Longhorn: State Space Models are Amortized Online Learners

ICLR 2025 Conference Submission3419 Authors

Keywords: Deep State Space Models, Linear Attention Models, Online Learning, Language Modeling

TL;DR: We present a unified framework to design state space models as solving online learning problems, and propose a new architecture that implicitly conducts online associative recall.

Abstract:

The most fundamental capability of modern AI methods such as Large Language Models (LLMs) is the ability to predict the next token in a long sequence of tokens, known as “sequence modeling.” Although the Transformers model is the current dominant approach to sequence modeling, its quadratic computational cost with respect to sequence length is a significant drawback. State-space models (SSMs) offer a promising alternative due to their linear decoding efficiency and high parallelizability during training. However, existing SSMs often rely on seemingly ad hoc linear recurrence designs.
In this work, we explore SSM design through the lens of online learning, conceptualizing SSMs as meta-modules for specific online learning problems. This approach links SSM design to formulating precise online learning objectives, with state transition rules derived from optimizing these objectives.
Based on this insight, we introduce a novel deep SSM architecture based on the implicit update for optimizing an online regression objective. Our experimental results show that our models outperform state-of-the-art SSMs, including the Mamba model, on standard sequence modeling benchmarks and language modeling tasks.

Primary Area: foundation or frontier models, including LLMs

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Submission Number: 3419