Summary of Unraveling Arithmetic in Large Language Models: the Role Of Algebraic Structures, by Fu-chieh Chang et al.
Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structures
by Fu-Chieh Chang, Pei-Yuan Wu
First submitted to arxiv on: 25 Nov 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Computation and Language (cs.CL)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Large language models (LLMs) have achieved impressive mathematical abilities through chain-of-thought (CoT) prompting, which breaks down complex reasoning into step-by-step solutions. This approach has led to significant advancements in benchmarks like GSM8K and MATH. However, the mechanisms behind LLMs’ ability to perform arithmetic in a single step of CoT remain unclear. Existing studies debate whether LLMs encode numerical values or rely on symbolic reasoning, while others explore attention and multi-layered processing in arithmetic tasks. Our proposed approach suggests that LLMs learn arithmetic by capturing algebraic structures, such as commutativity and identity properties. By leveraging these structures through input-output relationships, we can generalize to unseen data. We demonstrate the effectiveness of this approach using a custom dataset of arithmetic problems, enhancing LLMs’ arithmetic capabilities and offering insights into improving their performance. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about how big language models do math really well. They use something called “chain-of-thought” prompting to solve math problems step by step. This has helped them get better at doing math, as shown by tests like GSM8K and MATH. But we don’t fully understand how they can do math in just one step. Some people think these models are good at numbers or symbols, while others look at how they pay attention to different parts of the problem. Our idea is that these models learn math by recognizing patterns in algebra, like things being equal and commutative. By using these patterns to solve problems, we can make them even better at doing math. |
Keywords
» Artificial intelligence » Attention » Prompting
