Papers

We develop a finite-horizon calibration method for raw-score martingale posteriors, with von Mises–Fisher models as the main worked example. Starting from the maximum likelihood estimator, predictive paths are generated by simulating future observations from the current fitted model and updating the natural parameter by unpreconditioned score increments. The main methodological step is to separate predictive simulation from covariance calibration. Raw-score increments have Fisher-information covariance, whereas Bernstein–von Mises calibration requires inverse-information covariance. We therefore apply a terminal linear correction based on a local information estimate. For more efficient implementation, we also introduce a hybrid version that replaces the omitted tail of the infinite predictive continuation by a Gaussian approximation with matching leading-order quadratic variation. We prove fixed-n convergence, a finite-horizon approximation bound for the Gaussian tail, and a Bernstein–von Mises limit for the hybrid post-corrected sampler under local regularity and consistent terminal calibration. Simulations show that tail correction reduces truncation-induced underdispersion, and an OSCAR ocean-current example illustrates local directional uncertainty summaries.

We present an approach for determining sample sizes required to detect underestimations of the expected shortfall with a prescribed power when applying the recently proposed e-backtesting procedure. We consider scenarios in which the value-at-risk at level $p$ is always estimated correctly, while the difference between the true expected shortfall and the value-at-risk is underestimated by a given factor $r$. We show that exploiting the structure of the backtest e-statistic proposed for backtesting the expected shortfall at level $p$ enables the derivation of approximate lower bounds for the required sample sizes by considering a sequence of independent and identically distributed Bernoulli random variables. We also discuss potential limitations of this approximation and compare the resulting sample size requirements with those obtained in practical applications using Monte Carlo simulations. Furthermore, we present generalizations of the e-backtesting procedure, in particular to risk measures which constitute Bayes pairs.

We develop a framework for simultaneous change-point inference of high-dimensional functional time series. The observations are modeled as temporally dependent vectors whose coordinates take values in possibly different separable Hilbert spaces, thereby covering a broad class of functional data. Heterogeneous mean changes may occur at coordinate-specific locations, and the contemporaneous dependence across coordinates is left unrestricted. Our procedure is based on coordinatewise cumulative-sum statistics and a residual block multiplier bootstrap that provides a common critical value for the global test and all coordinatewise decisions. We establish a nonasymptotic Gaussian approximation, quantitative nonasymptotic bounds for strong family-wise error control under arbitrary mixtures of changed and unchanged coordinates, covariance-adaptive detection guarantees, and simultaneous high-probability bounds for change-point localization. The bounds accommodate high-dimensional regimes in which the number of functional coordinates grows exponentially in a power of the sample size. We investigate finite-sample performance in simulations and illustrate the method using river discharge curves and high-frequency financial log returns.

Conformal counterfactual inference enables network operators to use logged telemetry to reliably answer 'what-if' questions about network operation. These answers typically take the form of prediction sets that contain, with a user-defined probability, the key performance indicators (KPIs) that would have been observed under alternative control actions. A key challenge is that logged telemetry may omit variables used by the controller, resulting in hidden confounding and invalidating the statistical guarantees of counterfactual analysis. In principle, this issue can be addressed using randomized telemetry, collected by assigning control actions independently of the network state. However, because such randomization may disrupt normal operation, randomized telemetry is typically scarce, causing counterfactual analysis based solely on it to produce uninformative prediction sets. To address these challenges, we propose Confounding-Valid Counterfactual Conformal Inference (CV-CCI), which combines abundant, potentially confounded observational telemetry with limited randomized data through the General Synthetic-Powered Inference (GESPI) principle. CV-CCI leverages observational data to improve efficiency while using randomized data to retain finite-sample coverage guarantees under arbitrary hidden confounding. Experiments on two representative radio access network (RAN) control tasks show that CV-CCI remains valid under hidden confounding while producing more efficient prediction sets than state-of-the-art confounding-valid baselines.

