Program Induction by Rationale Generation : Learning to Solve and Explain Algebraic Word Problems (1705.04146v3)

Abstract: Solving algebraic word problems requires executing a series of arithmetic operations---a program---to obtain a final answer. However, since programs can be arbitrarily complicated, inducing them directly from question-answer pairs is a formidable challenge. To make this task more feasible, we solve these problems by generating answer rationales, sequences of natural language and human-readable mathematical expressions that derive the final answer through a series of small steps. Although rationales do not explicitly specify programs, they provide a scaffolding for their structure via intermediate milestones. To evaluate our approach, we have created a new 100,000-sample dataset of questions, answers and rationales. Experimental results show that indirect supervision of program learning via answer rationales is a promising strategy for inducing arithmetic programs.

Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems

The paper "Program Induction by Rationale Generation: Learning to Solve and Explain Algebraic Word Problems" presents a significant advancement in the intersection of natural language processing and mathematical reasoning. Authored by researchers from DeepMind and the University of Oxford, the paper proposes a novel approach to solving algebraic word problems by generating solution rationales that integrate natural language and mathematical expressions.

Overview

The primary challenge tackled by this paper is the induction of arithmetic programs directly from question-answer pairs—a problem compounded by the potentially complex nature of such programs. The authors introduce a strategy that leverages answer rationales, which serve as intermediate steps providing a scaffold for deriving the final answer. These rationales are natural language explanations interspersed with algebraic expressions, crucial for enhancing model interpretability and providing a structured guide to program learning.

Methodology

A key contribution is the development of a new dataset comprising over 100,000 algebraic word problems complete with annotated rationales. This dataset serves as a foundation for training a sequence-to-sequence model designed to generate programs that produce both the rationale and the final answer. The model's unique capability lies in an intelligent sampling technique that filters potential instructions to those plausible within the context, supported by a heuristic search mechanism.

Experimental Results

The authors demonstrate that standard sequence-to-sequence models perform poorly on this task, with accuracies barely surpassing random guessing. In contrast, their model significantly improves performance, achieving a near-doubling of accuracy compared to baselines. This suggests that the integration of rationale generation is a promising direction for inducing arithmetic programs from textual data.

Implications and Future Directions

The implications of this research are manifold. Practically, this approach could enhance AI systems' ability to perform complex reasoning tasks akin to those required in educational settings or professional domains requiring high-level mathematical reasoning. Theoretically, it paves the way for more profound explorations into the synthesis of program-like structures from language, thereby augmenting the capability of AI to bridge natural language understanding with computational execution.

Future work could explore richer datasets or more sophisticated models that might better handle the complexity of real-world problems. Another promising direction would be the integration of this approach with reinforcement learning techniques, potentially improving the robustness and adaptability of the generated solutions.

In summary, this paper presents a substantive stride toward bridging linguistic reasoning and mathematical computation, offering a robust framework for the educational technology space and beyond.