Previous math word problem solvers following the encoder-decoder paradigm fail to explicitly incorporate essential math symbolic constraints, leading to unexplainable and unreasonable predictions. Herein, we propose Neural-Symbolic Solver (NS-Solver) to explicitly and seamlessly incorporate different levels of symbolic constraints by auxiliary tasks. Our NS-Solver consists of a problem reader to encode problems, a programmer to generate symbolic equations, and a symbolic executor to obtain answers. Along with target expression supervision, our solver is also optimized via 4 new auxiliary objectives to enforce different symbolic reasoning: a) self-supervised number prediction task predicting both number quantity and number locations; b) commonsense constant prediction task predicting what prior knowledge (e.g. how many legs a chicken has) is required; c) program consistency checker computing the semantic loss between predicted equation and target equation to ensure reasonable equation mapping; d) duality exploiting task exploiting the quasi-duality between symbolic equation generation and problem’s part-of-speech generation to enhance the understanding ability of a solver. Besides, to provide a more realistic and challenging benchmark for developing a universal and scalable solver, we also construct a new largescale MWP benchmark CM17K consisting of 4 kinds of MWPs (arithmetic, one-unknown linear, one-unknown non-linear, equation set) with more than 17K samples. Extensive experiments on Math23K and our CM17k demonstrate the superiority of our NS-Solver compared to state-of-the-art methods.

Many real-world open-domain conversation applications have specific goals to achieve during open-ended chats, such as recommendation, psychotherapy, education, etc. We study the problem of imposing conversational goals on open-domain chat agents. In particular, we want a conversational system to chat naturally with human and proactively guide the conversation to a designated target subject. The problem is challenging as no public data is available for learning such a target-guided strategy. We propose a structured approach that introduces coarse-grained keywords to control the intended content of system responses. We then attain smooth conversation transition through turn-level supervised learning, and drive the conversation towards the target with discourse-level constraints. We further derive a keyword-augmented conversation dataset for the study. Quantitative and human evaluations show our system can produce meaningful and effective conversations, significantly improving over other approaches