We study how the response of a Bayesian posterior statistic to future observations changes as information accumulates. For a non-decreasing function $T$, define $\Pi_n^T=\E[T(\Theta)\vert \mathcal F_n]$, where $\Theta$ has an arbitrary prior and the observations come from a one-parameter exponential family. Conditioning on the same current value of $\Pi^T$, we show that the posterior statistic after additional observations is larger in convex order when the current posterior is based on fewer observations. We also prove preservation of convexity: the expected value of a convex function of the future posterior statistic is convex in the current posterior statistic. Together, these two properties provide structural tools for establishing time-monotonicity results in dynamic Bayesian decision and optimal stopping problems. If the exponential family contains an infinitely divisible distribution, the results extend to a continuous-time observation model through a family of Lévy processes.

We study regression under bounded responses in terms of excess mean squared error. When the comparator class is finite, this setting is known as model selection aggregation, and achieving minimax excess risk requires improper learning algorithms. Contrary to this, in the universal learning framework no improperness is needed, as simple empirical risk minimization achieves the best-possible exponential learning rate. Hence, the two frameworks suggest different optimal algorithmic principles. This poses the question of best-of-both-worlds guarantees: Are minimax and universal exponential rates achievable by the same algorithm? For finite hypothesis classes, we answer this question in the affirmative by showing that the $Q$-aggregation estimator - which is known to achieve minimax optimal tails - achieves exponential universal rates. A wide range of other estimators and algorithmic principles (ERM, sequential averaging, pruning, and star estimation) do not achieve both. For countably infinite hypothesis classes, we answer the question in the negative by showing that there is an inherent trade-off between achieving exponential universal and minimax uniform rates. This trade-off is exactly traced by combining optimal algorithms from each world using $Q$-aggregation. Besides these results, we prove several additional structural results about universal rates in learning with squared loss.

We consider density estimation under the relaxed local differential privacy condition that the privatized distributions are $\alpha$-close in total variation distance. We show that adding independent noise with a convenient symmetrized Gamma distribution to each sensitive observation attains the $\alpha$-TV-LDP. We prove that the deconvolution estimator of $r$-Sobolev smooth functions attains the pointwise rate $(n\alpha)^{-\frac{2r-1}{2r}}$ up to log factors which is faster than $(n\alpha^2)^{-\frac{2r-1}{2r+1}}$ under the classical $\alpha$-LDP and closer to the nonprivate minimax rate $n^{-\frac{2r-1}{2r}}$. Next, we use a Goldenshluger-Lepski procedure to build a free of the smoothness adaptive procedure and show optimality of our rates in the convolution model of our privatisation scheme. We illustrate the benefits of this simple privacy mechanism by implementing a neural network estimator which does not need to add more noise in the optimization steps. Numerical results show significant improvement of the estimation rate over the Laplace and the private-SGD mechanisms.

Self-supervised learning relies on so-called data augmentations $\phi(x)$ of unlabeled datapoints $x$ — for example, masking random pixels in an image $x$ — that should leave the label of $x$ invariant and are often used to learn a lower-complexity invariant subspace $\cal V$ for downstream tasks. In practice, such augmentations $\{ \phi_l(x_i) \}$ are pooled together to learn $\cal V$, despite obvious inter-dependencies between different augmentations $\phi_l(x), \phi_k(x)$ of the same datapoint $x$. However, theoretical works on the subject typically consider procedures that avoid such dependencies, and are therefore limited to operate on smaller subsets of independent data. We show in this work that pooling augmentations together, despite inter-dependencies, is a better alternative than the baseline of partitioning the data into subsets of independent data. More precisely, in the context of estimating $\cal V$, the statistical estimation error bounds for pooling are never worse than the partitioning baseline, and in some cases — such as masking or noise injection-based augmentations over a shallow neural network — naive pooling leads to faster rates in terms of the number of augmentations. The benefits of pooling are particularly prominent when the correlations between different augmentations $\phi_l(x), \phi_k(x)$ have mild effects on estimation or help decrease the estimation variance. The analysis, therefore, yields new insights into the success of pooling augmented samples in self-supervised pre-training, and provides an intuition behind the practical preference towards using many augmentations.

