Deep neural networks (DNNs) have achieved significant success in several fields including computer vision, natural language processing, and robot control. The common philosophy behind these success is the use of large amount of annotated data and end-to-end networks with task-specific constraints and priors implicitly incorporated into the trained model without the need for careful feature engineering. However, DNNs are shown to be vulnerable to distribution shifts and adversarial perturbations, which indicates that such implicit priors and constraints are not sufficient for real world applications. In this dissertation, we target three applications and design task-specific constraints and priors for improved performance of deep neural networks.

We first study the problem of subject clustering, the task of grouping face images of the same person together. We propose to utilize the prior structure in the feature space of DNNs trained for face identification to design a novel clustering algorithm. Specifically, the clustering algorithm exploits the local neighborhood structure of deep representations by exemplar-based learning based on k-nearest neighbors (k-NN). Extensive experiments show promising results for grouping face images according to subject identity. As an example, we apply the proposed clustering algorithm to automatically curate a large-scale face dataset with noisy labels and show that the performance of face recognition DNNs can be significantly improved by training on the curated dataset. Furthermore, we empirically find that the k-NN rule does not capture proper local structures for deep representations when each subject has very few face images. We then propose to improve upon the exemplar-based approach by a density-aware similarity measure and theoretically show its asymptotic convergence to a density estimator. We conduct experiments on challenging face datasets that show promising results.

Second, we study the problem of metal artifact reduction in computed tomography (CT). Unlike typical image restoration tasks such as super-resolution and denoising, metal artifacts in CT images are structured and non-local. Conventional DNNs do not generalize well when metal implants with unseen shapes are presented. We find that the imaging process of CT induces a data consistency prior that can be exploited for image enhancement. Based on this observation, we propose a dual-domain learning approach to CT metal artifact reduction. We design and implement a novel Radon inversion layer that allows gradients in the image domain to be backpropagated to the projection domain. Experiments conducted on both simulated datasets and clinical datasets show promising results. Compared to conventional DNN-based models, the proposed dual-domain approach leads to impressive metal artifact reduction and has improved generalization capability.

Finally, we study the problem of robust classification. In the past few years, the vulnerability of DNNs to small imperceptible perturbations has been widely studied, which raises concerns about the security and robustness of DNNs against possible threat models. To defend against threat models, Samangoui et al. proposed DefenseGAN, a preprocessing approach which removes adversarial perturbations by projecting the input images onto the learned data prior. However, the projection operation in DefenseGAN is time-consuming and may not yield proper reconstruction when images have complicated textures. We propose an inversion network to constrain the initial estimates of the latent code for input images. With the proposed constraint, the number of optimization steps in DefenseGAN can be reduced while achieving improved accuracy and robustness. Furthermore, we conduct empirical studies on attack methods that have claimed to break DefenseGAN, which shows that on-manifold robustness might be the key factor for ensuring adversarial robustness.