The aim of this paper is to extend the context of nonmonotone descent methods to the class of nonsmooth and nonconvex functions called upper-$\mathcal{C}^2$, which satisfy a nonsmooth and local version of the descent lemma. Under this assumption, we propose a general subgradient method that performs a nonmonotone linesearch, and we prove subsequential convergence to a stationary point of the optimization problem. Our approach allows us to cover the setting of various subgradient algorithms, including Newton and quasi-Newton methods. In addition, we propose a specification of the general scheme, named Self-adaptive Nonmonotone Subgradient Method (SNSM), which automatically updates the parameters of the linesearch. Particular attention is paid to the minimum sum-of-squares clustering problem, for which we provide a concrete implementation of SNSM. We conclude with some numerical experiments where we exhibit the advantages of SNSM in comparison with some known algorithms.

Humans possess an innate ability to group objects by similarity, a cognitive mechanism that clustering algorithms aim to emulate. Recent advances in community detection have enabled the discovery of configurations -- valid hierarchical clusterings across multiple resolution scales -- without requiring labeled data. In this paper, we formally characterize these configurations and identify similar emergent structures in register tokens within Vision Transformers. Unlike register tokens, configurations exhibit lower redundancy and eliminate the need for ad hoc selection. They can be learned through unsupervised or self-supervised methods, yet their selection or composition remains specific to the downstream task and input. Building on these insights, we introduce GraMixC, a plug-and-play module that extracts configurations, aligns them using our Reverse Merge/Split (RMS) technique, and fuses them via attention heads before forwarding them to any downstream predictor. On the DSN1 16S rRNA cultivation-media prediction task, GraMixC improves the R2 score from 0.6 to 0.9 across multiple methods, setting a new state of the art. We further validate GraMixC on standard tabular benchmarks, where it consistently outperforms single-resolution and static-feature baselines.

Decision trees are prized for their interpretability and strong performance on tabular data. Yet, their reliance on simple axis-aligned linear splits often forces deep, complex structures to capture non-linear feature effects, undermining human comprehension of the constructed tree. To address this limitation, we propose a novel generalization of a decision tree, the Shape Generalized Tree (SGT), in which each internal node applies a learnable axis-aligned shape function to a single feature, enabling rich, non-linear partitioning in one split. As users can easily visualize each node's shape function, SGTs are inherently interpretable and provide intuitive, visual explanations of the model's decision mechanisms. To learn SGTs from data, we propose ShapeCART, an efficient induction algorithm for SGTs. We further extend the SGT framework to bivariate shape functions (S$^2$GT) and multi-way trees (SGT$_K$), and present Shape$^2$CART and ShapeCART$_K$, extensions to ShapeCART for learning S$^2$GTs and SGT$_K$s, respectively. Experiments on various datasets show that SGTs achieve superior performance with reduced model size compared to traditional axis-aligned linear trees.

Class imbalance, where certain classes have insufficient data, poses a critical challenge for robust classification, often biasing models toward majority classes. Distribution calibration offers a promising avenue to address this by estimating more accurate class distributions. In this work, we propose Rebalancing with Calibrated Sub-classes (RCS) - a novel distribution calibration framework for robust imbalanced classification. RCS aims to fuse statistical information from the majority and intermediate class distributions via a weighted mixture of Gaussian components to estimate minority class parameters more accurately. An encoder-decoder network is trained to preserve structural relationships in imbalanced datasets and prevent feature disentanglement. Post-training, encoder-extracted feature vectors are leveraged to generate synthetic samples guided by the calibrated distributions. This fusion-based calibration effectively mitigates overgeneralization by incorporating neighborhood distribution information rather than relying solely on majority-class statistics. Extensive experiments on diverse image, text, and tabular datasets demonstrate that RCS consistently outperforms several baseline and state-of-the-art methods, highlighting its effectiveness and broad applicability in addressing real-world imbalanced classification challenges.

This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex system often exhibiting non-linear and high-dimensional dynamics that classical techniques may not fully capture. We compare clustering results based on TDA-derived features versus classical statistical features using monthly logarithmic returns of 13 major currency exchange rates (all against the euro). Two widely-used clustering algorithms, \(k\)-means and Hierarchical clustering, are applied on both types of features, and cluster quality is evaluated via the Silhouette score and the Calinski-Harabasz index. Our findings show that TDA-based feature clustering produces more compact and well-separated clusters than clustering on traditional statistical features, particularly achieving substantially higher Calinski-Harabasz scores. However, all clustering approaches yield modest Silhouette scores, underscoring the inherent difficulty of grouping FX time series. The differing cluster compositions under TDA vs. classical features suggest that TDA captures structural patterns in currency co-movements that conventional methods might overlook. These results highlight TDA as a valuable complementary tool for analysing financial time series, with potential applications in risk management where understanding structural co-movements is crucial.