Bridging the gap between animal and human experiments remains a major challenge in translational medicine, particularly in early drug development. Progress is constrained by financial cost, the difficulty of integrating heterogeneous in vitro and in vivo data, and the desire to reduce the use of animal testing balanced against minimising the risk to human participants. We present a statistical machine learning framework using multi-fidelity Gaussian processes, in which animal studies are considered as lower fidelity but informative approximations to human experiments. This allows cross-species similarities and nonlinear exposure-response relationships to be learned simultaneously, enabling principled extrapolation between species while quantifying uncertainty. By leveraging information from multiple experimental fidelities, our method improves estimation of clinically relevant quantities of interest and supports the replacement, reduction, and refinement of in vivo testing. We first illustrate this approach in a simulated scenario, before validating it on real clinical data. We simulate data for drug-induced QT-interval prolongation, a key cardiac safety assessment required for regulatory approval. This framework provides a probabilistic surrogate capable of integrating in vitro pharmacology, animal experiments and human data within a unified statistical model. Crucially, it achieves this at no additional experimental cost while also enabling transfer learning across compounds. As a result, predictions and uncertainty quantification for new drugs can be generated from in vitro findings alone, providing additional efficiency gains and accelerating decision making. For validation, we use a clinical dataset measuring change in heart rate under autonomic blockade, which represents some of the challenges commonly found in multi-species datasets.

Problem definition: Fixed parameters and inputs in a stochastic simulator induce a distribution over complete trajectories, not one trajectory. Calibration must assess this distribution, including variability and temporal dependence, against observations. Yet stochastic car-following models are commonly calibrated with trajectory-error objectives inherited from deterministic modelling. Methodology/results: We establish a scoring-rule theory of stochastic calibration. Strict propriety requires the data-generating distribution to uniquely minimise expected score. MRMean-I, the average run-wise error, drives separable stochastic spread to zero; MRMean-II, the error of the ensemble-mean trajectory, cannot identify a parameter that changes only spread; and MRMin, the error of the closest simulated run, has a population target that changes with ensemble size. These results are confirmed for stochastic Intelligent Driver Model extensions with additive acceleration noise and random desired headway. We recommend exact maximum likelihood when the correct transition density is available; otherwise, an unbiased simulation-based estimator of a strictly proper score. The energy score meets this requirement and gives the best held-out distributional prediction among the evaluated simulation-based objectives, although both models retain too-narrow bands and miss persistent disturbances. Implications:Strict propriety separates a valid calibration target from parameter identifiability and model adequacy. The theory applies to vector-valued outputs from stochastic transportation simulators; the car-following experiments illustrate its scope.

Multivariate correlated outcomes occur across disciplines, including ecology, social sciences, and psychometrics. This paper focuses on clustering these outcomes across observational units, specifically, finding groups of units with the same “outcome profile". Our motivation comes from bioregionalization in ecology, which aims to cluster sites into bioregions with the same species profiles, where site membership can depend on environmental or habitat covariates. To accomplish this, we propose finite mixtures of generalized estimating equations (MixGEE). Unlike existing approaches to model-based bioregionalization, MixGEE partitions sites into regions while accounting for between-species correlations through a region-specific working correlation structure. Thus, each region is characterized by a marginal species mean vector and a between-species correlation matrix. Unlike likelihood-based finite mixture models, MixGEE does not require a full joint distribution of the multivariate outcomes. Instead, we construct a pseudo-posterior probability for region membership motivated by the large-sample distribution of the estimating equation. This leads to an iterative algorithm alternating between updating these probabilities and solving weighted estimating equations. We determine the number of regions using cross-validation based on predictive performance for held-out sites and species components, and use a clustered Dirichlet random-weight bootstrap for uncertainty quantification. Simulations demonstrate reliable estimation and inference under various correlation structures and more stable selection of the number of groups than methods that ignore dependence. Applying MixGEE to presence–absence records of fish species around the Kerguelen Plateau reveals three distinct fish assemblage profiles with heterogeneous occurrence and within-site correlation patterns.

