arXiv:2603. 01227v3 Announce Type: replace Abstract: We propose the Lattice Representation Hypothesis of large language models: a symbolic backbone that grounds conceptual hierarchies and logical operations in embedding geometry.
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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.
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.
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.
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.
arXiv:2608. 07353v1 Announce Type: cross Abstract: Understanding concepts is fundamental to generalization.