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:2606. 08477v1 Announce Type: new Abstract: Knowledge extraction from symbolic data often produces abstractions that are formally defined but not immediately interpretable by users.
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.
arXiv:2608.29311v1 Announce Type: new Abstract: Classic Formal Concept Analysis (FCA) primarily focuses on the positive relationships between objects and attributes and does not have mechanisms for h...
arXiv:2404. 03082v3 Announce Type: replace Abstract: Partially ordered sets (posets) are discrete mathematical structures that formalize the notion of comparison without forcing every pair of objects to be comparable.
arXiv:2608. 16319v1 Announce Type: new Abstract: This first release of Prior Labs in relational learning shows our continued commitment to open science.
arXiv:2608. 02930v1 Announce Type: new Abstract: We revisit higher-arity atomic concept learning through the geometry of hypercubes and hyperplanes of ground instances.
The paper proposes a method for automated research‑idea generation that preserves the typed structure of scientific papers by modeling each paper as a small category with typed research entities as objects and asserted relations as morphisms. It introduces a three‑layer algorithm—categorical signature clustering, a functor‑preservation gate, and a six‑axis LLM plausibility judge—to identify cross‑domain analogies that maintain relation chains. Experiments on tens of thousands of papers show the categorical gate filters candidates at a 17:1 ratio while keeping a falsifier rate above 83%, and it logs rejected candidates with detailed rationale.
The paper introduces SD-Pcomp learning, a binary classification framework that jointly utilizes Similarity/Dissimilarity (SD) labels and Pairwise Comparison (Pcomp) labels from instance pairs. It proposes an objective function that can be decomposed into either an SD estimator plus ordering information or a Pcomp estimator plus pair-type information, thereby integrating complementary relational cues. Experiments on eight datasets demonstrate that combining both label types improves classification accuracy and AUC compared to using either alone or a simple convex combination.
arXiv:2512. 07355v2 Announce Type: replace Abstract: Two traditions of interpretability have evolved side by side but seldom spoken to each other: Concept Bottleneck Models (CBMs), which prescribe what a concept should be, and Sparse Autoencoders (SAEs), which discover what concepts emerge.
arXiv:2604. 12176v2 Announce Type: replace Abstract: Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables.
arXiv:2607. 01773v1 Announce Type: new Abstract: Ontology construction requires deciding which objects, attributes, and structural relations should be accepted as valid knowledge.
arXiv:2601.10485v5 Announce Type: replace Abstract: Domain-specific knowledge graphs (DKGs) are critical yet often suffer from limited coverage compared to General Knowledge Graphs (GKGs). Existing t...