Abstract
The quadratic embedding constant (QEC) of a finite, simple, connected graph originated from the classical work of Schoenberg [Ann. of Math., 1935] and [Trans. Amer. Math. Soc., 1938] on Euclidean distance geometry. In this article, we study the QEC of graphs in terms of two graph operations: the Cartesian product and the join of graphs. We derive a general formula for the QEC of the join of an arbitrary graph with a regular graph and with a complete multipartite graph. We then provide quadratic embedding constants for the Cartesian product of an arbitrary graph $G$ with a complete graph and with a complete bipartite graph in terms of QEC$(G)$.

Abstract
We study embeddings of graphs with bounded treewidth or bounded simple treewidth into the undirected graph underlying the directed product of two directed graphs. If the factors have bounded maximum indegrees, then the product graph has bounded maximum indegree and therefore is sparse. We prove that every graph of simple treewidth $k$ is contained in (ignoring edge directions) the directed product of directed graphs $\vec H_1$ and $\vec H_2$, with $\Delta^-(\vec H_1), \Delta^-(\vec H_2) \leq k-1 $ and $\text{tw}(H_1), \text{tw}(H_2) \leq k-1$. Further, we show that this treewidth bound is best possible. Several corollaries follow from our results: every outerplanar graph is contained in the directed product of trees with maximum indegree $1$, and every planar graph with treewidth $3$ is contained in a directed product of graphs with treewidth $2$ and maximum indegree $2$. However, for graphs of treewidth $k$, we prove a negative result: for any integers $s, t, k \geq 1$, there is a graph $G$ with treewidth $k$ not contained in the directed product of $\vec H_1$ and $\vec H_2$ for any directed graphs $\vec H_1$ and $\vec H_2$ with $\Delta^-(\vec H_1) \leq s$, $\Delta^-(\vec H_2) \leq t$, and $\text{tw}(H_1), \text{tw}(H_2) \leq k-1$. This result stands in stark contrast to the strong product case, where Liu, Norin and Wood [arXiv:2410.20333] proved that the optimal lower bound on the factors is about half the treewidth.

Abstract
We study the problem of fitting ontologies and constraints to positive and negative examples that take the form of a finite relational structure. As ontology and constraint languages, we consider the description logics $\mathcal{E\mkern-2mu L}$ and $\mathcal{E\mkern-2mu LI}$ as well as several classes of tuple-generating dependencies (TGDs): full, guarded, frontier-guarded, frontier-one, and unrestricted TGDs as well as inclusion dependencies. We pinpoint the exact computational complexity, design algorithms, and analyze the size of fitting ontologies and TGDs. We also investigate the related problem of constructing a finite basis of concept inclusions / TGDs for a given set of finite structures. While finite bases exist for $\mathcal{E\mkern-2mu L}$, $\mathcal{E\mkern-2mu LI}$, guarded TGDs, and inclusion dependencies, they in general do not exist for full, frontier-guarded and frontier-one TGDs.

Abstract
We study a fitting problem inspired by ontology-mediated querying: given a collection of positive and negative examples of the form $(\mathcal{A},q)$ with $\mathcal{A}$ an ABox and $q$ a Boolean query, we seek an ontology $\mathcal{O}$ that satisfies $\mathcal{A} \cup \mathcal{O} \vDash q$ for all positive examples and $\mathcal{A} \cup \mathcal{O}\not\vDash q$ for all negative examples. We consider the description logics $\mathcal{ALC}$ and $\mathcal{ALCI}$ as ontology languages and a range of query languages that includes atomic queries (AQs), conjunctive queries (CQs), and unions thereof (UCQs). For all of the resulting fitting problems, we provide effective characterizations and determine the computational complexity of deciding whether a fitting ontology exists. This problem turns out to be ${\scriptsize CO}NP$ for AQs and full CQs and $2E{\scriptsize XP}T{\scriptsize IME}$-complete for CQs and UCQs. These results hold for both $\mathcal{ALC}$ and $\mathcal{ALCI}$.