Artificial intelligence approaches are being adapted to many research areas, including digital humanities. We built a methodology for large-scale analyses in folkloristics. Using machine learning and natural language processing, we automatically detected motifs in a large collection of Cinderella variants and analysed their similarities and differences with clustering and dimensionality reduction. The results show that large language models detect complex interactions in tales, enabling computational analysis of extensive text collections and facilitating cross-lingual comparisons.

This study positions large language models (LLMs) as "subjective literary critics" to explore aesthetic preferences and evaluation patterns in literary assessment. Ten Japanese science fiction short stories were translated into English and evaluated by six state-of-the-art LLMs across seven independent sessions. Principal component analysis and clustering techniques revealed significant variations in evaluation consistency (α ranging from 1.00 to 0.35) and five distinct evaluation patterns. Additionally, evaluation variance across stories differed by up to 4.5-fold, with TF-IDF analysis confirming distinctive evaluation vocabularies for each model. Our seven-session within-day protocol using an original Science Fiction corpus strategically minimizes external biases, allowing us to observe implicit value systems shaped by RLHF and their influence on literary judgment. These findings suggest that LLMs may possess individual evaluation characteristics similar to human critical schools, rather than functioning as neutral benchmarkers.

Detecting AI-involved text is essential for combating misinformation, plagiarism, and academic misconduct. However, AI text generation includes diverse collaborative processes (AI-written text edited by humans, human-written text edited by AI, and AI-generated text refined by other AI), where various or even new LLMs could be involved. Texts generated through these varied processes exhibit complex characteristics, presenting significant challenges for detection. Current methods model these processes rather crudely, primarily employing binary classification (purely human vs. AI-involved) or multi-classification (treating human-AI collaboration as a new class). We observe that representations of texts generated through different processes exhibit inherent clustering relationships. Therefore, we propose DETree, a novel approach that models the relationships among different processes as a Hierarchical Affinity Tree structure, and introduces a specialized loss function that aligns text representations with this tree. To facilitate this learning, we developed RealBench, a comprehensive benchmark dataset that automatically incorporates a wide spectrum of hybrid texts produced through various human-AI collaboration processes. Our method improves performance in hybrid text detection tasks and significantly enhances robustness and generalization in out-of-distribution scenarios, particularly in few-shot learning conditions, further demonstrating the promise of training-based approaches in OOD settings. Our code and dataset are available at https://github.com/heyongxin233/DETree.

Scientific literature is increasingly siloed by complex language, static disciplinary structures, and potentially sparse keyword systems, making it cumbersome to capture the dynamic nature of modern science. This study addresses these challenges by introducing an adaptable large language model (LLM)-driven framework to quantify thematic trends and map the evolving landscape of scientific knowledge. The approach is demonstrated over a 20-year collection of more than 1,500 engineering articles published by the Proceedings of the National Academy of Sciences (PNAS), marked for their breadth and depth of research focus. A two-stage classification pipeline first establishes a primary thematic category for each article based on its abstract. The subsequent phase performs a full-text analysis to assign secondary classifications, revealing latent, cross-topic connections across the corpus. Traditional natural language processing (NLP) methods, such as Bag-of-Words (BoW) and Term Frequency-Inverse Document Frequency (TF-IDF), confirm the resulting topical structure and also suggest that standalone word-frequency analyses may be insufficient for mapping fields with high diversity. Finally, a disjoint graph representation between the primary and secondary classifications reveals implicit connections between themes that may be less apparent when analyzing abstracts or keywords alone. The findings show that the approach independently recovers much of the journal's editorially embedded structure without prior knowledge of its existing dual-classification schema (e.g., biological studies also classified as engineering). This framework offers a powerful tool for detecting potential thematic trends and providing a high-level overview of scientific progress.

While clustering methods such as spectral clustering and K-means effectively group genes by expression similarity, downstream interpretation is typically performed using enrichment-based statistics. These approaches provide high-level functional summaries but often fail to yield cluster-specific mechanistic insight or explicit links to supporting literature. As a result, biological interpretation frequently relies on manual curation, limiting reproducibility and scalability. Large language models (LLMs) have recently emerged as powerful tools for biomedical text mining and knowledge synthesis. Although LLMs can generate fluent biological narratives, they are optimized for linguistic coherence rather than evidential accountability. When applied directly to transcriptomic interpretation, they may produce plausible but unverifiable statements, omit explicit citations, or hallucinate unsupported claims. While retrieval-augmented and agentic systems partially address this issue, systematic verification and critic-based validation remain underexplored. This limitation is particularly consequential for antimicrobial resistance research in Salmonella enterica, a major foodborne pathogen responsible for substantial global morbidity.