# Inverting Non-Injective Functions with Twin Neural Network Regression

arXiv: https://arxiv.org/abs/2601.05378 · HTML: https://mlsanity.com/paper/2601.05378/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 8 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [NETT: Solving Inverse Problems with Deep Neural Networks](https://mlsanity.com/paper/1803.00092/) (2018)
- [Manifold Learning by Mixture Models of VAEs for Inverse Problems](https://mlsanity.com/paper/2303.15244/) (2023)
- [Spectral Reconstruction with Deep Neural Networks](https://mlsanity.com/paper/1905.04305/) (2019)
- [Regularization of Inverse Problems by Neural Networks](https://mlsanity.com/paper/2006.03972/) (2020)
- [Twin Neural Network Regression](https://mlsanity.com/paper/2012.14873/) (2020)
- [Twin Neural Network Regression is a Semi-Supervised Regression Algorithm](https://mlsanity.com/paper/2106.06124/) (2021)
- [Same or Different? Diff-Vectors for Authorship Analysis](https://mlsanity.com/paper/2301.09862/) (2023)
- [Twin Neural Network Improved k-Nearest Neighbor Regression](https://mlsanity.com/paper/2310.00664/) (2023)
- [Pairwise Difference Learning for Classification](https://mlsanity.com/paper/2406.20031/) (2024)
- [How to get the most out of Twinned Regression Methods](https://mlsanity.com/paper/2301.01383/) (2023)

## Abstract (arXiv)

Non-injective functions are not globally invertible. However, they can often be restricted to locally injective subdomains where the inversion is well-defined. In many settings a preferred solution can be selected even when multiple valid preimages exist or input and output dimensions differ. This manuscript describes a natural reformulation of the inverse learning problem for non-injective functions as a collection of locally invertible problems. More precisely, Twin Neural Network Regression is trained to predict local inverse corrections around known anchor points. By anchoring predictions to points within the same locally invertible region, the method consistently selects a valid branch of the inverse. In contrast to current probabilistic state-of-the art inversion methods, Inverse Twin Neural Network Regression is a deterministic framework for resolving multi-valued inverse mappings. I demonstrate the approach on problems that are defined by mathematical equations or by data, including multi-solution toy problems and robot arm inverse kinematics.