AI 中文总结
本文提出一种面向恢复的符号蒸馏流程，将神经似然转化为显式表达式，在保持参数恢复精度的同时实现超100倍加速，并适用于多种基于模拟的推断场景。
AI 中文摘要
摊销神经似然使得对具有解析上难以处理或未指定似然的模型进行计算昂贵的推断成为可能，但其黑箱性质限制了可解释性。我们引入了一种符号蒸馏流程，将训练好的神经似然转换为显式、可解释的表达式，并针对高效参数估计进行优化。我们的方法使用面向恢复的目标来引导符号回归，使表达式保持参数恢复的准确性，而不仅仅是近似似然函数。候选表达式在留出数据集上进行评估，并使用一个联合考虑表达式复杂度、参数恢复性能以及与学习到的似然之间的分布距离的标准进行选择。我们在扩散决策模型上评估该流程，这是一个经典的认知模型，其解析上可处理的似然为受控评估提供了真实基准。所提出的面向恢复的目标相比标准符号回归目标，改善了参数恢复。所得的符号似然在参数评估速度上比神经似然以及（在可用时）精确似然快100倍以上，同时保持了可管理的精度损失。我们进一步在经验数据的贝叶斯层次推断中展示了这些计算优势。我们的流程提供了一个轻量级接口，用于将符号蒸馏与现有的神经似然估计方法集成，并可适用于一系列基于模拟的推断设置。
英文摘要
Amortized neural likelihoods enable computationally expensive inference for models with analytically intractable or unspecified likelihoods, but their black-box nature limits interpretability. We introduce a symbolic distillation pipeline that converts trained neural likelihoods into explicit, interpretable expressions optimized for efficient parameter estimation. Our approach uses a recovery-directed objective to guide symbolic regression toward expressions that preserve parameter-recovery accuracy rather than merely approximating the likelihood function. Candidate expressions are evaluated on held-out datasets and selected using a criterion that jointly accounts for expression complexity, parameter-recovery performance, and distributional distance from the learned likelihood. We evaluate the pipeline on the diffusion decision model, a classical cognitive model, whose analytically tractable likelihood provides ground truth for controlled evaluation. The proposed recovery-directed objective improves parameter recovery over standard symbolic-regression objectives. The resulting symbolic likelihoods enable over 100 times faster parameter evaluation than both neural likelihoods and, when available, the exact likelihood, while maintaining a manageable loss in precision. We further demonstrate these computational benefits in Bayesian hierarchical inference on empirical data. Our pipeline provides a lightweight interface for integrating symbolic distillation with existing neural-likelihood estimation methods and can be adapted to a range of simulation-based inference settings.
Comments20 pages, 8 figures, 4 tables
