mlsanityData to 7 Oct 2026

Tensor learning with orthogonal, Lorentz, and symplectic symmetries

arXiv 2406.01552 ↗First posted 3 Jun 2024stat.ML cs.AI cs.LGcited by 3

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Abstract (arXiv)

Tensors are a fundamental data structure for many scientific contexts, such as time series analysis, materials science, and physics, among many others. Improving our ability to produce and handle tensors is essential to efficiently address problems in these domains. In this paper, we show how to exploit the underlying symmetries of functions that map tensors to tensors. More concretely, we develop universally expressive equivariant machine learning architectures on tensors that exploit that, in many cases, these tensor functions are equivariant with respect to the diagonal action of the orthogonal, Lorentz, and/or symplectic groups. We showcase our results on three problems coming from material science, theoretical computer science, and time series analysis. For time series, we combine our method with the increasingly popular path signatures approach, which is also invariant with respect to reparameterizations. Our numerical experiments show that our equivariant models perform better than corresponding non-equivariant baselines.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 44 of its 74 references that are in the map. First posted on arXiv 3 Jun 2024.

Builds on

44 of 74 references.

References · 44

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32 more
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Cited by year

Citing papers per year: 2025: 3.

3 papers.

  1. 2025Representing spherical tensors with scalar-based machine-learning modelscited by 2
  2. 2025Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equationscited by 1
  3. 2025Constructing 3D Rotational Invariance and Equivariance with Symmetric Tensor Networkscited by 0