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[2601.05378] Inverting Non-Injective Functions with Twin Neural Network Regression
Summary
This article presents a novel approach to inverting non-injective functions using Twin Neural Network Regression, focusing on locally invertible subdomains to resolve multi-valued mappings effectively.
Why It Matters
Understanding how to invert non-injective functions is crucial in various fields, including robotics and machine learning, where multiple valid outputs may exist for a given input. This research offers a deterministic method that improves upon probabilistic approaches, potentially enhancing accuracy and reliability in applications like inverse kinematics.
Key Takeaways
- Introduces Twin Neural Network Regression for inverting non-injective functions.
- Focuses on locally invertible subdomains to ensure valid inversions.
- Demonstrates effectiveness on mathematical and data-defined problems.
- Offers a deterministic framework, contrasting with existing probabilistic methods.
- Applicable in fields such as robotics and complex data analysis.
Computer Science > Machine Learning arXiv:2601.05378 (cs) [Submitted on 8 Jan 2026 (v1), last revised 18 Feb 2026 (this version, v2)] Title:Inverting Non-Injective Functions with Twin Neural Network Regression Authors:Sebastian J. Wetzel View a PDF of the paper titled Inverting Non-Injective Functions with Twin Neural Network Regression, by Sebastian J. Wetzel View PDF HTML (experimental) Abstract: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. Subjects: Machine Learning (...
