Tag: equivariant
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Improving Equivariant Networks with Probabilistic Symmetry Breaking
Improving Equivariant Networks with Probabilistic Symmetry Breaking arXiv:2503.21985v1 Announce Type: cross Abstract: Equivariance encodes known symmetries into neural networks, often enhancing generalization. However, equivariant networks cannot break symmetries: the output of an equivariant network must, by definition, have at least the same self-symmetries as the input. This poses an important problem, both (1) for prediction…
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Mathematical Foundation of Interpretable Equivariant Surrogate Models
Mathematical Foundation of Interpretable Equivariant Surrogate Models arXiv:2503.01942v1 Announce Type: new Abstract: This paper introduces a rigorous mathematical framework for neural network explainability, and more broadly for the explainability of equivariant operators called Group Equivariant Operators (GEOs) based on Group Equivariant Non-Expansive Operators (GENEOs) transformations. The central concept involves quantifying the distance between GEOs by…
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Generalization Bounds for Equivariant Networks on Markov Data
Generalization Bounds for Equivariant Networks on Markov Data arXiv:2503.00292v1 Announce Type: new Abstract: Equivariant neural networks play a pivotal role in analyzing datasets with symmetry properties, particularly in complex data structures. However, integrating equivariance with Markov properties presents notable challenges due to the inherent dependencies within such data. Previous research has primarily concentrated on establishing…
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Symmetry and Generalisation in Machine Learning
Symmetry and Generalisation in Machine Learning arXiv:2501.03858v1 Announce Type: cross Abstract: This work is about understanding the impact of invariance and equivariance on generalisation in supervised learning. We use the perspective afforded by an averaging operator to show that for any predictor that is not equivariant, there is an equivariant predictor with strictly lower test…