Papers

Existing training approaches for large language models learn a single set of parameters, based on large volumes of data, which is typically heterogeneous, conflicting and often outright contradictory. As a result, the model is forced to compress conflicting goals, and inherent uncertainties into a single, averaged pattern of behaviour. We propose an $\alpha$-Rényi variational framework for learning distributions over post-training parameters, offering an uncertainty-aware alternative to deep ensemble approaches. The resulting variational objective interpolates between classical variational Bayes and predictively oriented posterior learning, balancing between globally plausible individual models against systems of complementary specialists. We identify local stability criteria, demonstrating how model misspecification can make non-degenerate posterior spread locally favourable, manifesting contradictory or conflicting data as epistemic uncertainty. We apply our framework to LLM post-training, learning an ensemble of LoRA adapters attached to a shared, frozen base model, providing a scalable training procedure for both supervised fine-tuning and preference optimisation. Our approach enables training examples to be softly routed across ensemble members, promoting model specialisation and providing actionable uncertainty estimates across different tasks.

Reinforcement learning and data-driven autonomous controllers are commonly evaluated using cumulative reward and empirical success frequency under finite simulation trajectories. However, such empirical metrics do not necessarily provide sufficient statistical evidence regarding deployment readiness under uncertainty. This work develops a Bayesian approval framework for learned autonomous landing controllers under finite rollout evidence. A probabilistic landing capability formulation is introduced based on touchdown safety satisfaction under uncertain operating conditions, while Bayesian posterior inference is used to quantify uncertainty regarding the true deployment capability of learned policies. Posterior approval probability and posterior deployment risk are further introduced for deployment-oriented evaluation, together with a sequential validation framework supporting approve/reject/continue decisions during progressive rollout testing. Simulation experiments using PPO and SAC controllers demonstrate that empirical success and reward optimization may produce overconfident deployment interpretation under limited validation evidence, whereas posterior approval inference provides a more uncertainty-calibrated assessment of deployment readiness. The proposed framework provides a practical statistical connection between conventional reinforcement-learning evaluation and deployment-oriented validation under uncertainty and may be generalized to broader classes of learned autonomous systems.

Moment-based estimation is a theoretically attractive approach to parametric inference, especially when likelihood-based estimation is unavailable, misspecified, or computationally inconvenient. However, the moment equations involve sample averages, which makes moment-based estimation sensitive to outliers. We propose the SGR-GMM algorithm, a robust generalized method of moments (GMM) procedure that uses a spectral gradient reweighting (SGR) primitive to soft-reweight the per-observation gradients during the moment-matching optimization. Our analysis has three layers. First, for a fixed center, the SGR primitive is formulated as an entropy-regularized spectral game between a sample-weight player and a density-matrix player, which is analyzed using classical multiplicative-weights and matrix-multiplicative-weights regret bounds. Second, we establish explicit convergence radius and finite termination bound for the fixed-center updates in the SGR primitive. Third, we prove a local finite-sample parameter estimation error bound with explicit dependence on the contamination fraction, inlier gradient stability, local GMM identification strength, and optimization accuracy. We further specialize the SGR-GMM algorithm to obtain a robust diagonally-weighted GMM (DGMM) estimator for estimating heteroscedastic low-rank Gaussian mixtures observed under additive Gaussian noise and strong contamination. In the numerical experiments, the SGR primitive produces nearly-oracle gradient estimation and the robust DGMM specialization substantially improves over non-robust moment baselines. The code and data are available at https://github.com/liu-lzhang/sgr-gmm.

Leveraging external or historical data to improve the efficiency of randomized clinical trials without introducing bias or inflating the Type I error rate remains challenging. Recent work on externally trained prognostic scores, such as PROCOVA for continuous endpoint, has demonstrated a risk-free approach via covariate adjustment. However, extending this paradigm to time-to-event endpoints is nontrivial due to the non-collapsibility of the marginal hazard ratio (HR). In this paper, we address this challenge by proposing a unified framework for incorporating complex, high-dimensional prognostic information learned from external data into the primary analysis of RCTs with time- to-event endpoints, while targeting the marginal hazard ratio. The proposed procedure proceeds in two steps. First, a prognostic score is estimated from external or historical data by regressing martingale residuals on baseline covariates using flexible supervised learning methods. Second, the fitted score is included as an additional covariate in the nonparametric covariate-adjusted log-rank test and the associated marginal HR estimator of Ye et al. [2024]. The proposed method controls Type I error and provides asymptotic unbiased estimation of the marginal HR, irrespective of prognostic model misspecification, or population heterogeneity between external/historical and trial data. We show that the variance reduction, and corresponding event count savings, are approximately equal to the squared correlation between the prognostic score and the martingale pseudo-outcome in the trial. Extensions to stratified randomization are straightforward. Simulation studies demonstrate satisfactory finite-sample performance and meaningful efficiency gains when historical prognostic information is informative.

