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arXiv · 2601.16514

Finite-Time Analysis of Gradient Descent for Shallow Transformers

Enes Arda·Semih Cayci·Atilla Eryilmaz
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Abstract

Understanding why Transformers perform so well remains challenging due to their non-convex optimization landscape. In this work, we analyze a shallow Transformer with $m$ independent heads trained by projected gradient descent in the kernel regime. Our analysis reveals two main findings: (i) the width required for nonasymptotic guarantees scales only logarithmically with the sample size $n$, and (ii) the optimization error is independent of the sequence length $T$. This contrasts sharply with recurrent architectures, where the optimization error can grow exponentially with $T$. The trade-off is memory: to keep the full context, the Transformer's memory requirement grows with the sequence length. We validate our theoretical results numerically in a teacher-student setting and compare Transformers with recurrent architectures on an autoregressive task.

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Enes Arda, Semih Cayci, Atilla Eryilmaz. 2026-01-23. Finite-Time Analysis of Gradient Descent for Shallow Transformers. https://arxiv.org/abs/2601.16514

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