A single design choice determines whether machine learning models of materials make physically impossible predictions
- URL: http://arxiv.org/abs/2608.18714v1
- Date: Wed, 19 Aug 2026 09:14:55 GMT
- Title: A single design choice determines whether machine learning models of materials make physically impossible predictions
- Abstract summary: Machine-learned models are replacing first-principles calculations across materials discovery.<n>Some constraints are exact: symmetry forces certain property tensors to exactly zero, so a nonzero prediction is physically impossible rather than inaccurate.<n>We show that whether a model can make such predictions is decided before training by one rarely reported design bit.
- Score: 2.3982445219832678
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Machine-learned models are replacing first-principles calculations across materials discovery, and physical symmetry is the central guarantee built into them. The debate over how much symmetry to hard-wire rather than learn has run on rotations, where a symmetry error is an approximation error. Some constraints are exact: symmetry forces certain property tensors to exactly zero, so a nonzero prediction is physically impossible rather than inaccurate. Here we show that whether a model can make such predictions is decided before training by one rarely reported design bit, whether its features carry parity labels, and derive a criterion, the parity gap, that computes from group theory alone which properties and crystals are exposed. Across matched architecture pairs differing only in that bit, evaluated on two thousand centrosymmetric crystals whose piezoelectric tensor must vanish, parity-labelled arms sit at the floating-point floor while rotation-only arms predict forbidden responses on 90-96% of crystals, six orders of magnitude apart, at no accuracy cost. Training on explicit zeros does not recover exactness, and a head on a frozen universal potential inherits its backbone's symmetry group. One reflection at random initialization verifies the label in seconds.
Related papers
- More Data Cannot Break a Symmetry: Identifiability by Design [13.778717173535577]
Unsupervised representational alignment recovers a stimulus-by-stimulus correspondence from geometry alone.<n>The automorphism group of the stimulus geometry bounds what any such alignment can identify, before data exist.<n>We turn this known in geometry into a design-time diagnostic and intervention.
arXiv Detail & Related papers (2026-08-27T19:38:09Z) - Intrinsic Structure: Spectral Identifiability for Mechanistic Interpretability [51.56484100374058]
We prove the first identifiability theorem for a mechanistic-interpretability primitive.<n>The spectrum is an identifiable, model-intrinsic fingerprint with a stated error bar, not a legible decomposition.
arXiv Detail & Related papers (2026-08-10T19:42:01Z) - Exploiting More Than Symmetry in Variational Quantum Machine Learning [2.9695823613761316]
We use Tic-Tac-Toe as a fully enumerable and structurally transparent test case.<n>We find that suitable subgroups preserve most of the generalization benefit.<n>The dominant gains arise from gates acting directly on decisive task motifs.
arXiv Detail & Related papers (2026-06-18T14:52:54Z) - Aligning Network Equivariance with Data Symmetry: A Theoretical Framework and Adaptive Approach for Image Restoration [71.51826063983434]
Image restoration is an inherently ill posed inverse problem.<n>We use non strict symmetry as a constraint to formulate the restoration inverse problem.<n>We show that the equivariance error of the optimal restoration operator is strictly bounded by the data symmetry error and the discretization mesh size.
arXiv Detail & Related papers (2026-05-13T16:22:19Z) - Time Symmetry, Retrocausality, and Emergent Collapse: The Tlalpan Interpretation of Quantum Mechanics [51.56484100374058]
The Tlalpan Interpretation (QTI) proposes that the wavefunction collapse is not a primitive, axiomatic rule but an emergent phenomenon.<n>The novelty of QTI lies in its embedding of collapse within the conceptual language of critical phenomena in statistical physics.
arXiv Detail & Related papers (2025-08-25T20:30:56Z) - On Equivariant Model Selection through the Lens of Uncertainty [49.137341292207]
Equivariant models leverage prior knowledge on symmetries to improve predictive performance, but misspecified architectural constraints can harm it instead.<n>We compare frequentist (via Conformal Prediction), Bayesian (via the marginal likelihood), and calibration-based measures to naive error-based evaluation.<n>We find that uncertainty metrics generally align with predictive performance, but Bayesian model evidence does so inconsistently.
arXiv Detail & Related papers (2025-06-23T13:35:06Z) - Probing the effects of broken symmetries in machine learning [0.0]
We show that non-symmetric models can learn symmetries from data, and that doing so can even be beneficial for the accuracy of the model.
We focus specifically on physical observables that are likely to be affected -- directly or indirectly -- by symmetry breaking, finding negligible consequences when the model is used in an interpolative, bulk, regime.
arXiv Detail & Related papers (2024-06-25T17:34:09Z) - A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction [89.38877696273364]
We consider the prediction of general tensor properties of crystalline materials.
We propose a General Materials Network (GMTNet), which is carefully designed to satisfy the required symmetries.
Experimental results show that our GMTNet achieves promising performance on crystal tensors of various orders.
arXiv Detail & Related papers (2024-06-03T16:26:16Z) - Generative Adversarial Symmetry Discovery [19.098785309131458]
LieGAN represents symmetry as interpretable Lie algebra basis and can discover various symmetries.
The learned symmetry can also be readily used in several existing equivariant neural networks to improve accuracy and generalization in prediction.
arXiv Detail & Related papers (2023-02-01T04:28:36Z) - Don't Just Blame Over-parametrization for Over-confidence: Theoretical
Analysis of Calibration in Binary Classification [58.03725169462616]
We show theoretically that over-parametrization is not the only reason for over-confidence.
We prove that logistic regression is inherently over-confident, in the realizable, under-parametrized setting.
Perhaps surprisingly, we also show that over-confidence is not always the case.
arXiv Detail & Related papers (2021-02-15T21:38:09Z) - Breaking Symmetries of the Reservoir Equations in Echo State Networks [0.0]
We find that the simplest popular setup has a harmful symmetry, which leads to the prediction of what we call mirror-attractor.
Similar problems can arise in a general context, and we use them to explain the success or failure of some designs.
arXiv Detail & Related papers (2020-09-21T16:00:22Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.