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Conditions for Length Generalization in Learning Reasoning Skills (2311.16173v2)

Published 22 Nov 2023 in cs.AI, cs.CL, and cs.LG

Abstract: Reasoning is a fundamental capability of AI agents. Recently, LLMs have shown remarkable abilities to perform reasoning tasks. However, numerous evaluations of the reasoning capabilities of LLMs have also showed some limitations. An outstanding limitation is length generalization, meaning that when trained on reasoning problems of smaller lengths or sizes, the resulting models struggle with problems of larger sizes or lengths. This potentially indicates some theoretical limitations of generalization in learning reasoning skills. These evaluations and their observations motivated us to perform a theoretical study of the length generalization problem. This work focuses on reasoning tasks that can be formulated as Markov dynamic processes (MDPs) and/or directed acyclic graphs (DAGs). It identifies and proves conditions that decide whether the length generalization problem can be solved or not for a reasoning task in a particular representation. Experiments are also conducted to verify the theoretical results.

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Citations (5)
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Summary

  • The paper identifies critical factors for length generalization, emphasizing the role of maximal input elements distance in AI reasoning performance.
  • It employs rigorous theoretical analysis by modeling reasoning tasks as Markov processes and directed acyclic graphs.
  • Experimental results demonstrate that different problem representations can significantly alter the effectiveness of Chain of Thought learning.

Overview of Length Generalization in AI Reasoning

LLMs are rapidly growing computational architectures that display an increasing capacity for executing complex reasoning tasks. However, despite their sophistication, LLMs face critical challenges when scaling tasks to greater sizes, a phenomenon known as length generalization. This paper provides a theoretical investigation into the conditions that allow for length generalization in learning reasoning skills, a significant step in understanding the capabilities of artificial intelligence.

Theoretical Context and Methodology

The research spotlights reasoning tasks that can be structured as Markov dynamic processes (MDPs) and/or directed acyclic graphs (DAGs), foundational elements in representing complex systems and computational tasks. In a rigorous theoretical approach, the authors identify and substantiate specific conditions under which an AI can generalize reasoning tasks to handle greater lengths effectively. This exploration is paired with experiments designed to substantiate the theoretical conclusions drawn regarding these conditions, enhancing our understanding of the factors that influence an AI's ability to adapt its reasoning skills to tasks of varying sizes.

Findings and Implications

A central finding of the paper is the importance of maximal input elements distance, denoted as RR, in determining an AI's success in learning to generalize reasoning across different lengths. Intriguingly, the paper suggests that different representations of the same problem can substantially affect this critical value, potentially influencing the solvability of the length generalization problem itself. This raises the question of whether reasoning tasks can always be represented in a manner that makes them amenable to Chain of Thought (CoT) based learning, which is essential for effectively tackling length generalization.

Future Perspectives

The paper concludes with acknowledging the current limitations and posing open-ended questions about reasoning problems that cannot be modeled as DAGs, and whether all reasoning problems can be represented sufficiently to allow for finite maximal input elements distance. These unanswered questions lay the groundwork for future research, highlighting the need to further examine the representation of reasoning problems and the mechanisms through which length generalization may be learned and applied across various dimensions. The importance of dimensionality in problem representation—one that aligns with human reasoning processes—is also underscored, indicating potential paths for making AI learning paradigms more intuitive and robust.

The research commends the initial inspiration from discussions on LLMs and acknowledges the contributions of collaborators and funding sources that supported this pioneering work in the field of AI reasoning.

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