What question did this study set out to answer?

This research aims to connect various theoretical aspects of nonlinear approximation and their implications for deep learning models, particularly transformers.

June 20, 2026Open Access

Stability, Expressivity, and Spectra

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MAMiquel Noguer AlonsoAllen Institute for Artificial Intelligence

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Implication

Randomized trial explores stability and expressivity in transformer models, suggesting new optimization strategies.

Key Points

This research aims to connect various theoretical aspects of nonlinear approximation and their implications for deep learning models, particularly transformers.
Developed a theorem-based framework connecting nonlinear approximation and gradient-flow reachability.
Introduced finite-sample results and a uniform risk bound for classes generated from training samples.
Conducted eight reproducible numerical experiments to test various aspects of transformer models.
Risk bound confirmed on independent holdout samples; complexity controlled by initialization entropy and function-space path length.
Resolved residual ball dimension scales as O(√(d_T/n)) under bounded spectral leverage, showing dependence on target energy and spectral filter.
Gradient flow and optimal error scaling provide insights for improving transformer efficiency and performance.

Cite This Study

Miquel Noguer Alonso (2026) studied this question.

synapsesocial.com/papers/6a3632d2db0793dc1a5394fa https://doi.org/10.5281/zenodo.20750285

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Stability, Expressivity, and Spectra

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Implication

Key Points

Cite This Study

Stability, Expressivity, and Spectra

Discussion

Member takes

Implication

Key Points

Cite This Study

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