Further, this does not limit the shapes of symmetry groups we can learn. For instance, we find the Euclidean group, which is itself a curved manifold with non-trivial topology.🧵12/16
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If one wishes, we could extend to non-quadratic conserved quantities to model non-affine actions. More free-form conserved quantities would require ODE-solving instead of the matrix exponential and have more parameters, which could complicate the Bayesian model selection.🧵13/16
Our work demonstrates that approximate Bayesian model selection can be useful in neural nets, even in sophisticated use cases. We aim to further improve the efficiency and usability of neural model selection, making it a more integral part of training deep neural nets. 🧵14/16
Noether's razor allows symmetries to be parameterised in terms of conserved quantities and enables automatic symmetry at train time. This results in more accurate Hamiltonians that obey symmetry and trajectory predictions that remain more accurate over longer time spans.🧵15/16
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Come check out our poster at NeurIPS 2024 in Vancouver.
East Exhibit Hall A-C #4710, Fri 13 Dec 1-4 pm CST
Link: https://neurips.cc/virtual/2024/poster/94316
Paper/code: https://arxiv.org/abs/2410.08087
Thankful to co-authors @mvdw.bsky.social and @pimdehaan for their joint supervision of this project
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