Spectrum-Adaptive Generalization Bounds for Trained Deep Transformers

Mana Sakai; Masaaki Imaizumi

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arXiv · 2605.07297

Spectrum-Adaptive Generalization Bounds for Trained Deep Transformers

Mana Sakai·Masaaki Imaizumi

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Abstract

Understanding why trained Transformers generalize well is a fundamental problem in modern machine learning theory, and complexity-based generalization bounds provide a principled way to study this question. While existing norm-based bounds for Transformers remove the explicit polynomial dependence on the hidden dimension, they typically impose fixed norm constraints specified a priori and can exhibit unfavorable exponential dependence on depth. In this paper, we derive spectrum-adaptive post hoc generalization bounds for multi-layer Transformers. Under layerwise spectral norm control, the bounds are expressed in terms of layerwise Schatten quantities of the query-key, value, and feedforward weight matrices. Since the Schatten indices need not be fixed a priori and can instead be selected after training, separately for each matrix type and layer, the bounds adaptively trade off spectral complexity against the dimension- and depth-dependent factors according to the learned singular-value profiles. Empirical comparisons of BERT-adapted proxies for the leading complexity factors suggest that the proxies induced by our bounds grow more slowly with depth and hidden dimension than the corresponding norm-based proxies. Overall, our results provide a complexity-based perspective on how the spectral structure of trained Transformers is reflected in generalization analyses.

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BibTeX RIS

Mana Sakai, Masaaki Imaizumi. 2026-05-08. Spectrum-Adaptive Generalization Bounds for Trained Deep Transformers. https://arxiv.org/abs/2605.07297

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