在小型合成数据上预训练，免费实现大规模扩展：用于逻辑规则归纳的感知对称性基础模型
Pretrain on Small Synthetic Data, Scale Large for Free: Symmetry-Aware Foundation Model for Logic Rule Induction
- Institute of Science Tokyo（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出一种感知对称性的逻辑规则归纳基础模型，通过构造强制对称性将小型合成数据预训练的Neural Rule Inducer扩展至更大模式，提升了规则的可迁移性与保真度。
AI中文摘要：
逻辑规则归纳旨在寻找可在命题模式间迁移的可解释规则，这要求遵循原子命名、示例顺序、极性翻转和标签交换等对称性。通过构造强制精确对称性，可使训练得到的归纳器扩展至超出其训练模式的范围。我们的核心贡献是一种规范导出方法，该方法从字面分数中解码出离散规则，无需重新训练，且只要这些分数遵循对称性，该方法就具有精确等变性。我们将其实例化为Neural Rule Inducer（NRI），这是一种仅天然遵循示例顺序的析取范式（DNF）基础模型，我们通过架构、推理和训练恢复其余对称性。在合成压力测试中，支持标签的准确率在更大模式下保持稳定，且对新输入的规则保真度高于未修改的模型；在真实数据上，更大模式的准确率提升最显著。导出的规则在合成全群测试和模式有效的真实数据测试中均为精确的，这是导出方法的数学属性而非特定模型的属性，我们仅在NRI上进行了实证验证。通过构造强制对称性，该小型数据预训练模型转变为可迁移至更大模式的可复用、可解释归纳器。
英文摘要：
Logical rule induction seeks interpretable rules that transfer across propositional schemas. This requires respecting symmetries: atom naming, example order, polarity flips, and label swap. Enforcing exact symmetry by construction lets one trained inducer scale beyond its training schemas. Our central contribution is a canonical export that decodes a discrete rule from literal scores. It needs no retraining and is exactly equivariant whenever those scores respect the symmetries. We instantiate it on the Neural Rule Inducer, a disjunctive-normal-form (DNF) foundation model that natively respects only example order. We restore the remaining symmetries through architecture, inference, and training. On synthetic stress tests, accuracy on the support labels stays stable at much larger schemas, and rule fidelity on fresh inputs remains above the unmodified model. On real data, accuracy improves most on larger schemas. The exported rule is exact on synthetic full-group tests and on schema-valid real-data tests. This is a mathematical property of the export rather than of a specific model, and we validate it empirically only on the NRI. Enforcing symmetry by construction turns this small-data pretrained model into a reusable, interpretable inducer that transfers to larger schemas.
