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Computer Science > Machine Learning

arXiv:2410.11687 (cs)
[Submitted on 15 Oct 2024]

Title:State-space models can learn in-context by gradient descent

Authors:Neeraj Mohan Sushma, Yudou Tian, Harshvardhan Mestha, Nicolo
Colombo, David Kappel, Anand Subramoney
View a PDF of the paper titled State-space models can learn
in-context by gradient descent, by Neeraj Mohan Sushma and 5 other
authors
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    Abstract:Deep state-space models (Deep SSMs) have shown
    capabilities for in-context learning on autoregressive tasks,
    similar to transformers. However, the architectural requirements
    and mechanisms enabling this in recurrent networks remain
    unclear. This study demonstrates that state-space model
    architectures can perform gradient-based learning and use it for
    in-context learning. We prove that a single structured
    state-space model layer, augmented with local self-attention, can
    reproduce the outputs of an implicit linear model with least
    squares loss after one step of gradient descent. Our key insight
    is that the diagonal linear recurrent layer can act as a gradient
    accumulator, which can be `applied' to the parameters of the
    implicit regression model. We validate our construction by
    training randomly initialized augmented SSMs on simple linear
    regression tasks. The empirically optimized parameters match the
    theoretical ones, obtained analytically from the implicit model
    construction. Extensions to multi-step linear and non-linear
    regression yield consistent results. The constructed SSM
    encompasses features of modern deep state-space models, with the
    potential for scalable training and effectiveness even in general
    tasks. The theoretical construction elucidates the role of local
    self-attention and multiplicative interactions in recurrent
    architectures as the key ingredients for enabling the expressive
    power typical of foundation models.

Comments: 16 pages, 5 figures
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI);
          Neural and Evolutionary Computing (cs.NE)
Cite as:  arXiv:2410.11687 [cs.LG]
          (or arXiv:2410.11687v1 [cs.LG] for this version)
          https://doi.org/10.48550/arXiv.2410.11687
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Yudou Tian [view email]
[v1] Tue, 15 Oct 2024 15:22:38 UTC (585 KB)
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