Logical Phase Transitions: Understanding Collapse in LLM Logical Reasoning

2026-01-06

arXiv.org

AI Summary

This work addresses the significant performance degradation of large language models (LLMs) in high-complexity symbolic logical reasoning tasks. It reveals, for the first time, a “logical phase transition” phenomenon wherein LLMs’ reasoning capabilities sharply decline as logical depth increases. To mitigate this, the authors propose a neuro-symbolic curriculum tuning framework that adaptively aligns natural language with formal logical symbols and dynamically adjusts training near the phase transition boundary. Evaluated across five benchmarks, the approach effectively alleviates reasoning collapse at high complexity levels, yielding average accuracy improvements of 1.26 and 3.95 under naive prompting and chain-of-thought (CoT) settings, respectively. Moreover, it substantially enhances generalization to unseen logical compositions.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Natural Language Processing: (Large) Language Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Symbolic logical reasoning is a critical yet underexplored capability of large language models (LLMs), providing reliable and verifiable decision-making in high-stakes domains such as mathematical reasoning and legal judgment. In this study, we present a systematic analysis of logical reasoning under controlled increases in logical complexity, and reveal a previously unrecognized phenomenon, which we term Logical Phase Transitions: rather than degrading smoothly, logical reasoning performance remains stable within a regime but collapses abruptly beyond a critical logical depth, mirroring physical phase transitions such as water freezing beyond a critical temperature threshold. Building on this insight, we propose Neuro-Symbolic Curriculum Tuning, a principled framework that adaptively aligns natural language with logical symbols to establish a shared representation, and reshapes training dynamics around phase-transition boundaries to progressively strengthen reasoning at increasing logical depths. Experiments on five benchmarks show that our approach effectively mitigates logical reasoning collapse at high complexity, yielding average accuracy gains of +1.26 in naive prompting and +3.95 in CoT, while improving generalization to unseen logical compositions. Code and data are available at https://github.com/AI4SS/Logical-Phase-Transitions.

Problem

• logical reasoning
• large language models
• phase transitions
• logical complexity
• reasoning collapse

Innovation

• Logical Phase Transitions
• Neuro-Symbolic Curriculum Tuning
• logical reasoning collapse
• symbolic reasoning
• large language models