mlsanityData to 14 Oct 2026

Adjusted Cup-Product Neural Layer

arXiv 2606.13568 ↗First posted 11 Jun 2026cs.LG math-ph math.MPcited by 0

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Abstract (arXiv)

Many important observables in physics and geometry are cup products of cochains. The adjusted cup product neural layer has been introduced in this paper. It is a neural primitive that hard wires the cup product with an adjustment term from higher gauge theory. This creates a readout that is gauge invariant by design. Their main theoretical result shows that on a closed cycle the output relies entirely on the adjustment coefficient. Setting this coefficient to zero removes the output completely regardless of other parameters. Thus the adjustment is the only source of gauge invariant signal. They prove this observable is a nonzero quadratic form and is exactly invariant under one and two gauge transformations.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 15 of its 21 references that are in the map. First posted on arXiv 11 Jun 2026.

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15 of 21 references.

References · 15

  1. 2019Gauge Equivariant Convolutional Networks and the Icosahedral CNNcited by 267
  2. 2018A General Theory of Equivariant CNNs on Homogeneous Spacescited by 228
  3. 2021Weisfeiler and Lehman Go Topological: Message Passing Simplicial Networkscited by 221
  4. 2020Simplicial Neural Networkscited by 110
  5. 2021Principled Simplicial Neural Networks for Trajectory Predictioncited by 77
  6. 2020Lattice gauge equivariant convolutional neural networkscited by 45
  7. 2024E(n) Equivariant Topological Neural Networkscited by 22
  8. 2017Machine Learning Topological Invariants with Neural Networkscited by 19
  9. 2018Deep Learning Topological Invariants of Band Insulatorscited by 10
  10. 2026Gauge-Equivariant Graph Neural Networks for Lattice Gauge Theoriescited by 3
  11. 2021Persistent Cup-Lengthcited by 2
  12. 2023Higher Order Gauge Equivariant CNNs on Riemannian Manifolds and Applicationscited by 2
3 more
  1. 2025Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networkscited by 2
  2. 2022Cup Product Persistence and Its Efficient Computationcited by 1
  3. 2023Haldane Bundles: A Dataset for Learning to Predict the Chern Number of Line Bundles on the Toruscited by 1

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