Learning to Reason Deductively: Math Word Problem Solving as Complex Relation Extraction (2203.10316v4)

Abstract: Solving math word problems requires deductive reasoning over the quantities in the text. Various recent research efforts mostly relied on sequence-to-sequence or sequence-to-tree models to generate mathematical expressions without explicitly performing relational reasoning between quantities in the given context. While empirically effective, such approaches typically do not provide explanations for the generated expressions. In this work, we view the task as a complex relation extraction problem, proposing a novel approach that presents explainable deductive reasoning steps to iteratively construct target expressions, where each step involves a primitive operation over two quantities defining their relation. Through extensive experiments on four benchmark datasets, we show that the proposed model significantly outperforms existing strong baselines. We further demonstrate that the deductive procedure not only presents more explainable steps but also enables us to make more accurate predictions on questions that require more complex reasoning.

An Analytical Summary of Deductive Reasoning in Math Word Problem Solving

The paper presents a methodological advancement in math word problem (MWP) solving by reframing the task as a complex relation extraction problem rather than a mere sequence generation exercise. Traditional approaches in MWP solving largely depend on sequence-to-sequence (S2S) or sequence-to-tree (S2T) models, which concentrate on generating the target mathematical expression in either linear sequences or tree structures. These models, although effective empirically, lack the capability to elucidate the reasoning process, posing challenges for interpretability and for tasks requiring nuanced relational reasoning.

Core Contributions

This work introduces a novel deductive reasoning approach, which iteratively constructs mathematical expressions through a series of explainable operations between quantities. At each step, primitive arithmetic operations are performed to define specific relations, culminating in a target expression. This iterative process exhibits dual benefits: it enhances transparency in reasoning and improves prediction accuracy for complex problems requiring multiple reasoning steps.

Key contributions of the proposed model include:

• Reframing MWP Solving: Reformulating the task as complex relation extraction emphasizes identifying and utilizing the relations among quantities, offering a fresh perspective in MWP research.
• Explainability: The proposed model provides explicit reasoning steps making the solving process transparent and potentially more educational for human learners.
• Empirical Performance: Extensive experiments across four benchmark datasets demonstrate superior performance over strong baseline models, highlighting the model's effectiveness, especially in solving complex problems.

Methodological Innovations

The deductive reasoning model integrates several advanced components optimized for extracting, representing, and utilizing relationships between mathematical entities:

• Pre-trained LLMs: Utilized as quantity encoders, providing robust initialization for numerical and contextual representations.
• Feed-Forward Networks Specific to Operations: Dedicated networks are trained to encode expressions under particular operations, crucial for discerning correct arithmetic transformations.
• Rationalizer Mechanism: The model updates representations of existing quantities using intermediate expression representations, preventing high-ranked initial expressions from overshadowing other valid candidate expressions in subsequent steps. Rationalizers are realized through techniques like multi-head self-attention or gated recurrent units (GRU), ensuring dynamic and contextually informed updates.

Implications and Future Directions

The implications of this research are multifaceted, impacting both the theory and practice of AI-based educational tools:

• Theoretical Impact: Recasting MWP solving as complex relation extraction aligns closely with systematic deductive reasoning, facilitating a deeper inquiry into cognitive processes underlying math problem solving.
• Practical Application: Enhanced interpretability and step-by-step reasoning dovetail with pedagogical requirements, potentially informing the design of more intuitive human-computer interaction interfaces.
• Future Exploration: Future work could focus on integrating external commonsense knowledge, refining counterfactual reasoning mechanisms, and adopting beam search strategies within the iterative deductive framework to optimally balance precision and computational efficiency.

In summary, this paper offers a significant methodological pivot in MWP research, emphasizing relational reasoning over mere expression generation, thereby enhancing both the transparency and efficacy of AI models in educational problem-solving contexts. Further investigations into expanded applications may foster robust AI systems that mimic human-like reasoning more closely.