Longitudinal clinical data are increasingly available, offering opportunities to study treatment effects over time but also raising challenges related to time-varying confounding and evolving treatment decisions. We investigate how longitudinal treatment dynamics affect causal effect estimation when baseline and longitudinal methods target different causal estimands. Using a structural causal model (SCM), we simulate data with time-varying confounding, binary treatment, and an absorbing binary outcome under 9 scenarios combining functional complexity and treatment persistence. We compare three baseline and two longitudinal estimators against Monte Carlo ground-truth risk ratios (RRs) under sustained treatment regimes. Results show that treatment persistence is the main driver of estimator behaviour. High persistence reduces the discrepancy between baseline and sustained-regime estimands, making baseline estimators closer to the sustained-regime ground truth (average relative deviation of baseline IPTW/TMLE decreasing from 61% under low persistence to 10% under high persistence), whereas low persistence induces practical positivity challenges and increases the variability of longitudinal estimators, with empirical 95% interval widths increasing from 0.22 to 0.46 for longitudinal IPTW and from 0.20 to 0.36 for LTMLE when moving from high to low persistence. These findings emphasise that estimator performance should be interpreted jointly with the target intervention and the treatment process generating the observed data.

Testing whether two independent samples arise from the same underlying distribution is a fundamental statistical problem. We propose a new class of two-sample distribution tests based on a family of probability metrics $\Delta_{n,p}$, constructed from repeatedly integrated quantile functions. On their respective domains, these metrics are proved to be genuine distributional distances. The case $n=1$ recovers the $p$-Wasserstein distance, which requires finite $p$-th moments; for $n\geq2$, the proposed metrics are well defined and require only finite first moments. The asymptotic properties of the plug-in statistic are established, including strong consistency and limiting distributions under the null and fixed alternatives. A permutation calibration for finite-sample inference is also proposed. We further derive an asymptotic power function under local alternatives. Finally, the finite-sample performance of the proposed tests is examined through simulation studies, and their reduced sensitivity to extreme upper-tail observations is illustrated through a real data application.

The statistical analysis of heavy-tailed data has received considerable attention because extreme observations frequently arise in many practical applications. The Pareto type-I distribution is a fundamental heavy-tailed model used in economics, finance, actuarial science, insurance, reliability, and extreme value analysis. In this paper, we propose novel goodness-of-fit tests for the Pareto distribution using a mean residual life characterization. The test statistic is constructed using U-statistic theory, and its asymptotic behaviour is established under both the null and alternative hypotheses. Its finite-sample performance is evaluated through Monte Carlo simulations using maximum-likelihood and method-of-moments estimation and compared with existing tests. The results show that the proposed test controls the nominal significance level and performs competitively in terms of power across a broad range of alternatives. Finally, the proposed methodology is illustrated using the Danish fire insurance loss and pollution datasets.

We propose a Bayesian model-based approach for clustering functional data with an unknown number of clusters and within-curve correlated observations. Cluster-specific mean functions are represented using B-spline basis expansions, while within-curve dependence is modeled through an Ornstein–Uhlenbeck covariance structure. A truncated Dirichlet process mixture is used to infer the effective number of clusters, and a variational EM algorithm is developed for efficient posterior approximation. Simulation studies show that the proposed method performs well under both correctly specified and misspecified mean-function settings and achieves higher average values of the reported clustering metrics than the competing methods in the simulation settings considered. Comparisons with MCMC indicate that the variational approximation produces clustering results and parameter estimates that are in close agreement with those obtained by MCMC, while requiring substantially lower computational cost. An application to Canadian daily temperature curves further demonstrates the practical usefulness of the method in identifying interpretable functional clusters while accounting for within-curve dependence.

