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: The sign stochastic gradient descent method (signSGD) utilizes only the sign of the stochastic gradient in its updates. Since signSGD carries out one-bit quantization of the gradients, it is extremely practical for distributed optimization where gradients need to be aggregated from different processors. For the first time, we establish convergence rates for signSGD on general non-convex functions under transparent conditions. We show that the rate of signSGD to reach first-order critical points matches that of SGD in terms of number of stochastic gradient calls, up to roughly a linear factor in the dimension. We carry out simple experiments to explore the behaviour of sign gradient descent (without the stochasticity) close to saddle points and show that it often helps completely avoid them without using either stochasticity or curvature information.

SOLUTION: We prove a non-convex convergence rate for the sign stochastic gradient method. The algorithm has links to algorithms like Adam and Rprop, as well as gradient quantisation schemes used in distributed machine learning.

PROBLEM: We investigate methods to efficiently learn diverse strategies in reinforcement learning for a generative structured prediction problem: query reformulation. In the proposed framework an agent consists of multiple specialized sub-agents and a meta-agent that learns to aggregate the answers from sub-agents to produce a final answer. Sub-agents are trained on disjoint partitions of the training data, while the meta-agent is trained on the full training set. Our method makes learning faster, because it is highly parallelizable, and has better generalization performance than strong baselines, such as
 an ensemble of agents trained on the full data. We evaluate on the tasks of document retrieval and question answering. The
 improved performance seems due to the increased diversity of reformulation strategies. This suggests that multi-agent, hierarchical approaches might play an important role in structured prediction tasks of this kind. However, we also find that it is not obvious how to characterize diversity in this context, and a first attempt based on clustering did not produce good results. Furthermore, reinforcement learning for the reformulation task is hard in high-performance regimes. At best, it only marginally improves over the state of the art, which highlights the complexity of training models in this framework for end-to-end language understanding problems.

SOLUTION: We use reinforcement learning for query reformulation on two tasks and surprisingly find that when training multiple agents diversity of the reformulations is more important than specialisation.

PROBLEM: Knowledge Graphs (KG), composed of entities and relations, provide a structured representation of knowledge. For easy access to statistical approaches on relational data, multiple methods to embed a KG as components of R^d have been introduced. We propose TransINT, a novel and interpretable KG embedding method that isomorphically preserves the implication ordering among relations in the embedding space. TransINT maps set of entities (tied by a relation) to continuous sets of vectors that are inclusion-ordered isomorphically to relation implications. With a novel parameter sharing scheme, TransINT enables automatic training on missing but implied facts without rule grounding. We achieve new state-of-the-art performances with signficant margins in Link Prediction and Triple Classification on FB122 dataset, with boosted performance even on test instances that cannot be inferred by logical rules. The angles between the continuous sets embedded by TransINT provide an interpretable way to mine semantic relatedness and implication rules among relations.

SOLUTION:
We propose TransINT, a novel and interpretable KG embedding method that isomorphically preserves the implication ordering among relations in the embedding space in an explainable, robust, and geometrically coherent way.