arXiv:2608. 02930v1 Announce Type: new Abstract: We revisit higher-arity atomic concept learning through the geometry of hypercubes and hyperplanes of ground instances.
arXiv:2607. 21183v1 Announce Type: cross Abstract: The propositional abduction problem is a well-known form of non-monotonic reasoning where we are asked to find an explanation of a given manifestation.
arXiv:2608. 14004v1 Announce Type: new Abstract: In-context learning is commonly formalized as inference from examples of a function.
arXiv:2607. 26984v1 Announce Type: cross Abstract: Mapping an atomic structure to a compact set of geometric descriptors is an essential step in any machine-learning application to atomic-scale modeling.
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:2605. 11644v3 Announce Type: replace-cross Abstract: Positive data can show that two tuple occurrences share a successful sentence context without certifying that they are safely interchangeable.
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:2603. 23561v4 Announce Type: replace-cross Abstract: In the realm of machine learning theory, to prevent unnatural coding schemes between teacher and learner, No-Clash Teaching Dimension was introduced as provably optimal complexity measure for collusion-free teaching.
arXiv:2606. 07007v1 Announce Type: cross Abstract: We propose a unified mathematical framework for a geometric understanding of concept learning and neuron interpretation in sparse autoencoders (SAEs).
arXiv:2603. 07221v2 Announce Type: replace Abstract: Margin-based learning, exemplified by linear and kernel methods, is one of the few classical settings where generalization guarantees are independent of the number of parameters.
The paper investigates fundamental limits of algorithmic principles in multiclass learning, specifically proper learning and regularization. It shows that learning cannot always be reduced to proper learning even with an enlarged hypothesis class, that proper learners may need a sublinear number of errors that can be arbitrarily large, and that regularization (SRM or local) is not universally sufficient. The authors also provide a positive theory giving sufficient conditions for SRM learnability and a characterization via integrability of revealed preferences.
arXiv:2606. 28309v1 Announce Type: cross Abstract: Binary classification from positive-only samples is a variant of PAC learning in which the learner receives i.
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.