Teaching Algorithmic Reasoning via In-context Learning (2211.09066v1)

Abstract: 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 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.

Teaching Algorithmic Reasoning via In-context Learning

The research paper "Teaching Algorithmic Reasoning via In-context Learning" elucidates an innovative approach to teaching algorithmic reasoning to LLMs. It addresses the persistent challenge faced by LLMs in executing algorithmic reasoning tasks, despite their advancements in handling multi-step reasoning problems. The paper explores enhancing LLM capabilities by adopting a structured learning framework that revolves around algorithmic prompting, showing promising improvements in various arithmetic and reasoning tasks.

Key Research Contributions

The researchers articulate four pivotal stages for transferring algorithmic reasoning skills to LLMs:

1. Formulating Algorithms as Skills: By breaking down algorithms into discrete skills, the paper promotes a modular approach to learning. This decomposition is fundamental to rendering complex reasoning tasks more tractable for LLMs.
2. Skill Accumulation: This refers to teaching multiple skills simultaneously. The paper demonstrates that LLMs can effectively learn and retain multiple algorithmic skills when taught in conjunction with one another, without encountering significant interference between them.
3. Skill Composition: Learning to combine different skills to solve complex tasks is a critical aspect of this research. The paper showcases that skill composition enables LLMs to tackle more elaborate algorithmic tasks by building upon simpler learned skills.
4. Utilizing Skills as Tools: This involves the application of learned skills as tools within broader problem-solving contexts, such as solving math word problems. This tool use is indicative of the model's ability to apply learned reasoning in novel scenarios.

Experimental Results and Implications

The paper provides substantial evidence of the efficacy of algorithmic prompting through rigorous testing on tasks such as addition, subtraction, multiplication, and parity. The results are compelling, achieving error reductions of approximately 90% for addition and parity tasks compared to baseline approaches. Such improvements underscore the potential of algorithmic prompts to significantly enhance out-of-distribution generalization—a key obstacle for LLMs.

Algorithmic Prompting Approach

Algorithmic prompting, as presented in the paper, involves providing LLMs with explicit, detailed descriptions of algorithm execution running on examples. This method contrasts with traditional few-shot and chain-of-thought prompts by offering unambiguous and structured rationales, which drive the model to follow specific algorithmic logic closely.

The implementation of this method illustrates the capacity of LLMs to infer systematic rules from detailed prompts, adapting the learned procedures to solve longer instances of algorithmic tasks successfully. This fidelity to in-context instructions marks a departure from prior models that struggle with such generalization.

Future Directions and Challenges

While the results mark significant progress, the paper identifies challenges and future research trajectories. One notable challenge is the "interference" phenomenon observed when using learned algorithms within different reasoning contexts, which can detract from the model's broader reasoning capabilities.

Future research could explore mechanisms for selective attention or retrieval of specific skills, enhancing the robustness and flexibility of LLMs in practical applications. Additionally, scaling the approach to accommodate even more extensive context lengths and complex algorithms through architecture innovations like recurrence or external memory systems could offer further enhancements to model reasoning capabilities.

Conclusion

This paper makes noteworthy strides toward equipping LLMs with enhanced algorithmic reasoning abilities via in-context learning. By formulating and explicitly teaching algorithmic skills, the research illustrates the potential for LLMs to overcome generalization challenges—paving the way for more capable and versatile AI models in the field of mathematical and logical reasoning.