Abstract
Existing e-commerce platforms heavily rely on manual annotation for product categorization, which is inefficient and inconsistent. These platforms often employ a hierarchical structure for categorizing products; however, few studies have leveraged this hierarchical information for classification. Furthermore, studies that consider hierarchical information fail to account for similarities and differences across various hierarchical categories. Herein, we introduce a large-scale hierarchical dataset collected from the JD e-commerce platform (www.JD.com), comprising 1,011,450 products with titles and a three-level category structure. By making this dataset openly accessible, we provide a valuable resource for researchers and practitioners to advance research and applications associated with product categorization. Moreover, we propose a novel hierarchical text classification approach based on the widely used Bidirectional Encoder Representations from Transformers (BERT), called Hierarchical Fine-tuning BERT (HFT-BERT). HFT-BERT leverages the remarkable text feature extraction capabilities of BERT, achieving prediction performance comparable to those of existing methods on short texts. Notably, our HFT-BERT model demonstrates exceptional performance in categorizing longer short texts, such as books.

Abstract
Classification algorithms based on Artificial Intelligence (AI) are nowadays applied in high-stakes decisions in finance, healthcare, criminal justice, or education. Individuals can strategically adapt to the information gathered about classifiers, which in turn may require algorithms to be re-trained. Which collective dynamics will result from users' adaptation and algorithms' retraining? We apply evolutionary game theory to address this question. Our framework provides a mathematically rigorous way of treating the problem of feedback loops between collectives of users and institutions, allowing to test interventions to mitigate the adverse effects of strategic adaptation. As a case study, we consider institutions deploying algorithms for credit lending. We consider several scenarios, each representing different interaction paradigms. When algorithms are not robust against strategic manipulation, we are able to capture previous challenges discussed in the strategic classification literature, whereby users either pay excessive costs to meet the institutions' expectations (leading to high social costs) or game the algorithm (e.g., provide fake information). From this baseline setting, we test the role of improving gaming detection and providing algorithmic recourse. We show that increased detection capabilities reduce social costs and could lead to users' improvement; when perfect classifiers are not feasible (likely to occur in practice), algorithmic recourse can steer the dynamics towards high users' improvement rates. The speed at which the institutions re-adapt to the user's population plays a role in the final outcome. Finally, we explore a scenario where strict institutions provide actionable recourse to their unsuccessful users and observe cycling dynamics so far unnoticed in the literature.

Abstract
Large language models (LLMs) acquire vast knowledge from large text corpora, but this information can become outdated or inaccurate. Since retraining is computationally expensive, knowledge editing offers an efficient alternative -- modifying internal knowledge without full retraining. These methods aim to update facts precisely while preserving the model's overall capabilities. While existing surveys focus on the mechanism of editing (e.g., parameter changes vs. external memory), they often overlook the function of the knowledge being edited. This survey introduces a novel, complementary function-based taxonomy to provide a more holistic view. We examine how different mechanisms apply to various knowledge types -- factual, temporal, conceptual, commonsense, and social -- highlighting how editing effectiveness depends on the nature of the target knowledge. By organizing our review along these two axes, we map the current landscape, outline the strengths and limitations of existing methods, define the problem formally, survey evaluation tasks and datasets, and conclude with open challenges and future directions.

Abstract
Game-playing ability serves as an indicator for evaluating the strategic reasoning capability of large language models (LLMs). While most existing studies rely on utility performance metrics, which are not robust enough due to variations in opponent behavior and game structure. To address this limitation, we propose \textbf{Cognitive Hierarchy Benchmark (CHBench)}, a novel evaluation framework inspired by the cognitive hierarchy models from behavioral economics. We hypothesize that agents have bounded rationality -- different agents behave at varying reasoning depths/levels. We evaluate LLMs' strategic reasoning through a three-phase systematic framework, utilizing behavioral data from six state-of-the-art LLMs across fifteen carefully selected normal-form games. Experiments show that LLMs exhibit consistent strategic reasoning levels across diverse opponents, confirming the framework's robustness and generalization capability. We also analyze the effects of two key mechanisms (Chat Mechanism and Memory Mechanism) on strategic reasoning performance. Results indicate that the Chat Mechanism significantly degrades strategic reasoning, whereas the Memory Mechanism enhances it. These insights position CHBench as a promising tool for evaluating LLM capabilities, with significant potential for future research and practical applications.

