This paper targets the task with discrete and periodic class labels (e.g., pose/orientation estimation) in the context of deep learning. The commonly used cross-entropy or regression loss is not well matched to this problem as they ignore the periodic nature of the labels and the class similarity, or assume labels are continuous value. We propose to incorporate inter-class correlations in a Wasserstein training framework by pre-defining (i.e., using arc length of a circle) or adaptively learning the ground metric. We extend the ground metric as a linear, convex or concave increasing function w.r.t. arc length from an optimization perspective. We also propose to construct the conservative target labels which model the inlier and outlier noises using a wrapped unimodal-uniform mixture distribution. Unlike the one-hot setting, the conservative label makes the computation of Wasserstein distance more challenging. We systematically conclude the practical closed-form solution of Wasserstein distance for pose data with either one-hot or conservative target label. We evaluate our method on head, body, vehicle and 3D object pose benchmarks with exhaustive ablation studies. The Wasserstein loss obtaining superior performance over the current methods, especially using convex mapping function for ground metric, conservative label, and closed-form solution.

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AI Safety is a major concern in many deep learning applications such as autonomous driving. Given a trained deep learning model, an important natural problem is how to reliably verify the model's prediction. In this paper, we propose a novel framework --- deep verifier networks (DVN) to detect unreliable inputs or predictions of deep discriminative models, using separately trained deep generative models. Our proposed model is based on conditional variational auto-encoders with disentanglement constraints to separate the label information from the latent representation. We give both intuitive and theoretical justifications for the model. Our verifier network is trained independently with the prediction model, which eliminates the need of retraining the verifier network for a new model. We test the verifier network on both out-of-distribution detection and adversarial example detection problems, as well as anomaly detection problems in structured prediction tasks such as image caption generation. We achieve state-of-the-art results in all of these problems.

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AI Safety is a major concern in many deep learning applications such as autonomous driving. Given a trained deep learning model, an important natural problem is how to reliably verify the model's prediction. In this paper, we propose a novel framework -deep verifier networks (DVN) to verify the inputs and outputs of deep discriminative models with deep generative models. Our proposed model is based on conditional variational auto-encoders with disentanglement constraints. We give both intuitive and theoretical justifications of the model. Our verifier network is trained independently with the prediction model, which eliminates the need of retraining the verifier network for a new model. We test the verifier network on outof-distribution detection and adversarial example detection problems, as well as anomaly detection problems in structured prediction tasks such as image caption generation. We achieve state-of-the-art results in all of these problems.