While diffusion-based methods have recently emerged as effective tools for probing the intrinsic geometry of high-dimensional data, their statistical difficulty remains largely unexplored. We study estimation of the finite-scale population functional underlying FLIPD (Kamkari et al., 2024; arXiv:2406.03537), a diffusion-based local intrinsic dimension (LID) quantity defined through the logarithmic scale derivative of a Gaussian-smoothed density. Intuitively, Gaussian smoothing turns local dimension into a scale law: near a $d$-dimensional manifold, the kernel mass grows like $\sigma^d$, so differentiating with respect to the noise scale reveals the intrinsic exponent. Under a regular manifold model, we show uniformly over the model class that the finite-scale field differs from the manifold dimension $d$ by at most $O(\sigma^2)$. We then establish a minimax lower bound of order $(n\sigma^d)^{-1}$ for estimating this finite-scale field from $n$ observations, for $n^{-1/(2\alpha+d)}\lesssim\sigma\le\sigma_0$. At the smallest scale covered by our lower-bound construction, the bound becomes the nonparametric rate $n^{-2\alpha/(2\alpha+d)}$.

This study proposes two novel bivariate distributions for jointly modeling temperature and rainfall by integrating Kumaraswamy-Teissier marginals with Clayton and Gumbel copula structures. To capture a wide range of dependence patterns, including both positive and negative associations, rotated copula variants (90{\deg}, 180{\deg}, and 270{\deg}) are incorporated along with their corresponding tail dependence characteristics. Model parameters are estimated using maximum likelihood and the inference functions for margins (IFM) approach, and their finite-sample performance is assessed through a comprehensive Monte Carlo simulation study. The proposed models are applied to monthly gridded temperature and rainfall data from the Northwest Himalayas, a region characterized by complex hydro-climatic variability. Comparative analysis demonstrates that the proposed framework outperforms several existing bivariate models and effectively captures lower-tail, upper-tail, and asymmetric dependence structures across summer and winter seasons. Based on the selected best-fitting copula models, univariate, joint, and conditional return periods are derived to quantify the risk of compound extremes. The results highlight the capability of the proposed approach to provide a more realistic representation of hydro-climatic dependence and offer a robust framework for assessing the risk of extreme temperature and rainfall events in mountainous regions.

This paper introduces a quantile-based Kumaraswamy-Teissier autoregressive moving average (KTARMA) model for positive-valued time series. Leveraging the flexibility of the extended Kumaraswamy-Teissier distribution within an observation-driven framework, the random component of the distribution is conditioned on the historical process and time-varying covariates, and is parameterized explicitly via its $\rho$-th conditional quantile, where $\rho \in (0,1)$. To capture temporal dependence, the systematic component maps an ARMA-type structure to this conditional quantile via an appropriate link function. For inference, we implement a conditional maximum likelihood framework and derive explicit analytical expressions for the resulting score vector and conditional information matrix, followed by the development of model diagnostic and forecasting procedures. The finite-sample performance of the developed estimators is evaluated through a Monte Carlo simulation study across various parameter configurations and quantile levels. Finally, the practical utility of the study is demonstrated by modeling monthly rainfall data over the Northwest Himalayas (2001-2025), where 525 grids are grouped into four homogeneous zones using a Self-Organizing Map and relevant atmospheric variables and large-scale climate indices are incorporated as predictive regressors. Out-of-sample forecasting evaluations reveal that the KTARMA model delivers highly competitive predictive performance, achieving consistently lower mean squared errors across all identified zones compared to KARMA and $\beta$ARMA models.

