Saved in:
Bibliographic Details
Main Author: Wetzel, Sebastian J.
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.05378
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866915803288305664
author Wetzel, Sebastian J.
author_facet Wetzel, Sebastian J.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_05378
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Inverting Non-Injective Functions with Twin Neural Network Regression
Wetzel, Sebastian J.
Machine Learning
Robotics
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.
title Inverting Non-Injective Functions with Twin Neural Network Regression
topic Machine Learning
Robotics
url https://arxiv.org/abs/2601.05378