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.

Ex Input:
Discovering causal structure among a set of variables is a fundamental problem in many empirical sciences. Traditional score-based casual discovery methods rely on various local heuristics to search for a Directed Acyclic Graph (DAG) according to a predefined score function. While these methods, e.g., greedy equivalence search, may have attractive results with infinite samples and certain model assumptions, they are less satisfactory in practice due to finite data and possible violation of assumptions. Motivated by recent advances in neural combinatorial optimization, we propose to use Reinforcement Learning (RL) to search for the DAG with the best scoring. Our encoder-decoder model takes observable data as input and generates graph adjacency matrices that are used to compute rewards. The reward incorporates both the predefined score function and two penalty terms for enforcing acyclicity. In contrast with typical RL applications where the goal is to learn a policy, we use RL as a search strategy and our final output would be the graph, among all graphs generated during training, that achieves the best reward. We conduct experiments on both synthetic and real datasets, and show that the proposed approach not only has an improved search ability but also allows for a flexible score function under the acyclicity constraint.

Ex Output:
We apply reinforcement learning to score-based causal discovery and achieve promising results on both synthetic and real datasets


Ex Input:
We provide a theoretical algorithm for checking local optimality and escaping saddles at nondifferentiable points of empirical risks of two-layer ReLU networks. Our algorithm receives any parameter value and returns: local minimum, second-order stationary point, or a strict descent direction. The presence of M data points on the nondifferentiability of the ReLU divides the parameter space into at most 2^M regions, which makes analysis difficult. By exploiting polyhedral geometry, we reduce the total computation down to one convex quadratic program (QP) for each hidden node, O(M) (in)equality tests, and one (or a few) nonconvex QP. For the last QP, we show that our specific problem can be solved efficiently, in spite of nonconvexity. In the benign case, we solve one equality constrained QP, and we prove that projected gradient descent solves it exponentially fast. In the bad case, we have to solve a few more inequality constrained QPs, but we prove that the time complexity is exponential only in the number of inequality constraints. Our experiments show that either benign case or bad case with very few inequality constraints occurs, implying that our algorithm is efficient in most cases.

Ex Output:
A theoretical algorithm for testing local optimality and extracting descent directions at nondifferentiable points of empirical risks of one-hidden-layer ReLU networks.


Ex Input:
Multilingual machine translation, which translates multiple languages with a single model, has attracted much attention due to its efficiency of offline training and online serving. However, traditional multilingual translation usually yields inferior accuracy compared with the counterpart using individual models for each language pair, due to language diversity and model capacity limitations. In this paper, we propose a distillation-based approach to boost the accuracy of multilingual machine translation. Specifically, individual models are first trained and regarded as teachers, and then the multilingual model is trained to fit the training data and match the outputs of individual models simultaneously through knowledge distillation. Experiments on IWSLT, WMT and Ted talk translation datasets demonstrate the effectiveness of our method. Particularly, we show that one model is enough to handle multiple languages (up to 44 languages in our experiment), with comparable or even better accuracy than individual models.

Ex Output:

We proposed a knowledge distillation based method to boost the accuracy of multilingual neural machine translation.