Solving Math Word Problems via Cooperative Reasoning induced Language Models
CoRe method enhances math problem-solving via cooperative reasoning, achieving a 9.6% improvement.
Key Findings
Methodology
This study introduces a cooperative reasoning framework called CoRe, mimicking human dual-system reasoning. System 1 acts as a generator for reasoning paths, while System 2 serves as a verifier providing feedback. This cooperation enhances math problem-solving in both zero-shot and fine-tuning settings.
Key Results
- On the MultiArith dataset, CoRe outperformed the best existing baseline by 9.6%.
- In zero-shot settings, CoRe achieved 79.5% and 97.5% accuracy on SingleEq and MultiArith datasets, respectively.
- On the GSM8K dataset, CoRe surpassed GPT-3 350B in fine-tuning settings.
Significance
By introducing a dual-system model of human reasoning, this study significantly enhances language models' performance in solving math problems. It opens new research directions in academia and offers new possibilities in automated education and intelligent tutoring in the industry.
Technical Contribution
CoRe breaks the bottleneck of traditional language models' reasoning capabilities by introducing a cooperative reasoning mechanism. It not only provides a new theoretical framework but also achieves more efficient reasoning path searches in engineering.
Novelty
CoRe is the first study to apply the dual-system model of human reasoning to language models. Compared to existing methods, CoRe significantly enhances reasoning capabilities through cooperative reasoning.
Limitations
- In some complex problems, CoRe's reasoning path generation may be inaccurate, leading to incorrect results.
- Training time on large-scale datasets is lengthy.
Future Work
Future research could explore optimizing CoRe's reasoning path generation algorithm further and validate its generality on more diverse datasets.
AI Executive Summary
Solving math problems has long been a hallmark of human intelligence, but existing language models have limitations in this area. Traditional methods rely on memorizing patterns with large-scale parameters, lacking the flexibility of human reasoning. To address this, researchers propose the CoRe method, which mimics human dual-system reasoning to achieve breakthroughs in language models' math problem-solving capabilities.
The core of the CoRe method lies in using System 1 as a generator to create reasoning paths, while System 2 acts as a verifier providing feedback and guidance. This cooperative reasoning mechanism significantly enhances performance in both zero-shot and fine-tuning settings. In experiments, CoRe demonstrated outstanding performance across multiple mathematical reasoning datasets, notably improving accuracy by 9.6% on the MultiArith dataset.
Despite the significant advances in reasoning capabilities, CoRe still has limitations, such as instability in complex problems. Future research can further optimize the reasoning path generation algorithm and validate its generality on more diverse datasets.
Deep Analysis
Background
Solving math problems has been a crucial area of AI research. Early studies relied on symbolic reasoning and logic programming, but these methods struggled with complex natural language problems. Recently, with the development of large-scale pre-trained language models like GPT-3 and BERT, researchers have begun exploring their potential in solving math problems. However, these models still have limitations in reasoning capabilities.
Core Problem
Existing language models often lack the flexibility and adaptability of human reasoning when solving math problems. This is mainly because these models lack sufficient supervision in generating reasoning paths, leading to errors in handling complex problems.
Innovation
The CoRe method addresses the bottleneck in traditional language models' reasoning capabilities by introducing a dual-system model of human reasoning. Specifically, System 1 generates reasoning paths quickly, while System 2 verifies and provides feedback on these paths. This cooperative mechanism significantly enhances performance in both zero-shot and fine-tuning settings.
Methodology
- �� System 1 acts as a generator, creating multiple potential reasoning paths.
- �� System 2 serves as a verifier, scoring and providing feedback on each path.
- �� Monte Carlo Tree Search algorithm optimizes the selection of reasoning paths.
- �� Self-thinking strategy generates high-quality training data during training.
Experiments
Experiments were conducted on multiple mathematical reasoning datasets, including GSM8K, ASDiv-A, SingleOp, SingleEq, and MultiArith. Baselines included large-scale models like Instruct GPT-3 and PaLM. Accuracy was used as the evaluation metric, and multiple experiments were conducted to ensure result stability.
Results
CoRe outperformed the best existing baseline by 9.6% on the MultiArith dataset. In zero-shot settings, CoRe achieved 79.5% and 97.5% accuracy on SingleEq and MultiArith datasets, respectively. On the GSM8K dataset, CoRe surpassed GPT-3 350B in fine-tuning settings.
Applications
The CoRe method can be directly applied to automated education and intelligent tutoring systems, helping students better understand and solve math problems. Its efficient reasoning capabilities can also be used in scientific research and engineering design for complex problem-solving.
Limitations & Outlook
Despite significant advances in reasoning capabilities, CoRe still has limitations in stability on some complex problems. Additionally, training time on large-scale datasets is lengthy, potentially limiting its practical application.
Plain Language Accessible to non-experts
Imagine a factory where System 1 is like workers on the assembly line, quickly assembling products (reasoning paths), while System 2 is like quality inspectors, checking each product's quality (verifying paths). This cooperation ensures that each product (reasoning result) is of high quality.
ELI14 Explained like you're 14
Imagine you're playing a puzzle game. System 1 is like a player quickly guessing answers, while System 2 is like a referee checking if the answers are correct. With this teamwork, you can find the right answer faster!
Glossary
Pre-trained Language Model
A language model trained on large-scale data, capable of understanding and generating natural language.
Used for generating reasoning paths in math problems.
Cooperative Reasoning
A framework mimicking human reasoning, combining generation and verification mechanisms.
Enhances model's math problem-solving capabilities.
System 1
Part responsible for quickly generating reasoning paths, akin to human intuition.
Acts as a generator in CoRe.
System 2
Part responsible for verifying and providing feedback on reasoning paths, akin to human deliberation.
Acts as a verifier in CoRe.
Monte Carlo Tree Search
An algorithm used to optimize decision paths by simulating and providing feedback to select the best path.
Used to optimize reasoning path selection in CoRe.
Open Questions Unanswered questions from this research
- 1 How can CoRe's reasoning ability be enhanced for more complex math problems?
- 2 Can CoRe be applied to reasoning tasks in other domains?
Applications
Immediate Applications
Automated Education
CoRe can be used to develop intelligent tutoring systems, helping students better understand math problems.
Long-term Vision
Scientific Research
By enhancing reasoning capabilities, CoRe can be used to solve complex problems in scientific research.
Abstract
Large-scale pre-trained language models (PLMs) bring new opportunities to challenging problems, especially those that need high-level intelligence, such as the math word problem (MWPs). However, directly applying existing PLMs to MWPs can fail as the generation process lacks sufficient supervision and thus lacks fast adaptivity as humans. We notice that human reasoning has a dual reasoning framework that consists of an immediate reaction system (system 1) and a delicate reasoning system (system 2), where the entire reasoning is determined by their interaction. This inspires us to develop a cooperative reasoning-induced PLM for solving MWPs, called Cooperative Reasoning (CoRe), resulting in a human-like reasoning architecture with system 1 as the generator and system 2 as the verifier. In our approach, the generator is responsible for generating reasoning paths, and the verifiers are used to supervise the evaluation in order to obtain reliable feedback for the generator. We evaluate our CoRe framework on several mathematical reasoning datasets and achieve decent improvement over state-of-the-art methods, up to 9.6% increase over best baselines. Our codes are available at https://github.com/TianHongZXY/CoRe