Researchers have identified intrinsic geometric challenges in deep generative models (DGMs) that hinder their ability to accurately represent complex target distributions. These difficulties arise from the underlying transport problem, not specific architectures or training methods. The study establishes quantitative lower bounds on gradients and Jacobians, showing that heavy-tailed or multimodal target distributions necessitate larger gradients in the transport map, impacting expressivity and numerical stability. The findings suggest that these obstructions can be mitigated by using bijective reparametrizations for density approximation, as supported by numerical experiments. AI
IMPACT Identifies fundamental limitations in deep generative models, potentially guiding future research towards more stable and expressive architectures.
RANK_REASON Academic paper published on arXiv detailing theoretical findings about deep generative models. [lever_c_demoted from research: ic=1 ai=1.0]
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