Sequential Inverse Mapping of Multi-valued Functions using RNNs

Standard regression models utilizing Mean Squared Error (MSE) loss functions are fundamentally limited when applied to multi-valued mappings, as they converge toward the conditional mean of the target distribution. This paper explores an alternative to the classical Mixture Density Network (MDN) approach for solving such inverse problems. We propose a sequential generative framework using Recurrent Neural Networks (RNNs) to map a single scalar input to a set of multiple valid target values. By imposing a monotonic ordering on the output branches and utilizing a stop-condition mechanism, we demonstrate that a GRU-based architecture can successfully discover and reconstruct complex multi-valued manifolds. Our results show that this approach effectively eliminates the "mean-line" artifacts typically observed in inverse problems while maintaining computational efficiency through vectorized parallel sampling.