The paper investigates how large language models (LLMs) organize reasoning operations—such as problem formulation, goal decomposition, and deduction—within their hidden representation spaces. It shows that these operations are separable in held‑out representations, with peak separability in middle layers, and that token‑wise alignment of operations becomes more distributed across spans as layers deepen. Attention‑masking experiments reveal that representations aligned to operations at chunk onsets depend on prior reasoning context, indicating a geometric correspondence between linguistic reasoning expressions and internal model structure.
By Seogyeong Jeong, Jaehui Hwang, Dongyoon Han, Geonmo Gu, Alice Oh, Taekyung Kim
Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space. Because LLMs operate on discrete tokens, they lack native support for continuous spatial representations, explicit geometric computation, and structured spatial operators.
arXiv:2606. 04381v1 Announce Type: cross Abstract: Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space.
By Chen Chu, Bita Azarijoo, Li Xiong, Khurram Shafique, Cyrus Shahabi
The paper examines convergence problems in Relational Concept Analysis (RCA) when applied to AOC-posets instead of full concept lattices. It explains why RCA’s iterative process may fail to converge in the AOC-poset setting, identifies conditions that can still guarantee convergence, and proposes a convergent variant that preserves the AOC-poset structure by never removing relational attributes. The study also discusses data transformations that can restore convergence.
By Xavier Dolques, Agn\`es Braud, Alain Gutierrez, Marianne Huchard, Florence Le Ber
arXiv:2607. 10578v1 Announce Type: new Abstract: Existing hypotheses represent a concept in an LLM as a single point, a linear direction, or a Gaussian cluster, yet it remains unclear how and why such structures emerge.
By Chunwei Ma, Russell Wolfinger
arXiv:2608. 07353v1 Announce Type: cross Abstract: Understanding concepts is fundamental to generalization.
By Karim Radouane, Jose G Moreno, Lynda Tamine
arXiv:2505. 12369v2 Announce Type: replace Abstract: Multi-hop logical reasoning on knowledge graphs requires faithfully mapping the logical semantics to latent space.
By Fernando Zhapa-Camacho, Robert Hoehndorf
arXiv:2607. 23513v1 Announce Type: cross Abstract: Diagrams are widely used to support logical reasoning, and prior studies suggest that representations such as Euler diagrams can improve human reasoning performance.
By Risako Ando, Koji Mineshima
arXiv:2505.16782v3 Announce Type: replace
Abstract: Large Language Models (LLMs) have shown impressive performance on complex tasks through Chain-of-Thought (CoT) reasoning. However, conventional CoT...
By Xinghao Chen, Anhao Zhao, Heming Xia, Xuan Lu, Hanlin Wang, Yanjun Chen, Wei Zhang, Jian Wang, Wenjie Li, Xiaoyu Shen
The paper introduces a framework that combines a Geometric Vision Parser and a Symbolic Solver to enable a Large Language Model to solve complex plane geometry problems. By translating diagrams into symbolic representations and performing formal deductions, the approach reduces hallucinations and produces interpretable, human-like solutions. Experiments on a new benchmark from 2025 Chinese Zhongkao exams show performance comparable to Gemini 2.5 Pro.
By Weichen Dai, Rafael Medeiros Cabral, Ziyi Shou, Yan Cao, Xin Shen, Dongcai Lu, Yi Zhou
The paper reviews Cobweb, a computational model of categorization and concept formation, and extends it to include chunks and their acquisition. It introduces rellis/, an implementation that applies this unified theory to learning context-free grammars, demonstrating the system’s ability to represent syntactic knowledge, parse and generate sentences, and learn compositional structures from sample parses. The authors discuss related work on concepts and chunks and suggest directions for future research.
By Karthik Singaravadivelan, Pat Langley
arXiv:2607. 19360v1 Announce Type: new Abstract: Large language models (LLMs) often answer queries by mapping individual observations to more general rule-like structures.
By Bumjin Park, Jaesik Choi