Likelihood-based inference for multivariate extreme-value models is often unreliable or infeasible when likelihoods are intractable or supports are discrete. This challenge is particularly acute for multivariate discrete generalized Pareto models, where both marginal tail behavior and dependence must be inferred from sparse exceedance samples. We propose a two-stage likelihood-free inference procedure, termed AW–NBE (Adaptive Wasserstein Neural Bayes Estimator), that combines neural Bayes estimation with a targeted optimal transport refinement step based on the Sinkhorn discrepancy. In the first stage, a neural Bayes estimator trained on simulated data provides fast and stable initial parameter estimates. In the second stage, these estimates are locally refined by minimizing the Sinkhorn divergence between the empirical distributions of observed and simulated exceedances. This refinement reduces the Sinkhorn discrepancy between the empirical distributions of observed and simulated exceedances, while preserving dependence features learned by the neural estimator. Model adequacy is assessed using new optimal transport based multivariate Q–Q and potential diagnostics. Applications to financial log-returns and Swiss dry spell exceedances suggest that AW–NBE can improve parameter inferences compared to estimation using solely, either the Sinkhorn discrepancy, or the standard neural Bayes estimators and censored likelihood estimation.

Fine-tuning a pretrained language model on a curated dataset can produce spurious correlations between the fine-tuning task and unintended latent factors—such as misaligned personas or political slant—that the curation procedure has entangled with the task. The model can latch onto these spurious correlations, leading to bias and reduced out-of-distribution generalisation. We prove that under reasonable assumptions on task complexity and the spurious correlation, such latent factors can be identified, without supervision, from the weights of a naive LoRA fine-tune. Existing approaches to removing bias, such as activation steering, remove identified factors from residual-stream activations, either at inference or during training. We argue, however, that the goal should be to remove the spurious correlation, not the latent factor itself, as the pretrained model may rely on it for genuine task signal. To enable this, we propose GRASP, GRadient projection of Associated Spurious Patterns, which prevents the model from acquiring new reliance on the identified latent factor while preserving any pretrained content along it. We validate on three fine-tuning tasks. The first two involve emergent misalignment, where fine-tuning on a narrow task—in our case, writing insecure code and giving bad medical advice—leads to misaligned responses on unrelated topics. Here our method completely removes misalignment in the insecure code case and reduces it by ~5x in the bad medical advice case, beating all baselines in the trade-off between misalignment-reduction and task-preservation. The last is a novel political-bias experiment, where fine-tuning on right-skewed Reddit financial-advice data causes political-lean drift on unrelated topics. Here our method reduces drift by more than half, while improving financial task performance, beating all baselines.

Safety defenses for large language models (LLMs) are typically trained and evaluated on single-turn prompts, yet real attacks often unfold as indirect, multi-turn probing. To defend against this more nuanced form of deception, we present a unified pipeline that generates realistic multi-turn deceptive question sets via multi-objective genetic prompt optimization with co-evolving mutation operators. We validate this dataset through a human study, which also revealed that early generations yielded the most convincing deception and practical constraints such as adherence filtering and ordering effects. Using this data, we were able to detect deceptive attempts to access prohibited information using simple, explainable geometric signals in embedding space coupled with a lightweight feed-forward classifier. Three geometric features (angular coverage, distance ratio, and linearity) augmented with pairwise similarity statistics led to a compact predictive model that achieved consistently high recall (0.89) across base, reworded, and truncated (three-turn) scenarios, with test-time F1 ranging from 0.74-0.86. The results support a central hypothesis that multi-turn deceptive intent leaves a stable geometric footprint that enables lightweight, transparent screening without expensive end-to-end training. We further discuss responsible uses, limitations, and paths toward larger, more diverse human-evaluated datasets. The primary contribution to artificial intelligence is the multi-objective evolutionary framework for prompt generation, and the engineering application is the deployment of a lightweight geometric detection system for LLM safety infrastructure.

