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arXiv · 2508.12837

Learning In-context n-grams with Transformers: Sub-n-grams Are Near-stationary Points

Aditya Varre·Gizem Yüce·Nicolas Flammarion
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Abstract

Motivated by empirical observations of prolonged plateaus and stage-wise progression during training, we investigate the loss landscape of transformer models trained on in-context next-token prediction tasks. In particular, we focus on learning in-context $n$-gram language models under cross-entropy loss, and establish a sufficient condition for parameter configurations to be stationary points. We then construct a set of parameter configurations for a simplified transformer model that represent $k$-gram estimators (for $k \leq n$), and show that the gradient of the population loss at these solutions vanishes in the limit of infinite sequence length and parameter norm. This reveals a key property of the loss landscape: {sub-$n$-grams are near-stationary points of the population cross-entropy loss}, offering theoretical insight into widely observed phenomena such as stage-wise learning dynamics and emergent phase transitions. These insights are further supported by numerical experiments that illustrate the learning dynamics of $n$-grams, characterized by discrete transitions between near-stationary solutions.

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Aditya Varre, Gizem Yüce, Nicolas Flammarion. 2025-08-18. Learning In-context n-grams with Transformers: Sub-n-grams Are Near-stationary Points. https://arxiv.org/abs/2508.12837

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