Graph Representations for Higher-Order Logic and Theorem Proving

This paper presents the first use of graph neural networks (GNNs) for higher-order proof search and demonstrates that GNNs can improve upon state-of-the-art results in this domain. Interactive, higher-order theorem provers allow for the formalization of most mathematical theories and have been shown to pose a significant challenge for deep learning. Higher-order logic is highly expressive and, even though it is well-structured with a clearly defined grammar and semantics, there still remains no well-established method to convert formulas into graph-based representations. In this paper, we consider several graphical representations of higher-order logic and evaluate them against the HOList benchmark for higher-order theorem proving

Bilateral Multi-Perspective Matching for Natural Language Sentences

Natural language sentence matching is a fundamental technology for a variety of tasks. Previous approaches either match sentences from a single direction or only apply single granular (word-by-word or sentence-by-sentence) matching. In this work, we propose a bilateral multi-perspective matching (BiMPM) model under the "matching-aggregation" framework. Given two sentences $P$ and $Q$, our model first encodes them with a BiLSTM encoder. Next, we match the two encoded sentences in two directions $P \rightarrow Q$ and $P \leftarrow Q$. In each matching direction, each time step of one sentence is matched against all time-steps of the other sentence from multiple perspectives. Then, another BiLSTM layer is utilized to aggregate the matching results into a fix-length matching vector. Finally, based on the matching vector, the decision is made through a fully connected layer. We evaluate our model on three tasks: paraphrase identification, natural language inference and answer sentence selection. Experimental results on standard benchmark datasets show that our model achieves the state-of-the-art performance on all tasks.Comment: To appear in Proceedings of IJCAI 201

Attentive Convolution: Equipping CNNs with RNN-style Attention Mechanisms

In NLP, convolutional neural networks (CNNs) have benefited less than recurrent neural networks (RNNs) from attention mechanisms. We hypothesize that this is because the attention in CNNs has been mainly implemented as attentive pooling (i.e., it is applied to pooling) rather than as attentive convolution (i.e., it is integrated into convolution). Convolution is the differentiator of CNNs in that it can powerfully model the higher-level representation of a word by taking into account its local fixed-size context in the input text t^x. In this work, we propose an attentive convolution network, ATTCONV. It extends the context scope of the convolution operation, deriving higher-level features for a word not only from local context, but also information extracted from nonlocal context by the attention mechanism commonly used in RNNs. This nonlocal context can come (i) from parts of the input text t^x that are distant or (ii) from extra (i.e., external) contexts t^y. Experiments on sentence modeling with zero-context (sentiment analysis), single-context (textual entailment) and multiple-context (claim verification) demonstrate the effectiveness of ATTCONV in sentence representation learning with the incorporation of context. In particular, attentive convolution outperforms attentive pooling and is a strong competitor to popular attentive RNNs.Comment: Camera-ready for TACL. 16 page