Effective Reasoning Chains Reduce Intrinsic Dimensionality

• URL: http://arxiv.org/abs/2602.09276v1
• Date: Mon, 09 Feb 2026 23:32:12 GMT
• Title: Effective Reasoning Chains Reduce Intrinsic Dimensionality
• Authors: Archiki Prasad, Mandar Joshi, Kenton Lee, Mohit Bansal, Peter Shaw,
• Abstract summary: Intrinsic dimensionality is a measure of the minimum number of model dimensions needed to reach a given accuracy threshold.<n>We show that effective reasoning strategies consistently reduce the intrinsic dimensionality of the task.<n>Our findings suggest that effective reasoning chains facilitate learning by better compressing the task using fewer parameters.
• Score: 53.24264007741698
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Learning Structured Reasoning via Tractable Trajectory Control [99.75278337895024]
  Ctrl-R is a framework for learning structured reasoning via tractable trajectory control.<n>We show that Ctrl-R enables effective exploration and internalization of previously unattainable reasoning patterns.
  arXiv  Detail & Related papers  (2026-03-02T09:18:19Z)
• Identity Bridge: Enabling Implicit Reasoning via Shared Latent Memory [7.204534405819971]
  This paper introduces the Identity Bridge, a mechanism that resolves the compositionality gap by supervising the model on a zero-hop identity task.<n>We show that this mechanism enables models to successfully perform out-of-distribution two-hop reasoning.<n>We extend our investigation to large-scale models, observing that they still achieve two-hop reasoning through the latent memory.
  arXiv  Detail & Related papers  (2025-09-29T12:02:05Z)
• Is Long-to-Short a Free Lunch? Investigating Inconsistency and Reasoning Efficiency in LRMs [8.359909829007005]
  We investigate whether efficient reasoning strategies introduce behavioral inconsistencies in large reasoning models (LRMs)<n>$ICBENCH$ is a benchmark designed to measure inconsistency in LRMs across three dimensions.<n>We find that while larger models generally exhibit greater consistency than smaller ones, they all display widespread "scheming" behaviors.
  arXiv  Detail & Related papers  (2025-06-24T10:25:28Z)
• Exploring and Exploiting the Inherent Efficiency within Large Reasoning Models for Self-Guided Efficiency Enhancement [101.77467538102924]
  Large reasoning models (LRMs) exhibit overthinking, which hinders efficiency and inflates inference cost.<n>We propose two lightweight methods to enhance LRM efficiency.<n>First, we introduce Efficiency Steering, a training-free activation steering technique that modulates reasoning behavior via a single direction.<n>Second, we develop Self-Rewarded Efficiency RL, a reinforcement learning framework that dynamically balances task accuracy and brevity.
  arXiv  Detail & Related papers  (2025-06-18T17:18:12Z)
• A Theory of Inference Compute Scaling: Reasoning through Directed Stochastic Skill Search [15.387256204743407]
  Large language models (LLMs) demand considerable computational, energy, and financial resources during both training and deployment.<n>Inference costs now represent a significant and growing component of the overall resource burden.<n>We introduce directed skill search (DS3), a general framework that represents inference as expressive over a learned skill graph.
  arXiv  Detail & Related papers  (2025-06-10T14:47:48Z)
• PixelThink: Towards Efficient Chain-of-Pixel Reasoning [70.32510083790069]
  PixelThink is a simple yet effective scheme that integrates externally estimated task difficulty and internally measured model uncertainty.<n>It learns to compress reasoning length in accordance with scene complexity and predictive confidence.<n> Experimental results demonstrate that the proposed approach improves both reasoning efficiency and overall segmentation performance.
  arXiv  Detail & Related papers  (2025-05-29T17:55:49Z)
• Think or Not? Exploring Thinking Efficiency in Large Reasoning Models via an Information-Theoretic Lens [51.90059610606049]
  This paper revisits the efficiency of such reasoning processes through an information-theoretic lens.<n>We propose two metrics, InfoBias and InfoGain, to quantify divergence from ideal reasoning paths and stepwise information contribution.<n>Motivated by these findings, we introduce an entropy-based Adaptive Think strategy that dynamically halts reasoning once confidence is sufficiently high.
  arXiv  Detail & Related papers  (2025-05-23T13:38:56Z)
• Efficient Inference for Large Reasoning Models: A Survey [74.17203483365171]
  Large Reasoning Models (LRMs) significantly improve the reasoning ability of Large Language Models (LLMs) by learning to reason.<n>However, their deliberative reasoning process leads to inefficiencies in token usage, memory consumption, and inference time.<n>This survey provides a review of efficient inference methods designed specifically for LRMs, focusing on mitigating token inefficiency while preserving the reasoning quality.
  arXiv  Detail & Related papers  (2025-03-29T13:27:46Z)
• Stepwise Perplexity-Guided Refinement for Efficient Chain-of-Thought Reasoning in Large Language Models [56.37421741507468]
  Chain-of-Thought (CoT) reasoning has significantly enhanced the performance of large language models (LLMs)<n>We propose a method to identify critical reasoning steps using perplexity as a measure of their importance.
  arXiv  Detail & Related papers  (2025-02-18T20:04:51Z)
• Contextual Reinforcement in Multimodal Token Compression for Large Language Models [0.0]
  token compression remains a critical challenge for scaling models to handle increasingly complex and diverse datasets.<n>A novel mechanism based on contextual reinforcement is introduced, dynamically adjusting token importance through interdependencies and semantic relevance.<n>This approach enables substantial reductions in token usage while preserving the quality and coherence of information representation.
  arXiv  Detail & Related papers  (2025-01-28T02:44:31Z)
• The Role of Deductive and Inductive Reasoning in Large Language Models [35.43513487137371]
  We propose the Deductive and InDuctive(DID) method to enhance Large Language Models (LLMs) reasoning.<n>DID implements a dual-metric complexity evaluation system that combines Littlestone dimension and information entropy.<n>Our results demonstrate significant improvements in reasoning quality and solution accuracy.
  arXiv  Detail & Related papers  (2024-10-03T18:30:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.