Understanding and Mitigating Exploding Inverses in Invertible Neural Networks
This addresses stability issues in INNs, which are critical for applications like generative modeling and memory-efficient training, though it is incremental as it builds on existing INN frameworks.
The paper identified that invertible neural networks (INNs) suffer from exploding inverses, leading to numerical non-invertibility and failures in tasks like change-of-variables, gradient computation, and sampling. It proposed solutions including a regularizer for local invertibility and stable building blocks for global invertibility.
Invertible neural networks (INNs) have been used to design generative models, implement memory-saving gradient computation, and solve inverse problems. In this work, we show that commonly-used INN architectures suffer from exploding inverses and are thus prone to becoming numerically non-invertible. Across a wide range of INN use-cases, we reveal failures including the non-applicability of the change-of-variables formula on in- and out-of-distribution (OOD) data, incorrect gradients for memory-saving backprop, and the inability to sample from normalizing flow models. We further derive bi-Lipschitz properties of atomic building blocks of common architectures. These insights into the stability of INNs then provide ways forward to remedy these failures. For tasks where local invertibility is sufficient, like memory-saving backprop, we propose a flexible and efficient regularizer. For problems where global invertibility is necessary, such as applying normalizing flows on OOD data, we show the importance of designing stable INN building blocks.