Structured multiple-testing problems (gatekeeping trials, dose-finding, multi-tissue eQTL mapping, bundled-challenger A/B experiments) organize hypotheses into design-imposed blocks and demand strong family-wise error rate (FWER) control for confirmatory claims. Practitioners currently use objective-agnostic stepwise rules (Bonferroni, Holm, Hochberg, Hommel), closed-testing and graphical extensions, or hierarchical and resampling methods; none is power-optimal within the block-separable class these designs induce. We introduce BOOST (Block-Optimal Objective-driven Strong-FWER Testing), the power-optimal strong-FWER procedure for block size three, with three guarantees: (i) finite-sample strong-FWER validity at $O(K)$ cost (versus $O(K^2)$ for general closed testing) without independence assumptions, with a strict Sidak improvement under cross-block independence; (ii) power-optimal allocation across heterogeneous blocks via an equalized-marginal KKT condition, solvable by bisection in $O(B\log(1/\varepsilon))$; and (iii) a sample-split plug-in variant for unknown alternative density $g$, attaining $\alpha$-control up to $O(B_T \mathbb E\|g-\widehat g\|_\infty)$ inflation with per-hypothesis power deficit independent of $B_T$. Simulations across independent, equicorrelated, sparse, and mis-specified regimes show 1.4-1.7$\times$ power gains over the strongest existing baseline at calibrated FWER. On two published datasets (BLUEPRINT cross-lineage cis-eQTL and Upworthy bundled-challenger A/B experiments), BOOST certifies an order of magnitude more full-block discoveries than existing baselines at controlled FWER.

The International Council for Harmonization (ICH) E9 (R1) addendum provides the estimand framework to formulate treatment effects in a clinical trial. One of the attributes of an estimand the framework describes is intercurrent events. Among the five strategies to intercurrent events the guidance lists, the principal stratum strategy is the most conceptually and technically challenging because it defines treatment effects on unobserved strata. Its application to survival outcomes is particularly inaccessible to practitioners. This tutorial reviews the methodology and implementation of the estimand framework with the principal stratum strategy to address intercurrent events with survival outcomes. We illustrate using a clinical trial in oncology and focus on a simple case with binary treatment and a single binary intercurrent event of discontinuation of the assigned treatment. We define the causal effects and review two main methods for estimating the effects: the mixture model method and the weighting method. For each method, we elaborate the associated assumptions, models, sensitivity analysis, software and provide example R code. We conduct simulation studies that mimic the real study to study the operation characteristics of these methods.

When a player withdraws mid-tournament from a round-robin chess event, organizers face a fundamental problem: how should scores be assigned for games that were never played? Current FIDE guidelines specify annulment if withdrawal occurs before 50% of games are completed, and forfeit (awarding unplayed opponents a full point) thereafter. This dichotomous rule creates arbitrary discontinuities and can substantially distort final standings. We develop a Bayesian framework based on best linear unbiased prediction (BLUP) that optimally combines pre-tournament ratings with observed performance, producing imputed scores that reflect both the withdrawn player's current form and the strength differentials among unplayed opponents. The estimator is consistent, point-conserving, and minimizes mean squared error among linear unbiased predictors. A Monte Carlo simulation study on 180,000 simulated tournaments demonstrates that Bayesian BLUP imputation reduces prediction error by 26% overall compared to FIDE's current rule, with improvements of 41% over forfeit and 12% over annulment. The largest gains occur when the withdrawn player is underperforming, the most common withdrawal scenario. We further show that annulment achieves 15-45% lower RMSE than forfeit across all scenarios. The methodology is applied to GM Alireza Firouzja's withdrawal at Grand Chess Tour, Bucharest 2026, where Bayesian imputation would have awarded unplayed opponents 0.55-0.70 points rather than the 1.0 awarded under forfeit rules. An open-source R Shiny application is provided for tournament organizers. We recommend that FIDE adopt Bayesian imputation for World Championship cycle events, or at minimum replace the current dichotomous rule with uniform annulment.

