用期望最大化算法统一神经符号学习，无需符号部分可微。
EM-NeSy: Expectation Maximization for Neurosymbolic Learning
- 将神经符号学习建模为EM算法，分推断与优化两步。
- 在近似推理下仍有效，且不需符号组件可微。
- 兼顾效率与可解释性，适合复杂逻辑推理任务。
神经符号（NeSy）模型结合神经网络与符号推理，实现稳健且可解释的AI。现有先进NeSy模型要求符号部分可微，常导致近似推理复杂化。本文提出EM-NeSy，将概率性NeSy学习视为期望最大化（EM）算法实例。在期望步中，通过概率推理计算神经预测符号在标签条件下的后验分布；在最大化步中，仅通过神经组件使用梯度下降更新参数。该框架充分释放了EM算法在NeSy学习中的潜力，使模型自然扩展至近似推理，无需额外修改或符号组件可微性要求。同时，在精确推理下可恢复标准端到端梯度学习设定。实验表明，EM-NeSy具备良好的可扩展性与计算效率。
原文摘要 · Abstract (English)
Neurosymbolic (NeSy) models integrate neural networks and symbolic reasoning for robust and interpretable AI. State-of-the-art NeSy models require that the symbolic component is expressed in a differentiable way, often complicating the use of approximate inference. We propose EM-NeSy which casts probabilistic NeSy learning as an instance of the Expectation-Maximization (EM) algorithm. In the expectation step, we compute the posterior over the neurally predicted symbols conditioned on the label via probabilistic inference. In the maximization step, we update the neural parameters based on this posterior using gradient descent only through the neural component. This formulation unlocks the full potential of the EM algorithm for NeSy learning. It allows NeSy to extend naturally to approximate reasoning without any additional modifications or differentiability requirements of the symbolic component. Furthermore, it recovers the standard end-to-end gradient-based NeSy setting under exact inference. Our experimental results demonstrate the scalability and computational efficiency of EM-NeSy.
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