# Are Deep Neural Architectures Losing Information? Invertibility Is Indispensable

arXiv: https://arxiv.org/abs/2009.03173 · HTML: https://mlsanity.com/paper/2009.03173/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Sep 2020.

## Built on by (most cited first, 9 of 9)

- [Invertible Denoising Network: A Light Solution for Real Noise Removal](https://mlsanity.com/paper/2104.10546/) (2021)
- [Disentangling Noise from Images: A Flow-Based Image Denoising Neural Network](https://mlsanity.com/paper/2105.04746/) (2021)
- [Understanding and Leveraging the Learning Phases of Neural Networks](https://mlsanity.com/paper/2312.06887/) (2023)
- [Boundary-aware Decoupled Flow Networks for Realistic Extreme Rescaling](https://mlsanity.com/paper/2405.02941/) (2024)
- [The learning phases in NN: From Fitting the Majority to Fitting a Few](https://mlsanity.com/paper/2202.08299/) (2022)
- [HIDFlowNet: A Flow-Based Deep Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2306.17797/) (2023)
- [Synthetic CT Generation via Variant Invertible Network for All-digital Brain PET Attenuation Correction](https://mlsanity.com/paper/2310.01885/) (2023)
- [General Intelligent Imaging and Uncertainty Quantification by Deterministic Diffusion Model](https://mlsanity.com/paper/2408.13061/) (2024)
- [An inpainting approach to manipulate asymmetry in pre-operative breast images](https://mlsanity.com/paper/2502.05652/) (2025)

## Abstract (arXiv)

Ever since the advent of AlexNet, designing novel deep neural architectures for different tasks has consistently been a productive research direction. Despite the exceptional performance of various architectures in practice, we study a theoretical question: what is the condition for deep neural architectures to preserve all the information of the input data? Identifying the information lossless condition for deep neural architectures is important, because tasks such as image restoration require keep the detailed information of the input data as much as possible. Using the definition of mutual information, we show that: a deep neural architecture can preserve maximum details about the given data if and only if the architecture is invertible. We verify the advantages of our Invertible Restoring Autoencoder (IRAE) network by comparing it with competitive models on three perturbed image restoration tasks: image denoising, jpeg image decompression and image inpainting. Experimental results show that IRAE consistently outperforms non-invertible ones. Our model even contains far fewer parameters. Thus, it may be worthwhile to try replacing standard components of deep neural architectures, such as residual blocks and ReLU, with their invertible counterparts. We believe our work provides a unique perspective and direction for future deep learning research.