Natural language processing (NLP) has made significant strides in recent years, particularly with the development of large language models (LLMs) that excel in various applications. One key area where LLMs are being tested is in mathematical problem-solving, with benchmarks like GSM8K measuring their ability to solve grade-school math problems. However, there is ongoing debate about whether these models truly understand math concepts or simply rely on patterns in the training data to produce correct answers.
A new evaluation method called Compositional Grade-School Math (GSM) has been introduced by researchers from Mila, Google DeepMind, and Microsoft Research. This method involves chaining two math problems together, where the solution to the first problem becomes a variable in the second problem. By testing LLMs in this way, researchers can assess their ability to handle dependencies between questions, a crucial aspect that is often missing in existing benchmarks.
The evaluation revealed a significant gap in reasoning abilities among LLMs. Models that performed well on standard math benchmarks struggled with compositional reasoning tasks, showing a notable drop in accuracy when required to link answers between related problems. This suggests that more robust training strategies are needed to enhance the compositional capabilities of these models.
Furthermore, the study explored the impact of instruction tuning and code generation on model performance. While instruction tuning improved results for smaller models on standard math problems, generating code solutions instead of using natural language led to significant improvements on compositional math problems for some models. This indicates that while code generation can help reduce the reasoning gap, there are still systematic differences in reasoning capabilities among different models.
Overall, the research highlights the need for more comprehensive evaluation methods to assess the reasoning abilities of LLMs in complex problem-solving scenarios. The introduction of the Compositional GSM benchmark provides a valuable tool for researchers to evaluate the capabilities of these models beyond isolated problem-solving. Moving forward, it will be essential to prioritize the development of models that excel in multi-step reasoning tasks to bridge the existing gap in reasoning abilities among LLMs.
