Adaptive cooperation in multi-agent reinforcement learning (MARL) requires policies to express homogeneous, specialised, or mixed behaviours, yet achieving this adaptivity remains a critical challenge. While parameter sharing (PS) is standard for efficient learning, it notoriously suppresses the behavioural diversity required for specialisation. This failure is largely due to cross-agent gradient interference, a problem we find is surprisingly exacerbated by the common practice of coupling agent IDs with observations. Existing remedies typically add complexity through altered objectives, manual preset diversity levels, or sequential updates - raising a fundamental question: can shared policies adapt without these intricacies? We propose a solution built on a key insight: an agent-conditioned hypernetwork can generate agent-specific parameters and decouple observationand agent-conditioned gradients, directly countering the interference from coupling agent IDs with observations. Our resulting method, HyperMARL, avoids the complexities of prior work and empirically reduces policy gradient variance. Across diverse MARL benchmarks (22 scenarios, up to 30 agents), HyperMARL achieves performance competitive with six key baselines while preserving behavioural diversity comparable to non-parameter sharing methods, establishing it as a versatile and principled approach for adaptive MARL.

We study sparse semi-continuous tensor data with excess zeros, heavy right tails, and slice-specific dispersion. Such features arise naturally in monetary-valued multi-way data, such as international trade, where most exporter--importer--product--year cells are zero while positive values are continuous and highly variable. To model these data, we propose a Bayesian hierarchical tensor factorization model that places a low-rank CP structure on a latent Poisson rate tensor and couples it with a conditional Gamma model for positive outcomes, with rate parameters that can vary across slices within a mode. The model therefore separates the occurrence and magnitude of positive observations while borrowing strength across all tensor dimensions through a shared low-rank latent structure. To scale posterior inference to large arrays, we develop a hybrid variational--Monte Carlo algorithm that combines efficient coordinate ascent updates with a partially collapsed augmented-data sampler. Applied to approximately 60 million trade flows, the method surfaces multiway dependence across exporters, importers, products, and years that is difficult to recover from gravity-type or pairwise network analyses, which do not jointly model the product and temporal dimensions.

We introduce the \emph{Topological Stability Index} (TSI), a variance-based scalar measure for persistence barcodes that quantifies the dispersion of persistence lifetimes. Unlike persistent entropy, which depends only on normalized weights, the TSI captures absolute variability and is sensitive to heterogeneous feature scales. We establish fundamental properties of the TSI, including its scaling behavior, invariance under lifetime translation and explicit update formulas under insertion and deletion of bars. We also consider a complementary first-moment-type quantity, the Topological Signal Index (TSigI), which captures the typical scale of persistence lifetimes and provides additional interpretability alongside the TSI. We further introduce a normalized version, $cv\text{TSI}$, which is scale invariant and admits an explicit algebraic relation to the Rényi entropy of order two. In particular, $cv\text{TSI}$ is an affine function of the collision probability $\sum_i p_i^2$, and therefore a monotone reparametrization of the Rényi entropy, providing a direct link between variance-based and entropy-based summaries in topological data analysis. Numerical experiments on synthetic data and stochastic time series demonstrate that the TSI captures structural variability complementary to entropy: it is relatively insensitive to deterministic trends, while responding strongly to stochastic fluctuations and variations in persistence magnitude.

In healthcare, predictive models increasingly inform patient-level decisions, yet little attention is paid to the variability in individual risk estimates and its impact on treatment decisions. For overparameterized models, now standard in machine learning, a substantial source of variability often goes undetected. Even when the data and model architecture are held fixed, randomness introduced by optimization and initialization can lead to materially different risk estimates for the same patient. This problem is largely obscured by standard evaluation practices, which rely on aggregate performance metrics (e.g., log-loss, accuracy) that are agnostic to individual-level stability. As a result, models with indistinguishable aggregate performance can nonetheless exhibit substantial procedural arbitrariness, which can undermine clinical trust. We propose an evaluation framework that quantifies individual-level prediction instability by using two complementary diagnostics: empirical prediction interval width (ePIW), which captures variability in continuous risk estimates, and empirical decision flip rate (eDFR), which measures instability in threshold-based clinical decisions. We apply these diagnostics to simulated data and GUSTO-I clinical dataset. Across observed settings, we find that for flexible machine-learning models, randomness arising solely from optimization and initialization can induce individual-level variability comparable to that produced by resampling the entire training dataset. Neural networks exhibit substantially greater instability in individual risk predictions compared to logistic regression models. Risk estimate instability near clinically relevant decision thresholds can alter treatment recommendations. These findings that stability diagnostics should be incorporated into routine model validation for assessing clinical reliability.

Solution-processed electrochromic materials offer high potential for energy-efficient smart windows and displays. Their performance varies with material choice and processing conditions. Electrochromic thin film electrodes require a smooth, defect-free coating for optimal contrast between bleached and colored states. The complexity of optimizing the spin-coated electrochromic thin layer poses challenges for rapid development. This study demonstrates the use of self-driving laboratories to accelerate the development of electrochromic coatings by coupling automation with machine learning. Our system combines automated data acquisition, image processing, spectral analysis, and Bayesian optimization to explore processing parameters efficiently. This approach not only increases throughput but also enables a pointed search for optimal processing parameters. The approach can be applied to various solution-processed materials, highlighting the potential of self-driving labs in enhancing materials discovery and process optimization.

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).

Gossip has been shown to be a relatively efficient solution to problems of cooperation in reputation-based systems of exchange, but many studies don't conceptualize gossiping in a realistic way, often assuming near-perfect information or broadcast-like dynamics of its spread. To solve this problem, we developed an agent-based model that pairs realistic gossip processes with different variants of Trust Game. The results show that cooperators suffer when local interactions govern spread of gossip, because they cannot discriminate against defectors. Realistic gossiping increases the overall amount of resources, but is more likely to promote defection. Moreover, even partner selection through dynamic networks can lead to high payoff inequalities among agent types. Cooperators face a choice between outcompeting defectors and overall growth. By blending direct and indirect reciprocity with reputations we show that gossiping increases the efficiency of cooperation by an order of magnitude.