Set Prediction in the Latent Space

Set prediction tasks require the matching between predicted set and ground truth set in order to propagate the gradient signal. Recent works have performed this matching in the original feature space thus requiring predefined distance functions. We propose a method for learning the distance function by performing the matching in the latent space learned from encoding networks. This method enables the use of teacher forcing which was not possible previously since matching in the feature space must be computed after the entire output sequence is generated. Nonetheless, a naive implementation of latent set prediction might not converge due to permutation instability. To address this problem, we provide sufficient conditions for permutation stability which begets an algorithm to improve the overall model convergence. Experiments on several set prediction tasks, including image captioning and object detection, demonstrate the effectiveness of our method.