Recovery-Directed Symbolic Distillation of Neural Likelihoods
Abstract
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.
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BibTeX
@misc{fernandez2026recoverydirected,
title = {{Recovery-Directed Symbolic Distillation of Neural Likelihoods}},
author = {Kianté Fernandez and Xinwei Li},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32409},
eprint = {2609.32409},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32409},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Recovery-Directed Symbolic Distillation of Neural Likelihoods
AU - Kianté Fernandez
AU - Xinwei Li
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32409
UR - https://arxiv.org/abs/2609.32409
AB - 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.
ER -