VINA: Variational Invertible Neural Architectures

2026-02-24

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

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Probabilistic Inference
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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

• normalizing flows
• invertible neural networks
• theoretical guarantees
• posterior inference
• generative modeling

Innovation

• Variational Invertible Neural Architectures
• Normalizing Flows
• Invertible Neural Networks
• Theoretical Guarantees
• Unsupervised Loss Functions