We show that susceptibilities, an interpretability technique developed for neural networks, can identify the presence of algorithmic structure in Turing machines by probing the local loss landscape of a learning problem for noisy Turing machines introduced by Murfet and Troiani (arXiv:2504.08075). We prove that symmetries and path separation in the algorithm implemented by a Turing machine induce permutation symmetries and low-rank blocks in its susceptibility matrix. We study this empirically on a set of deterministic finite automata (DFAs) and demonstrate that algorithmic features can be recovered by principal component analysis and clustering methods in susceptibility space.

Through the seminal works of Peligrad and Bradley, the existing sufficient conditions for the central limit theorem for $\rho$-mixing sequences are known to be very close to necessary. Nevertheless, we show that further improvements to these conditions are achievable when the $\rho$-mixing coefficients are non-summable, bridging a long-standing gap in the borderline case. The key idea is an iterative block-size technique that enables precise evaluations of the slowly varying variance components. Finally, known examples and new extensions–including iterated logarithmic mixing rates–are investigated to demonstrate the sharpness of our criteria, revealing a clear parameter structure and posing related open problems.

In medical research, it is often of interest to evaluate the predictive performance of a biomarker. Statistical approaches based on the Receiver Operating Characteristic (ROC) curve and its summary measures, such as the area under the curve (AUC) and the Youden index, are widely used to evaluate the prognostic performance of these biomarkers. In time-to-event studies, ROC analysis poses additional challenges due to change in disease status over time and the presence of censored individuals. To address these issues, time-dependent ROC curves were introduced. In this paper, we propose a non-parametric estimator of the time-dependent two-way partial AUC for right-censored data. We also discuss the partial Youden index and the associated optimal biomarker cutoff estimator for the right-censored data. We conduct an extensive simulation study to investigate the finite sample performance of the proposed estimators. The simulation study indicates that the proposed non-parametric estimators efficiently account for right censoring. Finally, we illustrate the proposed methods using two real data sets, one from the Primary Biliary Cirrhosis study and the other from the Molecular Taxonomy of Breast Cancer International Consortium trial.

Modern ride-share platforms must commit to a price before a trip is taken, yet the realized fare depends on travel time that is uncertain at the moment of sale, which can occur days in advance. The upfront price thus decomposes into the expected fare and the premium on an insurance claim whose payoff is the shortfall between the realized and promised prices. This work computes the fair premium for such a claim, following from contingent-claim pricing. Recent advances in travel-time distribution modeling cast the asymptotic distribution of travel time as a Brownian motion on a metric graph carrying a cyclostationary travel-time process. We thus derive closed-form premiums under both a population and a route-conditional travel-time law. A single pricing equation then covers products of increasing informational difficulty, such as on-demand and scheduled rides and capped-membership and commuter products. To price on sparse data, we develop route and travel-time samplers and validate them out of sample on 2014 Quebec City GPS trips, where they reproduce the empirical trip-time distribution. We show that guarantee premiums are inexpensive, typically under 5% of the fare. Conditioning on the realized route roughly halves the premium while reducing tail risk. Analyzing membership abuse, we show that adverse selection acts precisely along the dimension the price fails to condition on, yielding a design principle: subsidies additive in the fare, such as a fixed per-ride discount, leave marginal incentives unchanged and are abuse-proof by construction, with deterministic closed-form cost.

We study estimation and inference for a semiparametric class of time series models that specify only the conditional expectation, which is a known link function applied to a linear combination of past observations and covariates. The class covers count, binary, bounded and conditionally heteroskedastic responses within a single formulation, and the parameter is estimated by a quasi-likelihood estimating equation based on the first conditional moment. Under stationarity and a weak-dependence condition expressed through the functional dependence measure, we establish two results. First, using a Fuk–Nagaev inequality for weakly dependent sequences, we show that the estimator is localized in a shrinking neighbourhood of the true value with probability $1-o(n^{-1/2})$. Second, combining a Berry–Esseen bound for weakly dependent sequences with a Gaussian anti-concentration argument to control the remainder of the linear expansion, we obtain a Berry–Esseen bound for linear projections of the estimator, uniform over projection directions. From the projected bound we derive studentized confidence intervals with explicit coverage error and a conservative Bonferroni test for linear hypotheses on the parameters. For real data analysis, we extend the Beta autoregression for double-bounded data to an arbitrary link given by the inverse of a distribution function, and apply it to ten pairwise realized correlations of large-cap technology-stock returns, using Nasdaq and Dow~Jones index returns as covariates.

