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.

翻译：非单射函数不具备全局可逆性，但通常可将其限制在局部单射的子域内，此时逆映射是良定义的。即使存在多个有效原像或输入输出维度不匹配，在许多场景中仍可选取特定解。本文提出将非单射函数的逆学习问题自然重构为若干局部可逆子问题的集合。具体而言，训练孪生神经网络回归模型以预测已知锚点附近的局部逆修正量。通过将预测结果锚定在同一局部可逆区域内的参考点，该方法能够一致地选择逆映射的有效分支。相较于当前最先进的概率式求逆方法，逆孪生神经网络回归为处理多值逆映射提供了确定性框架。本文通过数学方程定义问题及数据驱动问题验证了该方法的有效性，包括多解玩具问题与机械臂逆运动学求解。