexity of Transformers

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 Machine Learning
Sep 2

Performance-Efficiency Tradeoffs in Transformers: An Approximation Theory Perspective

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