TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: Deep neural networks are known to be vulnerable to adversarial perturbations. In this paper, we bridge adversarial robustness of neural nets with Lyapunov stability of dynamical systems. From this viewpoint, training neural nets is equivalent to finding an optimal control of the discrete dynamical system, which allows one to utilize methods of successive approximations, an optimal control algorithm based on Pontryagin's maximum principle, to train neural nets. This decoupled training method allows us to add constraints to the optimization, which makes the deep model more robust. The constrained optimization problem can be formulated as a semi-definite programming problem and hence can be solved efficiently. Experiments show that our method effectively improves deep model's adversarial robustness.

SOLUTION: An adversarial defense method bridging robustness of deep neural nets with Lyapunov stability

PROBLEM: The machine learning and computer vision community is witnessing an unprecedented rate of new tasks being proposed and addressed, thanks to the power of deep convolutional networks to find complex mappings from X to Y. The advent of each task often accompanies the release of a large-scale human-labeled dataset, for supervised training of the deep network. However, it is expensive and time-consuming to manually label sufficient amount of training data. Therefore, it is important to develop algorithms that can leverage off-the-shelf labeled dataset to learn useful knowledge for the target task. While previous works mostly focus on transfer learning from a single source, we study multi-source transfer across domains and tasks (MS-DTT), in a semi-supervised setting. We propose GradMix, a model-agnostic method applicable to any model trained with gradient-based learning rule. GradMix transfers knowledge via gradient descent, by weighting and mixing the gradients from all sources during training. Our method follows a meta-learning objective, by assigning layer-wise weights to the source gradients, such that the combined gradient follows the direction that can minimize the loss for a small set of samples from the target dataset. In addition, we propose to adaptively adjust the learning rate for each mini-batch based on its importance to the target task, and a pseudo-labeling method to leverage the unlabeled samples in the target domain. We perform experiments on two MS-DTT tasks: digit recognition and action recognition, and demonstrate the advantageous performance of the proposed method against multiple baselines.

SOLUTION: We propose a gradient-based method to transfer knowledge from multiple sources across different domains and tasks.

PROBLEM: Learning with a primary objective, such as softmax cross entropy for classification and sequence generation, has been the norm for training deep neural networks for years. Although being a widely-adopted approach, using cross entropy as the primary objective exploits mostly the information from the ground-truth class for maximizing data likelihood, and largely ignores information from the complement (incorrect) classes. We argue that, in addition to the primary objective, training also using a complement objective that leverages information from the complement classes can be effective in improving model performance. This motivates us to study a new training paradigm that maximizes the likelihood of the ground-truth class while neutralizing the probabilities of the complement classes. We conduct extensive experiments on multiple tasks ranging from computer vision to natural language understanding. The experimental results confirm that, compared to the conventional training with just one primary objective, training also with the complement objective further improves the performance of the state-of-the-art models across all tasks. In addition to the accuracy improvement, we also show that models trained with both primary and complement objectives are more robust to single-step adversarial attacks.

SOLUTION:
We propose Complement Objective Training (COT), a new training paradigm that optimizes both the primary and complement objectives for effectively learning the parameters of neural networks.