In this paper, we introduce an unsupervised learning approach to automatically discover, summarize, and manipulate artistic styles from large collections of paintings. Our method is based on archetypal analysis, which is an unsupervised learning technique akin to sparse coding with a geometric interpretation. When applied to deep image representations from a data collection, it learns a dictionary of archetypal styles, which can be easily visualized. After training the model, the style of a new image, which is characterized by local statistics of deep visual features, is approximated by a sparse convex combination of archetypes. This allows us to interpret which archetypal styles are present in the input image, and in which proportion. Finally, our approach allows us to manipulate the coefficients of the latent archetypal decomposition, and achieve various special effects such as style enhancement, transfer, and interpolation between multiple archetypes.

Large language models demonstrate impressive results across diverse tasks but are still known to hallucinate, generating linguistically plausible but incorrect answers to questions. Uncertainty quantification has been proposed as a strategy for hallucination detection, requiring estimates for both global uncertainty (attributed to a batch of responses) and local uncertainty (attributed to individual responses). While recent black-box approaches have shown some success, they often rely on disjoint heuristics or graph-theoretic approximations that lack a unified geometric interpretation. We introduce a geometric framework to address this, based on archetypal analysis of batches of responses sampled with only black-box model access. At the global level, we propose Geometric V olume, which measures the convex hull volume of archetypes derived from response embeddings. At the local level, we propose Geometric Suspicion, which leverages the spatial relationship between responses and these archetypes to rank reliability, enabling hallucination reduction through preferential response selection. Unlike prior methods that rely on discrete pairwise comparisons, our approach provides continuous semantic boundary points which have utility for attributing reliability to individual responses. Experiments show that our framework performs comparably to or better than prior methods on short form question-answering datasets, and achieves superior results on medical datasets where hallucinations carry particularly critical risks. We also provide theoretical justification by proving a link between convex hull volume and entropy. Large language models (LLMs) have achieved remarkable performance across diverse natural language processing tasks (Guo et al., 2025; Anthropic, 2025; Gemini Team, Google DeepMind, 2025; OpenAI, 2025) and are increasingly applied in areas such as medical diagnosis, law, and financial advice (Y ang et al., 2025; Chen et al., 2024; Kong et al., 2024). Hallucinations, however, where models generate plausible but false or fabricated content, pose significant risks for adoption in high-stakes applications (Farquhar et al., 2024). Recent work, for example, finds GPT -4 hallucinating in 28.6% of reference generation tasks (Chelli et al., 2024).

In this paper, we introduce an unsupervised learning approach to automatically discover, summarize, and manipulate artistic styles from large collections of paintings. Our method is based on archetypal analysis, which is an unsupervised learning technique akin to sparse coding with a geometric interpretation. When applied to deep image representations from a data collection, it learns a dictionary of archetypal styles, which can be easily visualized. After training the model, the style of a new image, which is characterized by local statistics of deep visual features, is approximated by a sparse convex combination of archetypes. This allows us to interpret which archetypal styles are present in the input image, and in which proportion. Finally, our approach allows us to manipulate the coefficients of the latent archetypal decomposition, and achieve various special effects such as style enhancement, transfer, and interpolation between multiple archetypes.

In this paper, we introduce an unsupervised learning approach to automatically discover, summarize, and manipulate artistic styles from large collections of paintings.

The decarbonization of transportation relies on the widespread adoption of electric vehicles (EVs), which requires an accurate understanding of charging behavior to ensure cost-effective, grid-resilient infrastructure. Existing work is constrained by small-scale datasets, simple proximity-based modeling of temporal dependencies, and weak generalization to sites with limited operational history. To overcome these limitations, this work proposes a framework that integrates clustering with few-shot forecasting to uncover site archetypes using a novel large-scale dataset of charging demand. The results demonstrate that archetype-specific expert models outperform global baselines in forecasting demand at unseen sites. By establishing forecast performance as a basis for infrastructure segmentation, we generate actionable insights that enable operators to lower costs, optimize energy and pricing strategies, and support grid resilience critical to climate goals.

Consequently, archetypes lie on the boundary of the convex hull of the data.

We thank all reviewers for their careful reading and their valuable comments. As seen in the figure on the right, the performance of Lucic et al. (2016) We now included this baseline in the paper. R1: The dimension of B is stated wrongly [..] Thank you for pointing "In contrast to k-means, we assume that the mean .." is not clear to me. Thank you for raising this issue. Reviewer 3 also pointed this out.

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Taskmaster is a British television show that combines comedic performance with a formal scoring system. Despite the appearance of structured competition, it remains unclear whether scoring dynamics contribute meaningfully to audience engagement. We conducted a statistical analysis of 162 episodes across 18 series, using fifteen episode-level metrics to quantify rank volatility, point spread, lead changes, and winner dominance. None of these metrics showed a significant association with IMDb ratings, even after controlling for series effects. Long-term trends suggest that average points have increased over time, while volatility has slightly declined and rank spread has remained stable. These patterns indicate an attempt to enhance competitive visibility without altering the show's structural equilibrium. We also analyzed contestant rank trajectories and identified five recurring archetypes describing performance styles. These patterns suggest that viewer interest is shaped more by contestant behavior than by game mechanics.

This research explores the evolution of the detective archetype in French detective fiction through computational analysis. Using quantitative methods and character-level embeddings, we show that a supervised model is able to capture the unity of the detective archetype across 150 years of literature, from M. Lecoq (1866) to Commissaire Adamsberg (2017). Building on this finding, the study demonstrates how the detective figure evolves from a secondary narrative role to become the central character and the "reasoning machine" [35] of the classical detective story. In the aftermath of the Second World War, with the importation of the hardboiled tradition into France, the archetype becomes more complex, navigating the genre's turn toward social violence and moral ambiguity.