In this paper we introduce the R package mccca, which implements multiple-class cluster correspondence analysis (MCCCA) proposed in M.Takagishi et al., (2022). MCCCA is a statistical method that identifies and visualizes heterogeneous tendencies specific to “classes” (e.g., gender and nationality) in a low dimensional space. In MCCCA, two kinds of variables, external and active variables, are distinguished. External variables directly define classes whereas the active variables are used to derive class-specific clusters of observations (individuals). In this paper, we show how to apply MCCCA and how to visualize its results using mccca. We illustrate the procedure for performing MCCCA by applying it to two data sets.

Measles, a highly contagious, deadly virus, is at risk of losing its eradication status in the Unites States. Understanding the pattern, including seasonality, of measles could provide great benefit for forecasting, prevention, and public health preparedness as the virus re-emerges. The novel Variable Band-pass Periodic Block Bootstrap (VBPBB), which suppresses noise and interfering signals, is more efficient and statistically powerful to find periodic components compared to other existing methods. Using this method, we have found several significant periodic components in historical New York City measles cases which other methods were incapable of identifying. These findings give us a reusable method for understanding measles and other diseases and greater insight into what may occur should measles vaccine rates continue to fall.

AI-workflow governance cannot be reduced to checking the final answer: an apparently safe answer may rest on a fragile evidence path that ordinary evaluation cannot see, localize or govern. We call this hidden fragility a "structural iceberg": hallucinations and unsupported claims may form its visible tip, while consequential weakness remains submerged. Stochastic semantic evidence graphs (SSEGs) expose these icebergs by preserving workflow channels, propagating local uncertainty and identifying the hidden paths on which an apparently safe output depends. ALCE and RAGTruth show that visible failures at the tip -unsupported citations and hallucinated spans -rest on distinct submerged weaknesses and therefore require different interventions. Across retrieval, tool-use and controlled stress tests, SSEG localizes those weaknesses, supports targeted repair, produces no false automatic passes in 35,000 known-truth cases and reduces ToolSandbox review by 28.8% across 96 executions from two agent models. The same structural view carries into end-to-end governance: in a separately sealed 1,200-case FinGovBench study, adding SSEG to GPT-OSS-20B reduces unsafe releases from 452/660 to 8/660 while releasing all 540 safe cases and correctly distinguishing 592/600 matched workflow pairs. An unchanged-gate transfer to Qwen3-8B releases all 540 safe cases and none of 660 unsafe cases, whereas flat-UQ releases 520 unsafe cases. SSEG therefore moves governance below surface-level output checking, turning hidden evidence dependencies into auditable, path-specific decisions about intervention, revalidation and release.

Millions worldwide require Renal Replacement Therapy (RRT) as a treatment essential for survival. However, optimizing RRT strategies via AI is challenging due to heterogeneous patient dynamics, missing data, and the absence of an AI-oriented health assessment criterion. We propose an AI-Oriented Comprehensive Normalized Assessment (CNA) for healthy status and apply it to optimize RRT strategies by using offline reinforcement learning (RL). The key idea of CNA is transforming vital-sign distributions into a standard normal space, enabling a unified, data-driven health-status score defined by deviations from referent intervals, which also provides an AI-oriented criterion to assess strategy quality and supports RL termination. We further design a structured 23-dimensional state representation that integrates 19 indicators with 4 RRT descriptors, and employ matrix decomposition to reconstruct missing vital signs, improving data completeness for learning. These components are incorporated into multiple offline RL algorithms and validated via systematic ablation studies on RRT feature subsets. Compared with physicians' observed treatments, the best learned strategy reduces mortality from 13.2% to 5.0% (reducing 62.24%) and shortens average in-hospital stay from 308.5 to 250.1 hours (reducing 18.93%), demonstrating both methodological innovation and the potential of CNA-guided RL to improve RRT outcomes in nephrology.

