Solving math word problem (MWP) remains a challenging task, as it requires to understand both the semantic meanings of the text and the mathematical logic among quantities, i.e., for both semantics modal and quantity modal learning. Current MWP encoders work in a uni-modal setting and map the given problem description to a latent representation, then for decoding. The generalizability of these MWP encoders is thus limited because some problems are semantics-demanding and others are quantity-demanding. To address this problem, we propose a Compositional Math Word Problem Solver (C-MWP) which works in a bi-modal setting encoding in an interactive way. Extensive experiments validate the effectiveness of C-MWP and show its superiority over state-of-the-art models on public benchmarks.

Text-based games present an exciting test-bed for reinforcement learning algorithms in the natural language environment. In these adventure games, an agent must learn to interact with the environment through text in order to accomplish tasks, facing large and combinational action space as well as partial observability issues. However, existing solutions fail to decompose the task and abstract the action autonomously, which either pre-specify the subtasks or pre-train on the human gameplay dataset. In this work, we introduce a novel skill-centric reinforcement learning framework, which is capable of abstracting the action in an end-to-end manner. To learn a more disentangled skill, we focus on the informativeness and distinguishability of the skill in accordance with the information bottleneck principle. Specifically, we introduce a discriminator to enable the skill to reflect the trajectory and push their representations onto the unit hypersphere to distribute uniformly. Moreover, a self-predictive mechanism is employed to learn inverse and forward dynamics, and a self-recovery mechanism is leveraged to refine the action representation, thus resulting in a more comprehensive perception of dynamics and more effective representations of textual state and action. Empirical experiments are carried out on the Jericho environment and the results validate the superiority against state-of-the-art baselines.

Math word problem (MWP) solving faces a dilemma in number representation learning. In order to avoid the number representation issue and reduce the search space of feasible solutions, existing works striving for MWP solving usually replace real numbers with symbolic placeholders to focus on logic reasoning. However, different from common symbolic reasoning tasks like program synthesis and knowledge graph reasoning, MWP solving has extra requirements in numerical reasoning. In other words, instead of the number value itself, it is the reusable numerical property that matters more in numerical reasoning. Therefore, we argue that injecting numerical properties into symbolic placeholders with contextualized representation learning schema can provide a way out of the dilemma in the number representation issue here. In this work, we introduce this idea to the popular pre-training language model (PLM) techniques and build MWP-BERT, an effective contextual number representation PLM. We demonstrate the effectiveness of our MWP-BERT on MWP solving and several MWP-specific understanding tasks on both English and Chinese benchmarks.

While the recent tree-based neural models have demonstrated promising results in generating solution expression for the math word problem (MWP), most of these models do not capture the relationships and order information among the quantities well. This results in poor quantity representations and incorrect solution expressions. In this paper, we propose Graph2Tree, a novel deep learning architecture that combines the merits of the graph-based encoder and tree-based decoder to generate better solution expressions. Included in our Graph2Tree framework are two graphs, namely the Quantity Cell Graph and Quantity Comparison Graph, which are designed to address limitations of existing methods by effectively representing the relationships and order information among the quantities in MWPs. We conduct extensive experiments on two available datasets. Our experiment results show that Graph2Tree outperforms the state-of-the-art baselines on two benchmark datasets significantly. We also discuss case studies and empirically examine Graph2Tree’s effectiveness in translating the MWP text into solution expressions.