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:2608.22044v1 Announce Type: new Abstract: Modern machine learning (ML) methods are highly effective for prediction tasks, but many commonly used representations reduce complex data to fixed dim...
arXiv:2609.37884v1 Announce Type: new Abstract: Topological structures such as simplicial complexes, hypergraphs, and cell complexes extend standard graph models by modeling higher-order relationship...
arXiv:2507. 21873v2 Announce Type: replace Abstract: Graph neural networks (GNNs) excel at predictive tasks on graph-structured data but often lack the ability to incorporate symbolic domain knowledge and perform general reasoning.
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. 12077v1 Announce Type: new Abstract: Time-series clustering remains challenging due to the inherent trade-off between clustering effectiveness and computational efficiency.
arXiv:2506.05626v3 Announce Type: replace Abstract: Real-world knowledge can take various forms, including structured, semi-structured, and unstructured data. Among these, Knowledge Graphs (KGs) are...
arXiv:2606. 15386v1 Announce Type: new Abstract: Open-ended intelligence is the capacity to adapt to novel problems and environments that are substantially different from those in training.
arXiv:2506. 20699v2 Announce Type: replace Abstract: Learning in non-stationary and multi-context environments requires more than ordinary within-task generalization.
arXiv:2609.37680v1 Announce Type: cross Abstract: One of the current premises of mechanistic interpretability research is that detailed accounts of the geometry of neural network representations can...
arXiv:2606. 30410v1 Announce Type: cross Abstract: Foundation models for predictive machine learning on tabular data have recently gained significant traction in academia and industry.
arXiv:2608. 15388v1 Announce Type: new Abstract: Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs.
arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.