# A Paired Autoencoder Framework for Inverse Problems via Bayes Risk Minimization

arXiv: https://arxiv.org/abs/2501.14636 · HTML: https://mlsanity.com/paper/2501.14636/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2025.

## Built on by (most cited first, 6 of 6)

- [Good Things Come in Pairs: Paired Autoencoders for Inverse Problems](https://mlsanity.com/paper/2505.06549/) (2025)
- [Latent Twins](https://mlsanity.com/paper/2509.20615/) (2025)
- [Optimal Linear Baseline Models for Scientific Machine Learning](https://mlsanity.com/paper/2508.05831/) (2025)
- [Latent Space Inference via Paired Autoencoders](https://mlsanity.com/paper/2601.11397/) (2026)
- [Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification](https://mlsanity.com/paper/2602.02948/) (2026)
- [A nonlinear extension of parametric model embedding for dimensionality reduction in parametric shape design](https://mlsanity.com/paper/2605.11759/) (2026)

## Abstract (arXiv)

In this work, we describe a new data-driven approach for inverse problems that exploits technologies from machine learning, in particular autoencoder network structures. We consider a paired autoencoder framework, where two autoencoders are used to efficiently represent the input and target spaces separately and optimal mappings are learned between latent spaces, thus enabling forward and inverse surrogate mappings. We focus on interpretations using Bayes risk and empirical Bayes risk minimization, and we provide various theoretical results and connections to existing works on low-rank matrix approximations. Similar to end-to-end approaches, our paired approach creates a surrogate model for forward propagation and regularized inversion. However, our approach outperforms existing approaches in scenarios where training data for unsupervised learning are readily available but training pairs for supervised learning are scarce. Furthermore, we show that cheaply computable evaluation metrics are available through this framework and can be used to predict whether the solution for a new sample should be predicted well.