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# Unlocking Algorithmic Reasoning: Teaching Language Models to Solve Arithmetic Problems

Title: Teaching AI Model Algorithmic Reasoning for Improved Performance

Introduction:
Large language models (LLMs) like GPT-3 and PaLM have made remarkable progress in recent years, thanks to larger models and training data. However, LLMs face challenges when it comes to reasoning symbolically, especially in tasks that require rule-based reasoning like arithmetic operations. In this blog post, we discuss an approach called “Teaching Algorithmic Reasoning via In-Context Learning” that enables LLMs to learn algorithmic reasoning capabilities. This approach leverages in-context learning and a novel algorithmic prompting technique to enhance the model’s generalization and performance on arithmetic problems.

Algorithmic Reasoning with In-Context Learning:

In-Context Learning:
In-context learning refers to a model’s ability to perform a task after being exposed to a few examples of it within the model’s prompt. This eliminates the need for weight updates. In our approach, we use algorithmic prompts to teach LLMs the rules of arithmetic through in-context learning.

Algorithmic Prompting Technique:
Algorithmic prompting is a technique that focuses on two key aspects: providing the steps needed for an algorithmic solution and explaining each step in detail to avoid misinterpretation by the LLM. By including explicit equations and non-ambiguous descriptions of indexing operations, the model can accurately learn and execute arithmetic algorithms.

Improving Generalization:
We test our approach by evaluating the model’s performance on addition problems of increasing length using algorithmic prompts. The results show that the model maintains high accuracy even for questions significantly longer than those seen in the prompt. This demonstrates the model’s ability to solve tasks by executing an input-agnostic algorithm.

Utilizing Algorithmic Skills:
To assess the model’s ability to leverage algorithmic reasoning in broader contexts, we evaluate its performance on grade school math word problems (GSM8k). By replacing addition calculations with algorithmic solutions, we observe a significant performance improvement. We accomplish this by combining different models specialized in informal mathematical reasoning and addition calculations.

Conclusion:
Our approach employing in-context learning and algorithmic prompting has proven effective in teaching algorithmic reasoning to LLMs. The results highlight the potential of using longer contexts and giving more detailed explanations to enhance reasoning performance. This research opens up promising avenues for further exploration in the field of AI.

Acknowledgments:
We extend our gratitude to our co-authors for their valuable contributions to the paper, as well as our thanks to Tom Small for creating the animations used in this post. This work was completed during Hattie Zhou’s internship at Google Research.