Kosko's Bidirectional Associative Memory [17] first formalised this idea for two layers, showing that stable recallContent-addressable memory--the recovery of a complete stored record from a partial or degraded cue--is aarises from the same energy-descent principle as in Hopcornerstone of neural computation and a paradigmaticfield networks but across two distinct pattern spaces: a problem in the statistical mechanics of disordered sys-cue presented to one layer drives the other toward the tems. The Hopfield model [1] demonstrated that binarymatching stored pattern, enabling cross-modal compleNtion. Multi-species spin-glass analyses [18] subsequentlypatterns in { 1,+1} can be stored as fixed-point attractors of an energy landscape shaped by Hebbian couplings, provided a rigorous thermodynamic foundation for arwhile Little's earlier stochastic formulation [2] cast thechitectures with an arbitrary number of interacting popsame architecture in the language of equilibrium statisti-ulations, generalising the classical single-species phase cal mechanics through parallel probabilistic updates.

Public attitudes toward artificial intelligence are heterogeneous, ordinally measured, and poorly captured by any single dependency graph. Existing ordinal structure learners assume a shared directed acyclic graph (DAG) across all respondents; recent heterogeneous ordinal graphical-model approaches focus on subgroup discovery rather than confirmatory cluster-specific DAG estimation; and latent profile analyses discard dependency structure entirely. We introduce a heterogeneous ordinal structure-learning framework combining monotone Gaussian score embedding, Bayesian nonparametric (BNP) complexity discovery via a truncated stick-breaking prior, and confirmatory fixed-K estimation with cluster-specific sparse DAG learning. The key methodological insight is a discovery-to-confirmation workflow: the nonparametric stage calibrates plausible archetype complexity, while inner-validated confirmatory refitting yields stable, interpretable structural estimates. On the 2024 Pew American Trends Panel AI attitudes survey, Wave 152 (W152) survey, (N = 4,788, 8 ordinal items), the confirmatory K*=5 model reduces holdout transformed-score mean squared error (MSE) by 25.8% over a single-graph baseline and by 4.6% over mixture-only clustering. A controlled tiered semi-synthetic benchmark calibrated to W152 structure validates recovery across difficulty regimes and transparently reveals failure modes under stress conditions.

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.

Preference-based many-objective optimization faces two obstacles: an expanding space of trade-offs and heterogeneous, context-dependent human value structures. Towards this, we propose a Bayesian framework that learns a small set of latent preference archetypes rather than assuming a single fixed utility function, modelling them as components of a Dirichlet-process mixture with uncertainty over both archetypes and their weights. To query efficiently, we designing hybrid queries that target information about (i) mode identity and (ii) within-mode trade-offs. Under mild assumptions, we provide a simple regret guarantee for the resulting mixture-aware Bayesian optimization procedure. Empirically, our method outperforms standard baselines on synthetic and real-world many-objective benchmarks, and mixture-aware diagnostics reveal structure that regret alone fails to capture.

Federated learning enables collaborative training without sharing raw data, but struggles under client heterogeneity and streaming distribution shifts, where drift and novel data can impair convergence and cause forgetting. We propose a federated associative-memory framework that learns shared archetypes in heterogeneous, continual settings, where client data are independent but not necessarily balanced. Each client encodes its experience as a low-rank Hebbian operator, sent to a central server for aggregation and factorization into global archetypes. This approach preserves privacy, avoids centralized replay buffers, and is robust to small, noisy, or evolving datasets. We cast aggregation as a low-rank-plus-noise spectral inference problem, deriving theoretical thresholds for detectability and retrieval robustness. An entropy-based controller balances stability and plasticity in streaming regimes. Experiments with heterogeneous clients, drift, and novelty show improved global archetype reconstruction and associative retrieval, supporting the spectral view of federated consolidation.

Several approaches have been proposed to remedy the edacious nature of archetypal analysis, proposing, e.g.,efficient active-set quadratic programming (Chen etal.,2014),

This enables us tointerpret which archetypal styles are present inthe input image, and inwhich proportion.

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.