Technology Category
Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Probabilistic InferenceComputer Vision: Generative Adversarial Networks (GANs) for Vision
VINA: Variational Invertible Neural Architectures
🤖 AI Summary
This work addresses the lack of theoretical guarantees in existing invertible neural networks and normalizing flows for posterior inference and generative modeling under realistic assumptions. The authors propose a unified framework based on a variational unsupervised loss that provides provable approximation quality for both tasks under weaker, more practical assumptions. By leveraging tools such as the Precision-Recall divergence, they derive general design principles and practical guidelines that effectively integrate invertible architectures with generative modeling techniques. The efficacy of the approach is demonstrated in real-world applications, including ocean acoustic inversion, where it significantly enhances modeling accuracy and practical utility.
Technology Category
Application Category
📝 Abstract
The distinctive architectural features of normalizing flows (NFs), notably bijectivity and tractable Jacobians, make them well-suited for generative modeling. Invertible neural networks (INNs) build on these principles to address supervised inverse problems, enabling direct modeling of both forward and inverse mappings. In this paper, we revisit these architectures from both theoretical and practical perspectives and address a key gap in the literature: the lack of theoretical guarantees on approximation quality under realistic assumptions, whether for posterior inference in INNs or for generative modeling with NFs. We introduce a unified framework for INNs and NFs based on variational unsupervised loss functions, inspired by analogous formulations in related areas such as generative adversarial networks (GANs) and the Precision-Recall divergence for training normalizing flows. Within this framework, we derive theoretical performance guarantees, quantifying posterior accuracy for INNs and distributional accuracy for NFs, under assumptions that are weaker and more practically realistic than those used in prior work. Building on these theoretical results, we conduct extensive case studies to distill general design principles and practical guidelines. We conclude by demonstrating the effectiveness of our approach on a realistic ocean-acoustic inversion problem.
Problem
Research questions and friction points this paper is trying to address.
normalizing flows
invertible neural networks
theoretical guarantees
posterior inference
generative modeling
Innovation
Methods, ideas, or system contributions that make the work stand out.
Variational Invertible Neural Architectures
Normalizing Flows
Invertible Neural Networks
Theoretical Guarantees
Unsupervised Loss Functions
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