Fires and explosions in pyrotechnics retail markets recur worldwide with predictable regularity, killing dozens to hundreds of people in single events. This paper argues that the global topology of the market is the dominant determinant of mortality, acting through two independent geometric channels. The first, propagation, concerns ballistic dispersal of ignited articles: the probability that fire spreads between blocks scales with the spatial density of blocks within the dispersal range. The second, evacuation, concerns the distance an occupant must traverse to reach the perimeter, which is set by the global geometry of the market footprint, not by any stall-level parameter. Because mortality risk grows approximately exponentially in evacuation time, topology amplifies modest differences in egress distance into large differences in casualties. Current standards in the United States, the European Union, and Mexico prescribe local parameters such as aisle width and stall separation, but leave the global topology of the market unregulated. We argue that topology should be a regulable design variable, and propose a market geometry that simultaneously slows propagation and shortens evacuation, derived from contact-process models of seed dispersal in spatial ecology.

In this paper, we consider the problem of simultaneous testing of multivariate normal means under arbitrary covariance dependence. Specifically, let $\boldsymbol{X}\sim N_n(\boldsymbol{\theta},\boldsymbol{\Sigma})$, where $\boldsymbol{\theta}\in\mathbb{R}^n$ is unknown and $\boldsymbol{\Sigma}$ is a known positive definite covariance matrix. The objective is to test $H_{0i}:\theta_i=0$ against $H_{Ai}:\theta_i\neq 0$, simultaneously for $i=1,\ldots,n$. We establish a general admissibility theorem for a broad class of monotone residual-based step-down multiple testing procedures which iteratively rank the active hypotheses using statistics obtained through locally adaptive strictly increasing transformations of suitably standardized residual statistics arising from conditional normal distributions. Our main result shows that every such procedure is admissible with respect to a vector-valued loss function whose components are the usual individual $0$–$1$ testing losses. The proof relies on a delicate geometric analysis of the induced acceptance regions together with structural invariance properties of the adaptive stagewise rejection indices. The theorem substantially extends the admissibility theory developed for the maximum residual down procedure of Cohen et al. (2009) and reveals that admissibility under dependence is fundamentally driven by the monotone ordering structure induced by the residual statistics rather than by the precise functional form of the testing rule itself.

Composites are often created to facilitate the work of decision-makers. Therefore, practical or theoretical considerations may lead to a priori weights of the indicators forming a composite. Composites that are created a weighted aggregates are not the result of data analysis and may therefore be termed 'analytic composites'. However, it has already been shown that the variance contributions of indicators within analytic composites are affected by the indicator variance and indicator inter-correlations. In the present study purely analytic composites are proposed, having exactly the variance contribution of indicators within the composites that are a priori defined by the indicator weights. An example based on simulated data illustrates the difference between analytic composites and purely analytic composites. As an application area, we propose that purely analytic composites could be of interest in the exchange-traded fund. An R-script for the computation of purely analytic composites is given in the Appendix.

We study the problem of computationally efficient proper agnostic learning of multidimensional concept classes under the Gaussian distribution. In this setting, given i.i.d. labeled samples from an unknown distribution over $\mathbb{R}^d \times \{\pm 1\}$ whose marginal on $\mathbb{R}^d$ is Gaussian, the goal is to output a hypothesis from a target class $\mathcal{F}$ whose 0-1 loss is within $\epsilon$ of that of the best classifier in $\mathcal{F}$. We give the first efficient proper agnostic learning algorithm for arbitrary Boolean functions of $K$ halfspaces under Gaussian marginals. Our algorithm runs in time $d^{O(K^2 \log(1/\epsilon)/\epsilon^2)} + (K/\epsilon)^{O(K^3/\epsilon^{2.5})}$. Prior to our work, the only known algorithm for $K \geq 2$ was brute-force search, with run-time exponential in $d$. Moreover, the dependence of our run-time on the dimension $d$ matches that of the best known improper learning algorithm, namely $d^{\widetilde{O}(K^2/\epsilon^2)}$. For the special case of a single halfspace ($K=1$), the best previous run-time was $d^{O(1/\epsilon^4)} + (1/\epsilon)^{O(1/\epsilon^6)}$. Our algorithm improves this to $d^{O(1/\epsilon^2)} + (1/\epsilon)^{O(1/\epsilon^{2.5})}$. Once again, the dependence on $d$ matches that of the best known improper algorithm, namely $d^{O(1/\epsilon^2)}$. Furthermore, the dependence of our run-time on the dimension $d$ is essentially optimal in the statistical query model.

