Part of Advances in Neural Information Processing Systems 37 (NeurIPS 2024) Main Conference Track
Yubo Ye, Maryam Tolou, Sumeet Vadhavkar, Xiajun Jiang, Huafeng Liu, Linwei Wang
The interest in leveraging physics-based inductive bias in deep learning has resulted in recent development of hybrid deep generative models (hybrid-DGMs) that integrates known physics-based mathematical expressions in neural generative models. To identify these hybrid-DGMs requires inferring parameters of the physics-based component along with their neural component. The identifiability of these hybrid-DGMs, however, has not yet been theoretically probed or established. How does the existing theory of the un-identifiability of general DGMs apply to hybrid-DGMs? What may be an effective approach to consutrct a hybrid-DGM with theoretically-proven identifiability? This paper provides the first theoretical probe into the identifiability of hybrid-DGMs, and present meta-learning as a novel solution to construct identifiable hybrid-DGMs. On synthetic and real-data benchmarks, we provide strong empirical evidence for the un-identifiability of existing hybrid-DGMs using unconditional priors, and strong identifiability results of the presented meta-formulations of hybrid-DGMs.