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Teaching Algorithmic Reasoning via In-context Learning
Hattie Zhou · Azade Nova · aaron courville · Hugo Larochelle · Behnam Neyshabur · Hanie Sedghi

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in MATH-AI: Toward Human-Level Mathematical Reasoning »

Large language models (LLMs) have shown increasing in-context learning capabilities through scaling up model and data size. Despite this progress, LLMs are still unable to solve algorithmic reasoning problems. While providing a rationale with the final answer has led to further improvements in multi-step reasoning problems, Anil et al. 2022 showed that even simple algorithmic reasoning tasks such as parity are far from solved. In this work, we identify and study four key stages for successfully teaching algorithmic reasoning to LLMs: (1) formulating algorithms as skills, (2) teaching multiple skills simultaneously (skill accumulation), (3) teaching how to combine skills (skill composition) and (4) teaching how to use skills as tools. We show that it is possible to teach algorithmic reasoning to LLMs via in-context learning, which we refer to as \emph{algorithmic prompting}. We evaluate our approach on a variety of arithmetic and quantitative reasoning tasks, and demonstrate significant boosts in performance over existing prompting techniques. In particular, for long parity, addition, multiplication and subtraction, we achieve an error reduction of approximately 10x, 9x, 5x and 2x respectively compared to the best available baselines.

Author Information

Hattie Zhou (Mila)
Azade Nova (Google Brain)
aaron courville (Université de Montréal)
Hugo Larochelle (Google Brain)
Behnam Neyshabur (Google)
Hanie Sedghi (Google Research, Brain team)
Hanie Sedghi

I am a senior research scientist at Google Brain, where I lead the “Deep Phenomena” team. My approach is to bond theory and practice in large-scale machine learning by designing algorithms with theoretical guarantees that also work efficiently in practice. Over the recent years, I have been working on understanding and improving deep learning. Prior to Google, I was a Research Scientist at Allen Institute for Artificial Intelligence and before that, a postdoctoral fellow at UC Irvine. I received my PhD from University of Southern California with a minor in mathematics in 2015.

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