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arXiv · 2610.32748

On the Identifiability of Hybrid Deep Generative Models: Meta-Learning as a Solution

Yubo Ye·Maryam Toloubidokhti·Sumeet Vadhavkar·Xiajun Jiang·Huafeng Liu·Linwei Wang
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Abstract

The interest in leveraging physics-based inductive bias in deep learning has resulted in recent development of hybrid deep generative models (hybrid-DGMs) that integrate 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 construct a hybrid-DGM with theoretically-proven identifiability? This paper provides the first theoretical probe into the identifiability of hybrid-DGMs, and presents 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. Code is available at https://github.com/GoForIt-YYB/Meta-Hybrid-VAE.

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Yubo Ye, Maryam Toloubidokhti, Sumeet Vadhavkar, Xiajun Jiang, Huafeng Liu, Linwei Wang. 2026-10-23. On the Identifiability of Hybrid Deep Generative Models: Meta-Learning as a Solution. https://doi.org/10.52202/079017-0247

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