用双神经网络解决多解反问题，稳定选出正确解。
Inverting Non-Injective Functions with Twin Neural Network Regression
- 以已知锚点为中心，学习局部逆映射的修正量
- 在多解场景下始终选择同一分支，结果稳定可靠
- 适合需要确定性解的机器人逆运动学等任务
非单射函数全局不可逆，但可在局部单射子域内定义逆映射。许多场景下即使存在多个有效原像，仍可选定偏好解，或处理输入输出维度不同的情况。本文将非单射函数的逆学习问题重新表述为一系列局部可逆问题。具体而言，双神经网络回归模型训练用于预测围绕已知锚点的局部逆映射修正值。通过将预测锚定在同一局部可逆区域内，该方法始终选择逆映射的有效分支。与现有概率型先进方法不同，逆双神经网络回归是一种确定性框架，用于解决多值逆映射问题。实验展示了该方法在数学方程和数据驱动问题上的应用，包括多解玩具问题和机器人臂逆运动学。
原文摘要 · Abstract (English)
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.
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