arXiv:2607. 00005v1 Announce Type: cross Abstract: Identifying where to innovate in a dense technical domain - such as operating systems or hardware/software co-design - is fundamentally a search problem in a high-dimensional knowledge space.
arXiv:2606. 15656v1 Announce Type: new Abstract: Modern artificial intelligence remains fundamentally divided between the continuous, probabilistic spaces of Foundation Models and the discrete, deterministic structures of Knowledge Graphs.
arXiv:2606. 13566v1 Announce Type: new Abstract: Current discussions of AI in scientific discovery are often dominated by two visible capabilities: search over existing knowledge and execution through optimization, simulation, and automation.
arXiv:2511. 04873v2 Announce Type: replace-cross Abstract: Prototype selection methods compress a training set, but the existing taxonomy of condensation, edition, hybrid, competence-based, optimization-based, and clustering-based families does not include methods that operate on the multi-scale topological structure of the data.
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:2606. 06342v1 Announce Type: cross Abstract: Topological Data Analysis (TDA) offers a principled, intrinsic lens for comparing neural representations.
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.
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...
arXiv:2606. 29763v1 Announce Type: cross Abstract: Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.
The paper shows that large language models (LLMs) naturally organize their hidden state manifolds into small‑world networks, enabling efficient multi‑hop reasoning. By converting similarity matrices into unweighted graphs, the authors trace connectivity between distant semantic anchors and find a sharp topological phase transition: deep reasoning layers compress conceptual distances into paths bounded by six semantic hops, while early syntactic layers remain fragmented. The framework is applied to zero‑shot hallucination detection in Retrieval‑Augmented Generation, revealing that factual generations preserve a ~3‑hop structure, whereas hallucinations collapse the topology.
arXiv:2605. 00725v2 Announce Type: replace Abstract: Topological neural networks have emerged as effective tools for modeling higher-order relational structures beyond pairwise graphs, including hypergraphs, simplicial complexes, and cell complexes.
arXiv:2605. 22093v3 Announce Type: replace Abstract: Knowledge graphs have become the primary vehicle for data integration and are critical to the success of modern AI, but the diversity of KG modelling practices, from lightweight vocabularies to richly axiomatised ontologies, makes integration and reuse expensive and brittle.
arXiv:2606. 17531v1 Announce Type: new Abstract: We investigate the learning of interpretable bases in non-negative matrix factorisation (NMF) by regularising the topology of the learned basis functions.