We prove an elementary bounded-differences inequality for functions of non-isotropic Gaussian vectors. Specifically, if $f$ has bounded coordinate differences and $X\sim\mathcal N(\mu,\Sigma)$, then the resulting concentration bound depends on the condition number $\kappa(\Sigma)$. As an application, we answer a question of Simone Bombari concerning the subgaussianity of sign-quantized linear maps $Y=\mathrm{sgn}(Wx)$. In the special case where $f$ is the coordinatewise sign function, an argument was initially suggested to us by Gemini 3.5 Flash without attribution. We subsequently discovered that it closely resembles an earlier argument of Barber and Kolar [Ann. Statist. 46 (2018), Lemma 4.5]. This revision corrects the attribution and documents the episode as an instance of AI-assisted mathematical discovery.

Card payment fraud detection is usually framed as a supervised classification problem. Although this approach has generated practical progress, improvement has remained incremental despite major advances in model architecture. We argue that this is not mainly a failure of function approximation or optimization, but a consequence of structural information impairments inherent to the payment ecosystem. We formalize card authorization as a sequential decision problem with delayed, censored, corrupted, and counterfactually missing feedback. We derive a minimax regret lower bound showing that these impairments enter multiplicatively in the denominator of the achievable learning rate. The bound implies that improving issuer reporting quality or reducing censorship can yield larger reductions in the regret floor than increasing model complexity. We also show that heterogeneity across issuers worsens learnability beyond what average impairment rates suggest. The paper contributes a theory of why fraud detection in payment networks is fundamentally harder than in standard online learning settings, identifies ecosystem information quality as the key bottleneck, and provides a theoretical basis for prioritizing investments in reporting infrastructure, dispute process quality, and selective exploration. The paper is theory-first and does not rely on proprietary transaction data.

High-fidelity simulation models are widely used to analyze complex stochastic systems, but their high computational cost motivates the development of cheaper surrogate models that approximate the simulation model's input-output relationship. In parallel, reinforcement learning (RL) has emerged as a powerful framework for making online decisions in stochastic environments, with increasing attention being given to the use of simulation models as training environments for RL models. We investigate a class of surrogate models suitable for accelerating RL training in settings where the reward structure, model parameters, or system dynamics change over time and explore their interactions with simulation models and RL models. Through numerical experiments on a stochastic service system modeled via discrete-event simulation, we demonstrate that leveraging surrogate models can substantially accelerate RL training and re-training.

We develop semiparametrically efficient inference for kernel measures of noise heterogeneity in additive noise models. In many applications, the regression function is estimated using flexible machine learning methods. Downstream procedures based on the resulting residuals can then inherit first-stage bias: regression error may induce spurious dependence between covariates and residuals, invalidating the assumptions needed for standard analysis. We construct a novel Hilbert-valued one-step estimator of the kernel covariance operator between covariates and residuals. Our estimator yields bootstrap-calibrated tests for residual independence and goodness of fit in additive noise models, while also providing asymptotically efficient confidence intervals for the kernel dependence measure under noise heterogeneity. The framework extends to settings with additional covariates, enabling inference on distributional heterogeneity of residual noise across treatment groups. Simulations show improved calibration and power relative to naive plug-in residual methods.

Deep generative models offer powerful tools for multivariate data analysis, but their black-box architectures are often unidentified and difficult to interpret. We introduce the Deep Discrete Encoder (DDE) Copula, an identifiable and interpretable generative model for multivariate data with arbitrary marginal distributions. The model places a hierarchical directed network of binary latent variables inside a copula framework, enabling flexible dependence modeling for mixed discrete and continuous data. Estimation is based on rank likelihoods, which decouple marginal modeling from posterior inference on the DDE parameters and avoid specifying the marginal distributions. We establish conditions for identification of the DDE copula parameters, ensuring that layer-specific parameters provide meaningful summaries of multivariate dependence. We also prove quotient-space posterior consistency for continuous margins under the exact rank likelihood and treat the extended rank likelihood for tied or mixed margins as a generalized likelihood, with concentration under an additional contrast condition. For computation, we propose a stochastic expectation-maximization algorithm for maximum a posteriori estimation, together with initialization strategies that improve convergence. To learn network dimension adaptively, we extend Bayesian rank-selection priors to infer layer-specific widths. Simulations show strong finite-sample performance, and a personality-survey analysis reveals interpretable hierarchical latent structure in complex multivariate data.

