The Geometry of Thought: How Scale Restructures Reasoning In Large Language Models
Scale does not uniformly improve reasoning - it restructures it. Analyzing 25,000+ chain-of-thought trajectories across four domains (Law, Science, Code, Math) and two scales (8B, 70B parameters), we discover that neural scaling laws trigger domain-specific phase transitions rather than uniform capability gains. Legal reasoning undergoes Crystallization: 45% collapse in representational dimensionality (d95: 501 -> 274), 31% increase in trajectory alignment, and 10x manifold untangling. Scientific and mathematical reasoning remain Liquid - geometrically invariant despite 9x parameter increase. Code reasoning forms a discrete Lattice of strategic modes (silhouette: 0.13 -> 0.42). This geometry predicts learnability. We introduce Neural Reasoning Operators - learned mappings from initial to terminal hidden states. In crystalline legal reasoning, our operator achieves 63.6% accuracy on held-out tasks via probe decoding, predicting reasoning endpoints without traversing intermediate states. We further identify a universal oscillatory signature (coherence ~ -0.4) invariant across domains and scales, suggesting attention and feedforward layers drive reasoning through opposing dynamics. These findings establish that the cost of thought is determined not by task difficulty but by manifold geometry - offering a blueprint for inference acceleration where topology permits.
Code (0)
등록된 구현이 없습니다.
Tasks
Mathematical ReasoningLegal ReasoningSimilar Papers 제목 키워드 기반
Baby's CoThought: Leveraging Large Language Models for Enhanced Reasoning in Compact Models
Large Language Models (LLMs) demonstrate remarkable performance on a variety of natural language understanding (NLU) tasks, primarily due to their in-context learning ability. This ability could be applied to building ba…
In-Context LearningNatural Language UnderstandingQuestion AnsweringCan Reasoning Models Reason about Hardware? An Agentic HLS Perspective
Recent Large Language Models (LLMs) such as OpenAI o3-mini and DeepSeek-R1 use enhanced reasoning through Chain-of-Thought (CoT). Their potential in hardware design, which relies on expert-driven iterative optimization, …
High-Level SynthesisGeoThought: A Dataset for Enhancing Mathematical Geometry Reasoning in Vision-Language Models
Large language models (LLMs) have demonstrated strong reasoning capabilities in text-based mathematical problem solving; however, when adapted to visual reasoning tasks, particularly geometric problem solving, their perf…
Mathematical ReasoningVisual ReasoningBridging Formal Language with Chain-of-Thought Reasoning to Geometry Problem Solving
Large vision language models exhibit notable limitations on Geometry Problem Solving (GPS) because of their unreliable diagram interpretation and pure natural-language reasoning. A recent line of work mitigates this by u…
Reinforcement LearningLearning Geometric Representations from Videos for Spatial Intelligent Multimodal Large Language Models
Multimodal Large Language Models (MLLMs) excel at 2D semantic understanding but lack intrinsic 3D awareness, resulting in representations that fail to maintain geometric and spatial consistency across video frames. Given…
Spatial Reasoning