Algorithmic Phase Transitions in Language Models: A Mechanistic Case Study of Arithmetic

• URL: http://arxiv.org/abs/2412.07386v1
• Date: Tue, 10 Dec 2024 10:32:01 GMT
• Title: Algorithmic Phase Transitions in Language Models: A Mechanistic Case Study of Arithmetic
• Authors: Alan Sun, Ethan Sun, Warren Shepard,
• Abstract summary: Large language models can zero-shot some tasks but not others.<n>Algorithm instability may be a contributing factor to language models' poor zero-shot performance.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Zero-shot capabilities of large language models make them powerful tools for solving a range of tasks without explicit training. It remains unclear, however, how these models achieve such performance, or why they can zero-shot some tasks but not others. In this paper, we shed some light on this phenomenon by defining and investigating algorithmic stability in language models -- changes in problem-solving strategy employed by the model as a result of changes in task specification. We focus on a task where algorithmic stability is needed for generalization: two-operand arithmetic. Surprisingly, we find that Gemma-2-2b employs substantially different computational models on closely related subtasks, i.e. four-digit versus eight-digit addition. Our findings suggest that algorithmic instability may be a contributing factor to language models' poor zero-shot performance across certain logical reasoning tasks, as they struggle to abstract different problem-solving strategies and smoothly transition between them.

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