Flow and diffusion generative models have established themselves as widely adopted density estimators for simulation-based inference (SBI), extending naturally from neural posterior estimation to likelihood and joint density estimation. Their principled optimization objectives and freedom from architectural constraints have driven rapid adoption across the natural sciences. Yet the most widely used SBI libraries remain PyTorch-based, leaving researchers who develop their forward models and analysis pipelines in JAX without a native option. We present GenSBI, an open-source library that implements flow matching, score matching, and denoising diffusion entirely in JAX. The library offers three transformer-based architectures - SimFormer, Flux1, and a novel Flux1Joint that extends gate-modulated transformer blocks to joint density estimation - all interchangeable through a unified interface that decouples generative method, neural backbone, and inference mode. GenSBI provides an end-to-end workflow from training through posterior calibration (SBC, TARP, LC2ST) and supports custom architectures with domain-specific embedding networks. We validate the framework on standard SBI benchmarks, achieving near-ideal mean C2ST scores (0.50-0.56, where 0.50 is ideal) on SBIBM tasks with minimal per-task tuning and well-calibrated posterior coverage across all tested configurations. The code is publicly available at https://github.com/aurelio-amerio/GenSBI.

Model–based clustering for directional data data has attracted a lot of interest, but most methods utilize rotationally symmetric distributions. This paper suggests the use of elliptically symmetric distributions, namely the elliptically symmetric angular Gaussian and the spherical elliptically symmetric projected Cauchy distributions that were recently proposed in the literature for modelling spherical data. The expectation–maximization algorithm is employed and the inclusion of covariates is also examined. Simulation studies compare the two distributions in terms of choosing the optimal number of clusters and computational cost. We use the mixtures of these two distributions to cluster two datasets on the sphere (earthquake locations) and two hyper–spherical datasets.

Schrödinger bridges for time series (SBTS) generate synthetic paths by projecting, in relative entropy, a Brownian reference onto the path laws that match the joint distribution of the data on the observation grid. The Brownian reference, however, fixes the quadratic variation of the generated paths, which is restrictive when stochastic volatility, correlated noise, or rank-deficient covariance structures must be reproduced. We introduce "Triangular-Reference Schrödinger Bridges for Time Series" (TR-SBTS), which keeps the entropy-projection backbone of SBTS but replaces the Brownian reference by a triangular, volatility-informed, intervalwise frozen reference on a state augmented with latent covariance descriptors. The construction remains a single entropy projection on the augmented state: the minimiser is the \(h\)-transform of the reference, and on each frozen interval the optimal drift has the logarithmic-gradient form \(b^\star(t,x)=A\,\nabla\log H(t,x)\), intrinsic to the active covariance directions when the frozen covariance \(A\) is degenerate. We prove stability of the frozen approximation and consistency of the associated regularised kernel estimators, describe a reference-aware Nadaraya–Watson implementation of the conditional next-increment law, and evaluate the construction on numerical experiments.

Causal-discovery algorithms return a directed graph, yet provide no principled means of distinguishing edge directions identified by the data from those assigned without an identifying assumption. Under the standard Markov and faithfulness conditions, the observational distribution identifies only a Markov equivalence class; orientations within that class are not determined by the joint distribution and cannot be recovered from additional samples alone, but require either a functional restriction or an intervention. We introduce a protocol for observational causal discovery on continuous data that attaches to each candidate edge a discrete impossibility certificate: a RESOLVED code records the identifiability theorem under which the direction was committed, while an IMPOSSIBLE code records the failure mode together with the specific question a domain expert must answer to resolve it. The bivariate cascade is extended with five gated identifiability tiers LSNM, IGCI, Stein, MDL, and PEIT that abstain when their precondition test rejects. Two oracle primitives, the meta-hub query and the node-children query, jointly establish an upper bound of $1+K$ expert interactions sufficient to recover any DAG, where $K$ denotes the number of non-leaf vertices. Under an ideal-oracle assumption, the bound is met exactly on the asia, sachs, child, and alarm benchmarks.

