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.

We propose a novel deep network architecture for lifelong learning which we refer to as Dynamically Expandable Network (DEN), that can dynamically decide its network capacity as it trains on a sequence of tasks, to learn a compact overlapping knowledge sharing structure among tasks. DEN is efficiently trained in an online manner by performing selective retraining, dynamically expands network capacity upon arrival of each task with only the necessary number of units, and effectively prevents semantic drift by splitting/duplicating units and timestamping them. We validate DEN on multiple public datasets in lifelong learning scenarios on multiple public datasets, on which it not only significantly outperforms existing lifelong learning methods for deep networks, but also achieves the same level of performance as the batch model with substantially fewer number of parameters.
We propose a novel deep network architecture that can dynamically decide its network capacity as it trains on a lifelong learning scenario.

Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, and understanding the dynamics of (stochastic) gradient algorithms for solving such formulations has been a grand challenge. As a first step, we restrict to bilinear zero-sum games and give a systematic analysis of popular gradient updates, for both simultaneous and alternating versions. We provide exact conditions for their convergence and find the optimal parameter setup and convergence rates. In particular, our results offer formal evidence that alternating updates converge "better" than simultaneous ones.
We systematically analyze the convergence behaviour of popular gradient algorithms for solving bilinear games, with both simultaneous and alternating updates.

Deep neural networks (DNNs) had great success on NLP tasks such as language modeling, machine translation and certain question answering (QA) tasks. However, the success is limited at more knowledge intensive tasks such as QA from a big corpus. Existing end-to-end deep QA models (Miller et al., 2016; Weston et al., 2014) need to read the entire text after observing the question, and therefore their complexity in responding a question is linear in the text size. This is prohibitive for practical tasks such as QA from Wikipedia, a novel, or the Web. We propose to solve this scalability issue by using symbolic meaning representations, which can be indexed and retrieved efficiently with complexity that is independent of the text size. More specifically, we use sequence-to-sequence models to encode knowledge symbolically and generate programs to answer questions from the encoded knowledge. We apply our approach, called the N-Gram Machine (NGM), to the bAbI tasks (Weston et al., 2015) and a special version of them (“life-long bAbI”) which has stories of up to 10 million sentences. Our experiments show that NGM can successfully solve both of these tasks accurately and efficiently. Unlike fully differentiable memory models, NGM’s time complexity and answering quality are not affected by the story length. The whole system of NGM is trained end-to-end with REINFORCE (Williams, 1992). To avoid high variance in gradient estimation, which is typical in discrete latent variable models, we use beam search instead of sampling. To tackle the exponentially large search space, we use a stabilized auto-encoding objective and a structure tweak procedure to iteratively reduce and refine the search space.


We propose a framework that learns to encode knowledge symbolically and generate programs to reason about the encoded knowledge.