[Submitted on 20 Oct 2026]
Title:Motion Equivariant Convolutional LSTM: When Motion Becomes a Gauge Symmetry
View a PDF of the paper titled Motion Equivariant Convolutional LSTM: When Motion Becomes a Gauge Symmetry, by Vahid Hosseinzadeh and 2 other authors
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Abstract:Objects move, cameras pan, and weather drifts with the wind: much of what changes in sequential data is motion. Motion changes where things are, not what they are, and is therefore a symmetry of the data. Yet standard recurrent networks are not equivariant to it: their memory stays put while the input moves on. Flow equivariant recurrent networks first brought this symmetry into sequence models, for motions of constant velocity, or flows, by enumerating a bank of velocities. We extend this idea in three directions: from simple recurrent networks to convolutional LSTMs, from flows to motions whose velocity changes in time, and from enumerating velocities to estimating them. Treating a sequence as a field over time, we show that motion becomes a gauge symmetry: a global symmetry made local in time. Built on this view, our motion equivariant convolutional LSTM (MELSTM) uses its velocity model as the gauge field and is provably equivariant to every motion. Across future-frame prediction, classification of digits visible only through their motion, and action recognition under camera shake, MELSTM outperforms a convolutional LSTM and its flow equivariant counterpart with the same number of parameters: it is more accurate, generalizes to longer horizons and to unseen motions, and carries a fraction of the flow equivariant model's state.
Comments: Code: this https URL
Subjects:
Machine Learning (cs.LG); Computer Vision and Pattern Recognition (cs.CV)
Cite as: arXiv:2610.28771 [cs.LG]
(or arXiv:2610.28771v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.28771
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Vahid Hosseinzadeh [view email] [v1] Tue, 20 Oct 2026 18:08:45 UTC (5,780 KB)
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