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.

Q:   Analysis methods which enable us to better understand the
  representations and functioning of neural models of language are
  increasingly needed as deep learning becomes the dominant approach
  in NLP. Here we present two methods based on Representational
  Similarity Analysis (RSA) and Tree Kernels (TK) which allow us to
  directly quantify how strongly the information encoded in neural
  activation patterns corresponds to information represented by
  symbolic structures such as syntax trees. We first validate our
  methods on the case of a simple synthetic language for arithmetic
  expressions with clearly defined syntax and semantics, and show that
  they exhibit the expected pattern of results. We then apply our methods to
  correlate neural representations of English sentences with their
  constituency parse trees.

A: Two methods based on Representational Similarity Analysis (RSA) and Tree Kernels (TK) which directly quantify how strongly information encoded in neural activation patterns corresponds to information represented by symbolic structures.
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Q: 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.

A: A theoretical algorithm for testing local optimality and extracting descent directions at nondifferentiable points of empirical risks of one-hidden-layer ReLU networks.
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Q: The demand for abstractive dialog summary is growing in real-world applications. For example, customer service center or hospitals would like to summarize customer service interaction and doctor-patient interaction. However, few researchers explored abstractive summarization on dialogs due to the lack of  suitable datasets. We propose an abstractive dialog summarization dataset based on MultiWOZ. If we directly apply previous state-of-the-art document summarization methods on dialogs, there are two significant drawbacks: the informative entities such as restaurant names are difficult to preserve, and the contents from different dialog domains are sometimes mismatched. To address these two drawbacks, we propose Scaffold Pointer Network (SPNet) to utilize the existing annotation on speaker role, semantic slot and dialog domain. SPNet incorporates these semantic scaffolds for dialog summarization. Since ROUGE cannot capture the two drawbacks mentioned, we also propose a new evaluation metric that considers critical informative entities in the text. On MultiWOZ, our proposed SPNet outperforms state-of-the-art abstractive summarization methods on all the automatic and human evaluation metrics.

A:
We propose a novel end-to-end model (SPNet) to incorporate semantic scaffolds for improving abstractive dialog summarization.
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