让普通模型学会对称性，无需预设结构。
Symmetry From Scratch: Group Equivariance as a Supervised Learning Task
- 将对称性学习当作监督任务，从等变模型中克隆对称行为。
- 普通MLP可直接学习并保留或打破特定对称性。
- 适合需要灵活对称性控制的模型设计者。
在具有对称性的机器学习数据集中，传统方法通过放宽等变架构约束，并额外引入权重来区分关注的对称性。然而，当模型针对特定对称性/非对称性进行硬编码时，该方法会变得过度工程化。本文提出对称性克隆（symmetry-cloning）方法，使通用机器学习架构（如MLP）能够直接作为监督学习任务，从等变架构中学习对称性，并在下游任务中选择保留或打破所学对称性。该方法使无群结构依赖的模型能获得等变架构的归纳偏置。
原文摘要 · Abstract (English)
In machine learning datasets with symmetries, the paradigm for backward compatibility with symmetry-breaking has been to relax equivariant architectural constraints, engineering extra weights to differentiate symmetries of interest. However, this process becomes increasingly over-engineered as models are geared towards specific symmetries/asymmetries hardwired of a particular set of equivariant basis functions. In this work, we introduce symmetry-cloning, a method for inducing equivariance in machine learning models. We show that general machine learning architectures (i.e., MLPs) can learn symmetries directly as a supervised learning task from group equivariant architectures and retain/break the learned symmetry for downstream tasks. This simple formulation enables machine learning models with group-agnostic architectures to capture the inductive bias of group-equivariant architectures.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。