# Logical Phase Transitions: Understanding Collapse in LLM Logical Reasoning

arXiv: https://arxiv.org/abs/2601.02902 · HTML: https://mlsanity.com/paper/2601.02902/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 33 of its 67 references that are in the map.
- First posted on arXiv 6 Jan 2026.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 33)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Towards Reasoning in Large Language Models: A Survey](https://mlsanity.com/paper/2212.10403/) (2022)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Qwen2.5-1M Technical Report](https://mlsanity.com/paper/2501.15383/) (2025)
- [MathCoder: Seamless Code Integration in LLMs for Enhanced Mathematical Reasoning](https://mlsanity.com/paper/2310.03731/) (2023)
- [Faithful Logical Reasoning via Symbolic Chain-of-Thought](https://mlsanity.com/paper/2405.18357/) (2024)
- [Cumulative Reasoning with Large Language Models](https://mlsanity.com/paper/2308.04371/) (2023)
- [Harnessing the Power of Large Language Models for Natural Language to First-Order Logic Translation](https://mlsanity.com/paper/2305.15541/) (2023)
- [Rethinking Entropy Interventions in RLVR: An Entropy Change Perspective](https://mlsanity.com/paper/2510.10150/) (2025)
- [AMO-Bench: Large Language Models Still Struggle in High School Math Competitions](https://mlsanity.com/paper/2510.26768/) (2025)
- [Semantic-Aware Logical Reasoning via a Semiotic Framework](https://mlsanity.com/paper/2509.24765/) (2025)
- [Coupled Mamba: Enhanced Multi-modal Fusion with Coupled State Space Model](https://mlsanity.com/paper/2405.18014/) (2024)
- [Think-While-Generating: On-the-Fly Reasoning for Personalized Long-Form Generation](https://mlsanity.com/paper/2512.06690/) (2025)
- [Large Language Models Meet Symbolic Provers for Logical Reasoning Evaluation](https://mlsanity.com/paper/2502.06563/) (2025)
- [Divide and Translate: Compositional First-Order Logic Translation and Verification for Complex Logical Reasoning](https://mlsanity.com/paper/2410.08047/) (2024)
- [SF2T: Self-supervised Fragment Finetuning of Video-LLMs for Fine-Grained Understanding](https://mlsanity.com/paper/2504.07745/) (2025)
- [STAGE: Storyboard-Anchored Generation for Cinematic Multi-shot Narrative](https://mlsanity.com/paper/2512.12372/) (2025)
- [Deep SE(3)-Equivariant Geometric Reasoning for Precise Placement Tasks](https://mlsanity.com/paper/2404.13478/) (2024)
- [LoRA-Mixer: Coordinate Modular LoRA Experts Through Serial Attention Routing](https://mlsanity.com/paper/2507.00029/) (2025)
- [Aristotle: Mastering Logical Reasoning with A Logic-Complete Decompose-Search-Resolve Framework](https://mlsanity.com/paper/2412.16953/) (2024)
- [MVP: Winning Solution to SMP Challenge 2025 Video Track](https://mlsanity.com/paper/2507.00950/) (2025)
- [DualVLA: Building a Generalizable Embodied Agent via Partial Decoupling of Reasoning and Action](https://mlsanity.com/paper/2511.22134/) (2025)
- [InSPO: Unlocking Intrinsic Self-Reflection for LLM Preference Optimization](https://mlsanity.com/paper/2512.23126/) (2025)

## Built on by (most cited first, 25 of 25)

- [Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Models](https://mlsanity.com/paper/2601.11340/) (2026)
- [Reason in Chains, Learn in Trees: Self-Rectification and Grafting for Multi-turn Agent Policy Optimization](https://mlsanity.com/paper/2604.07165/) (2026)
- [Recursive Self-Evolving Agents via Held-Out Selection](https://mlsanity.com/paper/2606.28374/) (2026)
- [Rethinking Layer-Wise Information Allocation for Vision Foundation Model Adaptation](https://mlsanity.com/paper/2607.21973/) (2026)
- [From log π to π: Taming Divergence in Soft Clipping via Bilateral Decoupled Decay of Probability Gradient Weight](https://mlsanity.com/paper/2603.14389/) (2026)
- [One Refiner to Unlock Them All: Inference-Time Reasoning Elicitation via Reinforcement Query Refinement](https://mlsanity.com/paper/2604.25444/) (2026)
- [PERM: Psychology-grounded Empathetic Reward Modeling for Large Language Models](https://mlsanity.com/paper/2601.10532/) (2026)
- [Seeing Further and Wider: Joint Spatio-Temporal Enlargement for Micro-Video Popularity Prediction](https://mlsanity.com/paper/2604.20311/) (2026)
- [Large Language Model as Token Compressor and Decompressor](https://mlsanity.com/paper/2603.25340/) (2026)
- [ActorMind: Emulating Human Actor Reasoning for Speech Role-Playing](https://mlsanity.com/paper/2604.11103/) (2026)
- [Sparse Growing Transformer: Training-Time Sparse Depth Allocation via Progressive Attention Looping](https://mlsanity.com/paper/2603.23998/) (2026)
- [STRIDE-ED: A Strategy-Grounded Stepwise Reasoning Framework for Empathetic Dialogue Systems](https://mlsanity.com/paper/2604.07100/) (2026)
- [HotComment: A Benchmark for Evaluating Popularity of Online Comments](https://mlsanity.com/paper/2604.25614/) (2026)
- [CurEvo: Curriculum-Guided Self-Evolution for Video Understanding](https://mlsanity.com/paper/2604.26707/) (2026)
- [OmniTrend: Content-Context Modeling for Scalable Social Popularity Prediction](https://mlsanity.com/paper/2604.26252/) (2026)
- [IMAGINE: Adaptive Schema-Imagery Enhanced Composition for Composed Video Retrieval](https://mlsanity.com/paper/2606.08144/) (2026)
- [Semiotic logical hexagon theory for LLM logical reasoning](https://mlsanity.com/paper/2607.21933/) (2026)
- [Surfacing the Unsaid: CUE-Bench for Affective Stance in Chinese Discourse](https://mlsanity.com/paper/2608.10810/) (2026)
- [From Topology to Trajectory: LLM-Driven World Models For Supply Chain Resilience](https://mlsanity.com/paper/2604.11041/) (2026)
- [GateMOT: Q-Gated Attention for Dense Object Tracking](https://mlsanity.com/paper/2604.26353/) (2026)
- [When Does Critique Improve AI-Assisted Theoretical Physics? SCALAR: Structured Critic--Actor Loop for Agentic Reasoning](https://mlsanity.com/paper/2605.06772/) (2026)
- [Customer-Agent: Overcoming Context Limitations in Ultra-Long Shopping Trajectories via Tool-Augmented Agents and RLVR](https://mlsanity.com/paper/2606.07995/) (2026)
- [BV-Blend: Uncertainty-Weighted Historical Baselines for Stable Critic-Free RL with Verifiable Rewards](https://mlsanity.com/paper/2606.28707/) (2026)
- [LightAIR: Lightweight Action Inversion and Riemannian Rectification for Text-based Person Anomaly Search](https://mlsanity.com/paper/2608.09152/) (2026)
- [Too Good to Be Real? Diagnosing and Reducing the Gap Between AI Preference and Real User Engagement](https://mlsanity.com/paper/2609.18282/) (2026)

## Abstract (arXiv)

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.