Large language models increasingly rely on long chain-of-thought (CoT) trajectories for complex reasoning, but autoregressive generation brings substantial memory and inference costs. Latent reasoning models (LRMs) offer a more efficient alternative by compressing intermediate reasoning into a small number of continuous latent vectors. Despite their efficiency, however, the adversarial robustness of LRMs remains largely underexplored. In this work, we systematically evaluate the robustness of latent reasoning across textual and multimodal settings, covering eight models and six benchmarks. We find that, across our evaluated settings, LRMs are generally less robust than explicit CoT baselines under adversarial perturbations, with particularly severe degradation under white-box attacks. Further analysis reveals distinct failure modes across modalities: textual latent states exhibit brittle dynamics and high sensitivity to specific input patterns, while latent states in multimodal models can remain largely invariant to input perturbations and have limited influence on final predictions. These findings expose robustness limitations of current latent reasoning approaches and highlight the need to jointly consider efficiency and robustness when designing implicit reasoning systems. We have open-sourced our code to facilitate reproduction of our research https://github.com/PKU-ML/latent-reasoning-model-assessment.

Decode-time alignment methods steer a frozen language model by scoring candidate continuations with an external reward and selecting the maximiser. We argue that this shared design is a single degenerate point in a much larger space. We introduce Swiss-Knife, a framework for externalised multi-objective alignment in which the alignment specification is a first-class runtime object: hot-swappable scoring blades, a batch normaliser, a pairwise aggregation operator, and a selection rule. Six axioms characterise the admissible aggregation operators, and we prove a representation theorem: every operator satisfying them has the form $R_i = \sum_{j \neq i} g((\mu_i - \mu_j)/s(\sigma_i,\sigma_j))$, a two-parameter family containing probit and logistic comparison rules and pointwise argmax as named coordinates. Within it, pairwise aggregation is Lipschitz-stable under adversarial reward contamination while argmax is not, and Candidate-Batch Normalization (CBN) makes the weight simplex invariant to the rescalings under which reward models are only ever identified. Our reference instantiation pairs DPO-LoRA blades with an uncertainty-aware pairwise tournament. Sweeping the helpfulness/honesty/harmlessness simplex, it attains the best balanced frontier of six decode-time methods (harmonic $F_1$ 0.797 vs. 0.750 for the strongest baseline, $p < 10^{-14}$) with the lowest refusal rate and highest helpfulness of any arm, and reconfigures its objectives in 0.05 ms with no gradient computation. Ablating CBN costs 0.217 $F_1$, and the metadata confirms the predicted mechanism: the lowest-variance blade retains 9% of its nominal 33% influence, and the collapse follows the predicted ordering.

This paper develops a random-effects extension of the ergodic basic affine jump-diffusion (BAJD) model for a population of independent trajectories with individual unobserved jump intensities and common structural parameters. Under continuous-time observation, each intensity is estimated by the empirical jump frequency. We establish the strong consistency and stable mixed-normal limit of this estimator as the observation horizon tends to infinity. The estimated intensities are then used as pseudo-observations to construct a Bernstein-polynomial estimator of their common density. Its bias, variance, mean integrated squared error, and pointwise asymptotic normality are derived under a sequential asymptotic framework. The theory is developed for general positive jump-size distributions with finite activity and specialized to the Gamma$(k,\lambda)$ family, including the exponential and Erlang cases. For this family, we derive a pooled estimator of the common rate parameter and establish its consistency, asymptotic normality, and first-order conditional asymptotic independence from the individual intensity estimators. We also propose a consistent plug-in estimator of the population stationary mean. The methodology is illustrated through simulations and an empirical application to financial realized-volatility data.