Machine learning has demonstrated great potential across a wide range of applications such as computer vision, robotics, speech recognition, drug discovery, material science, and physics simulation. Despite its current success, however, there are still two major challenges for machine learning algorithms: limited robustness and generalizability.

The robustness of a neural network is defined as the stability of the network output under small input perturbations. It has been shown that neural networks are very sensitive to input perturbations, and the prediction from convolutional neural networks can be totally different for input images that are visually indistinguishable to human eyes. Based on such property, hackers can reversely engineer the input to trick machine learning systems in targeted ways. These adversarial attacks have shown to be surprisingly effective, which has raised serious concerns over safety-critical applications like autonomous driving. In the meantime, many established defense mechanisms have shown to be vulnerable under more advanced attacks proposed later, and how to improve the robustness of neural networks is still an open question.

The generalizability of neural networks refers to the ability of networks to perform well on unseen data rather than just the data that they were trained on. Neural networks often fail to carry out reliable generalizations when the testing data is of different distribution compared with the training one, which will make autonomous driving systems risky under new environment. The generalizability of neural networks can also be limited whenever there is a scarcity of training data, while it can be expensive to acquire large datasets either experimentally or numerically for engineering applications, such as material and chemical design.

In this dissertation, we are thus motivated to improve the robustness and generalizability of neural networks. Firstly, unlike traditional bottom-up classifiers, we use a pre-trained generative model to perform top-down reasoning and infer the label information. The proposed generative classifier has shown to be promising in handling input distribution shifts. Secondly, we focus on improving the network robustness and propose an extension to adversarial training by considering the transformation invariance. Proposed method improves the robustness over state-of-the-art methods by 2.5% on MNIST and 3.7% on CIFAR-10. Thirdly, we focus on designing networks that generalize well at predicting physics response. Our physics prior knowledge is used to guide the designing of the network architecture, which enables efficient learning and inference. Proposed network is able to generalize well even when it is trained with a single image pair.