arXiv Machine Learning By Lan V. Truong

On Generalisation Error Bounds for Transformers

Read the original on arXiv Machine Learning →

arXiv:2410. 11500v2 Announce Type: replace-cross Abstract: In this paper, we establish a collection of covering number bounds for linear function classes under various norm constraints on the inputs and matrices.

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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 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
Aug 11

How Many Different Outputs Can a Transformer Generate?

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 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