Estimating how an outcome responds to a continuous treatment (the Average Dose-Response Function, or ADRF) is a core causal-inference primitive. However, when outcomes possess heavy tails, standard robust double machine learning (DML) deliberately suppresses these extremes to stabilize the bulk average. In high-stakes settings, such as financial returns or climate losses, this omitted 1-in-1000 extreme event is the actual target quantity. Furthermore, current methods that read the tail from a model's residuals suffer from circular dependence, causing tail shape inferences to shift drastically based solely on whether the core estimator is switched between Huber and Welsch. The research proposes an ADRF estimator that emits a structured tail-shape output alongside the standard point estimate. Its tail diagnostic (PDHTE+JK) evaluates the per-treatment tail shape from the outcome centered by a pilot median, successfully breaking the circular dependence and rendering the diagnostic invariant to the choice of core method. The output encompasses four treatment-conditional quantities: tail shape $\hat{\xi}(t)$, deep-tail return levels $\hat{Q}_{\alpha}(t)$, conditional shortfalls $\hat{S}_{\alpha}(t)$, the recovered mean ADRF, and an explicit refusal mechanism that declines extrapolation when extreme-value modeling is unsupported by the data. Compared to kernel-weighted quantile regression (QR), the proposed estimator reduces deep-tail ($\alpha=0.001$) return-level MAE by 11% and conditional-shortfall MAE by 25.5% across a heavy-tailed panel. It also achieves a 20-29% MAE reduction in sample-scarce regimes ($n\le2000$). On freMTPL2 motor-insurance claims, it successfully triggered an explicit extrapolation refusal on the log-claim scale, which neither QR nor loss-only DML can produce.

Estimating how much an intervention helps a given individual the conditional average treatment effect (CATE) is increasingly central to decision-making in medicine, economics, and policy, where an estimate is most useful when accompanied by a calibrated uncertainty interval. We study the few-placebo regime, in which one treatment arm is much smaller than the other, as arises in unequal-allocation trials and small-holdout $A/B$ tests. The standard estimator in this setting is the X-Learner, and a natural way to obtain credible intervals is to make its second stage Bayesian. We show that these intervals under-cover: they contain the true effect less often than their nominal level. We trace this to a structural cause the X-Learner's regression target inherits the bias of a nuisance model fitted to the small arm, so the posterior is centered away from the true effect and we find that the standard remedy, regressing an orthogonal doubly-robust score, is also unreliable here, since the regime's limited overlap leaves the estimator either highly variable or, once stabilized, biased once more. Both consequences reflect a pattern that extends beyond causal inference: a separately estimated variance is attached to a point estimate of a hard-to-learn quantity, and the point estimate's bias is not captured by that variance. We propose GP-CATE, which models each arm's outcome surface with a Gaussian process, so the scarce arm's uncertainty enters the posterior directly rather than as an unmodelled bias. Across synthetic and semi-synthetic benchmarks, GP-CATE attains calibrated coverage where the estimators we compare against including Causal Forest and BART do not, at the cost of intervals that are appropriately wide when the data are uninformative.

Multi-agent systems built on large language models (LLMs) require many coordination choices that are difficult to fix a priori: which skill protocol to invoke, which agent role should perform a subtask, which model to bind to each role, how roles should interact, when to use retrieval or verification, and when to omit a step entirely. These choices interact with task regime and operational constraints, so static pipelines and one-off model comparisons provide only a limited view of the design space. This paper introduces AgensFlow, an open-source framework that treats multi-agent coordination as an online policy-learning problem under partial observability. The framework makes coordination decisions observable and learnable from repeated trajectories, rather than treating skill, role, model, topology, and evaluation choices as fixed pipeline design. AgensFlow is evaluated on two corpora: distributed-systems incident tasks and security-advisory tasks. The evaluation shows three main results: learned routing reaches a higher-quality operating point than a fixed pipeline baseline on coordination-heavy classes; skip:X isolates topology compression as a meaningful part of the substrate; and warm-started policy graphs can reduce exploration cost while preserving plateau quality. Overall, the results support that learned, auditable routing can improve coordination-heavy multi-agent workflows over static wiring.