Abstract
Human perceptual systems excel at inducing and recognizing objects across both known and novel categories, a capability far beyond current machine learning frameworks. While generalized category discovery (GCD) aims to bridge this gap, existing methods predominantly focus on optimizing objective functions. We present an orthogonal solution, inspired by the human cognitive process for novel object understanding: decomposing objects into visual primitives and establishing cross-knowledge comparisons. We propose ConGCD, which establishes primitive-oriented representations through high-level semantic reconstruction, binding intra-class shared attributes via deconstruction. Mirroring human preference diversity in visual processing, where distinct individuals leverage dominant or contextual cues, we implement dominant and contextual consensus units to capture class-discriminative patterns and inherent distributional invariants, respectively. A consensus scheduler dynamically optimizes activation pathways, with final predictions emerging through multiplex consensus integration. Extensive evaluations across coarse- and fine-grained benchmarks demonstrate ConGCD's effectiveness as a consensus-aware paradigm. Code is available at github.com/lytang63/ConGCD.

Abstract
Continuous category discovery (CCD) aims to automatically discover novel categories in continuously arriving unlabeled data. This is a challenging problem considering that there is no number of categories and labels in the newly arrived data, while also needing to mitigate catastrophic forgetting. Most CCD methods cannot handle the contradiction between novel class discovery and classification well. They are also prone to accumulate errors in the process of gradually discovering novel classes. Moreover, most of them use knowledge distillation and data replay to prevent forgetting, occupying more storage space. To address these limitations, we propose Independence-based Diversity and Orthogonality-based Discrimination (IDOD). IDOD mainly includes independent enrichment of diversity module, joint discovery of novelty module, and continuous increment by orthogonality module. In independent enrichment, the backbone is trained separately using contrastive loss to avoid it focusing only on features for classification. Joint discovery transforms multi-stage novel class discovery into single-stage, reducing error accumulation impact. Continuous increment by orthogonality module generates mutually orthogonal prototypes for classification and prevents forgetting with lower space overhead via representative representation replay. Experimental results show that on challenging fine-grained datasets, our method outperforms the state-of-the-art methods.

Abstract
Retrieval-Augmented Generation (RAG) plays a crucial role in grounding Large Language Models by leveraging external knowledge, whereas the effectiveness is often compromised by the retrieval of contextually flawed or incomplete information. To address this, knowledge graph-based RAG methods have evolved towards hierarchical structures, organizing knowledge into multi-level summaries. However, these approaches still suffer from two critical, unaddressed challenges: high-level conceptual summaries exist as disconnected ``semantic islands'', lacking the explicit relations needed for cross-community reasoning; and the retrieval process itself remains structurally unaware, often degenerating into an inefficient flat search that fails to exploit the graph's rich topology. To overcome these limitations, we introduce LeanRAG, a framework that features a deeply collaborative design combining knowledge aggregation and retrieval strategies. LeanRAG first employs a novel semantic aggregation algorithm that forms entity clusters and constructs new explicit relations among aggregation-level summaries, creating a fully navigable semantic network. Then, a bottom-up, structure-guided retrieval strategy anchors queries to the most relevant fine-grained entities and then systematically traverses the graph's semantic pathways to gather concise yet contextually comprehensive evidence sets. The LeanRAG can mitigate the substantial overhead associated with path retrieval on graphs and minimizes redundant information retrieval. Extensive experiments on four challenging QA benchmarks with different domains demonstrate that LeanRAG significantly outperforming existing methods in response quality while reducing 46\% retrieval redundancy. Code is available at: https://github.com/RaZzzyz/LeanRAG

Abstract
Soil organic carbon is crucial for climate change mitigation and agricultural sustainability. However, understanding its dynamics requires integrating complex, heterogeneous data from multiple sources. This paper introduces the Soil Organic Carbon Knowledge Graph (SOCKG), a semantic infrastructure designed to transform agricultural research data into a queryable knowledge representation. SOCKG features a robust ontological model of agricultural experimental data, enabling precise mapping of datasets from the Agricultural Collaborative Research Outcomes System. It is semantically aligned with the National Agricultural Library Thesaurus for consistent terminology and improved interoperability. The knowledge graph, constructed in GraphDB and Neo4j, provides advanced querying capabilities and RDF access. A user-friendly dashboard allows easy exploration of the knowledge graph and ontology. SOCKG supports advanced analyses, such as comparing soil organic carbon changes across fields and treatments, advancing soil carbon research, and enabling more effective agricultural strategies to mitigate climate change.