Effective Reasoning Chains Reduce Intrinsic Dimensionality

2026-02-09

AI Summary

This study addresses the lack of quantifiable mechanistic understanding regarding how reasoning strategies influence the generalization capabilities of language models. It introduces intrinsic dimensionality as a novel quantitative metric to evaluate the effectiveness of chain-of-thought reasoning, analyzing how different strategies compress task representations on the GSM8K benchmark. Using fixed model architectures (Gemma-3 1B and 4B), the work systematically assesses the efficiency of various reasoning approaches. Experimental results reveal a strong negative correlation between the intrinsic dimensionality induced by a reasoning strategy and its generalization performance—both in-distribution and out-of-distribution—demonstrating that effective reasoning enhances generalization by reducing the representational dimensionality required to solve the task.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Machine Learning: Large Multimodal Models (LMMs)

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Chain-of-thought (CoT) reasoning and its variants have substantially improved the performance of language models on complex reasoning tasks, yet the precise mechanisms by which different strategies facilitate generalization remain poorly understood. While current explanations often point to increased test-time computation or structural guidance, establishing a consistent, quantifiable link between these factors and generalization remains challenging. In this work, we identify intrinsic dimensionality as a quantitative measure for characterizing the effectiveness of reasoning chains. Intrinsic dimensionality quantifies the minimum number of model dimensions needed to reach a given accuracy threshold on a given task. By keeping the model architecture fixed and varying the task formulation through different reasoning strategies, we demonstrate that effective reasoning strategies consistently reduce the intrinsic dimensionality of the task. Validating this on GSM8K with Gemma-3 1B and 4B, we observe a strong inverse correlation between the intrinsic dimensionality of a reasoning strategy and its generalization performance on both in-distribution and out-of-distribution data. Our findings suggest that effective reasoning chains facilitate learning by better compressing the task using fewer parameters, offering a new quantitative metric for analyzing reasoning processes.

Problem

• Chain-of-thought
• intrinsic dimensionality
• generalization
• reasoning strategies
• language models

Innovation

• intrinsic dimensionality
• chain-of-thought reasoning
• generalization
• reasoning strategies
• language models