Generative surveying – where collections of LLM-based personas provide feedback on messages – has emerged as a cheap and scalable alternative to traditional market research. However, LLMs are sensitive to small variations in prompt design and conclusions drawn from generative surveys may depend on arbitrary phrasing choices. Controlling for this sensitivity requires including semantically equivalent perturbations in the analysis. In this paper, we show that standard hypothesis tests, including the sign test and Wilcoxon signed-rank test, are invalid under a statistical model for generative surveying that includes realistic perturbation structure. We propose a permutation test that is valid under this model and formally characterize the conditions under which standard tests fail. Applying our framework to a simple generative surveying problem, we estimate relevant parameters, characterize the power of the permutation test under realistic conditions, and provide practical guidance on budget allocation across personas, perturbations, and replicates. Finally, we show that both the magnitude and direction of the estimated effect are sensitive to the choice of model, even within the same model family.

Discrete diffusion models have achieved strong empirical performance in text and other symbolic domains, but, especially for uniform-rate models, they often require many steps to generate a single sample. Existing acceleration methods either rely on training additional quantities or suffer from slow mixing. In this work, we propose a novel Gibbs-based corrector for discrete diffusion models, termed Gibbs-Accelerated Discrete Diffusion (GADD). GADD leverages the structure of the concrete score function to construct Gibbs posterior likelihoods directly, without requiring any additional training beyond standard score estimation. We show that GADD achieves an overall sampling complexity of $\mathcal{O}(\mathrm{polylog} (\varepsilon^{-1}))$, yielding the first such rate for diffusion-based samplers for uniform-rate discrete diffusion models. We also conduct numerical experiments demonstrating the practical advantages of GADD across synthetic data, zero-shot text sampling, and zero-shot conditional music generation. These results corroborate the theory and show that GADD consistently improves sample quality and wall-clock efficiency over standard baselines, including vanilla Euler methods and CTMC correctors. Beyond this, our theoretical analysis introduces a novel framework for analyzing predictor-corrector methods in discrete diffusion models, which may be of independent interest. Unlike existing approaches that rely on the Girsanov change-of-measure technique, our method is based on an induction argument that tracks error propagation across predictor iterations while accounting for inaccuracies in the corrector updates.

Modern weather stations in Germany record daily temperatures every 10 minutes, whereas measurements from historical reference periods are often only available at much coarser temporal resolutions, typically hourly. This discrepancy must be accounted for when comparing historical and current daily temperature patterns. Motivated by this problem, we develop two-sample inference procedures for functional data under sampling schemes where one sample is densely observed while the other is relatively sparse. Building on recent ideas from transfer learning for functional data, we derive estimators of the difference of the mean functions that attain optimal convergence rates in the supremum norm. We further establish a functional central limit theorem in the space of continuous functions and develop multiplier bootstrap methods for constructing uniform confidence bands. Extensions to functional time series are also discussed. Applying the proposed methodology to daily temperature curves from German weather stations, analyzed separately by month, reveals that climate change has altered not only average temperatures but also intraday temperature patterns. In particular, for stations such as Berlin, warming from morning to early afternoon exceeds the daily average increase, whereas evening and nighttime temperatures exhibit comparatively smaller increases.

Modern clinical trials and cohort studies gather low-cost data on all participants but may have limited resources to assess expensive exposures such as biomarkers or genomic data. When interest lies in associations involving expensive exposures, two-phase designs provide a cost-effective framework by using information available on all participants to guide the targeted selection of a subset for additional measurements. We extend this framework to studies with ordinal outcomes, a common yet previously unexplored setting. We propose three outcome-informed phase 2 sampling designs – outcome-dependent sampling (ODS), covariate-stratified ODS, and residual-dependent sampling – that leverage phase 1 data to enrich phase 2 selection with informative subjects. We then develop analysis methods for valid and efficient estimation/inference, including conditional likelihood methods with ascertainment-corrected maximum likelihood estimation, multiple imputation, and a full likelihood method using sieve maximum likelihood estimation. Across a range of scenarios, simulation studies show that the proposed methods substantially improve efficiency over simple random sampling with standard maximum likelihood estimation. We further demonstrate their practical utility by examining the association between interleukin-6 and a four-level clinical status outcome – discharged, hospitalized but not in the ICU, hospitalized in the ICU, and death – 14 days after randomization into the Crystalloid Liberal or Vasopressors Early Resuscitation in Sepsis trial.