MatrixNet通过学习群表示，提升对称性任务的样本效率与泛化能力。
MatrixNet: Learning over symmetry groups using learned group representations
- 用学习的矩阵表示替代预定义群表示，灵活建模对称性
- 在有限群与辫群上，相比基线模型提升样本效率和泛化性能
- 能保持群运算关系，推广至训练时未见的长词序列
群论在机器学习中为机器人学、蛋白质建模等任务提供了基于对称变换的理论框架。现有方法依赖预定义的群表示构建等变神经网络。本文提出MatrixNet，一种通过学习矩阵形式表示群元素输入的神经网络架构。该方法在多个有限群及Artin辫群上的预测任务中，显著提升了样本效率与泛化能力。同时，MatrixNet能保持群运算关系，实现对训练集中未出现的更长词序列的泛化。
原文摘要 · Abstract (English)
Group theory has been used in machine learning to provide a theoretically grounded approach for incorporating known symmetry transformations in tasks from robotics to protein modeling. In these applications, equivariant neural networks use known symmetry groups with predefined representations to learn over geometric input data. We propose MatrixNet, a neural network architecture that learns matrix representations of group element inputs instead of using predefined representations. MatrixNet achieves higher sample efficiency and generalization over several standard baselines in prediction tasks over the several finite groups and the Artin braid group. We also show that MatrixNet respects group relations allowing generalization to group elements of greater word length than in the training set.
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