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arXiv · 2411.01035

Provable Length Generalization in Sequence Prediction via Spectral Filtering

Annie Marsden·Evan Dogariu·Naman Agarwal·Xinyi Chen·Daniel Suo·Elad Hazan
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Abstract

We consider the problem of length generalization in sequence prediction. We define a new metric of performance in this setting -- the Asymmetric-Regret -- which measures regret against a benchmark predictor with longer context length than available to the learner. We continue by studying this concept through the lens of the spectral filtering algorithm. We present a gradient-based learning algorithm that provably achieves length generalization for linear dynamical systems. We conclude with proof-of-concept experiments which are consistent with our theory.

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Annie Marsden, Evan Dogariu, Naman Agarwal, Xinyi Chen, Daniel Suo, Elad Hazan. 2024-11-01. Provable Length Generalization in Sequence Prediction via Spectral Filtering. https://arxiv.org/abs/2411.01035

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