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Computer Science > Machine Learning

arXiv:2312.06937 (cs)
[Submitted on 12 Dec 2023]

Title:Can a Transformer Represent a Kalman Filter?

Authors:Gautam Goel, Peter Bartlett
Download a PDF of the paper titled Can a Transformer Represent a
Kalman Filter?, by Gautam Goel and 1 other authors
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    Abstract:Transformers are a class of autoregressive deep learning
    architectures which have recently achieved state-of-the-art
    performance in various vision, language, and robotics tasks. We
    revisit the problem of Kalman Filtering in linear dynamical
    systems and show that Transformers can approximate the Kalman
    Filter in a strong sense. Specifically, for any observable LTI
    system we construct an explicit causally-masked Transformer which
    implements the Kalman Filter, up to a small additive error which
    is bounded uniformly in time; we call our construction the
    Transformer Filter. Our construction is based on a two-step
    reduction. We first show that a softmax self-attention block can
    exactly represent a certain Gaussian kernel smoothing estimator.
    We then show that this estimator closely approximates the Kalman
    Filter. We also investigate how the Transformer Filter can be
    used for measurement-feedback control and prove that the
    resulting nonlinear controllers closely approximate the
    performance of standard optimal control policies such as the LQG
    controller.

Subjects: Machine Learning (cs.LG); Machine Learning (stat.ML)
Cite as:  arXiv:2312.06937 [cs.LG]
          (or arXiv:2312.06937v1 [cs.LG] for this version)
          https://doi.org/10.48550/arXiv.2312.06937
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Gautam Goel [view email]
[v1] Tue, 12 Dec 2023 02:13:50 UTC (27 KB)
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