Papers

Effective connectivity analysis in functional magnetic resonance imaging (fMRI) studies directional interactions among brain regions and experimental stimuli. Dynamic causal modeling (DCM) is a widely used method to estimate effective connectivity, based on a state-space representation consisting of a latent neural signal model and an observation model transforming the neural signal into the observed blood-oxygen-level-dependent (BOLD) response. A standard DCM combines ordinary differential equation (ODE) dynamics for the latent signal with a complex neural-hemodynamic system for the observation model, and typically uses variational Bayes for parameter estimation. While physically well-motivated, this approach can lead to practical challenges such as inexact solutions and underestimated uncertainty. We introduce Canonical DCM (CDCM), a Markov chain Monte Carlo (MCMC)-based method that adopts a simpler observation model and the No-U-Turn Sampler for posterior sampling. The simpler observation model admits a piecewise analytic solution to the neural ODE, increasing computational efficiency and enabling explicit derivation of sufficient conditions for parameter identifiability. The results indicate that CDCM provides reliable uncertainty quantification and consistent estimation of parameters related to experimental inputs for simulated and real data. We use publicly available data from the Wellcome Centre for Human Neuroimaging and the Human Connectome Project (HCP) to benchmark CDCM against standard DCM methods and examine replicability of estimated connectivity patterns in small- and large-scale neuroimaging settings.

Deep learning excels at prediction but often lacks finite-sample guarantees and calibrated uncertainty; RKHS (Reproducing Kernel Hilbert Space)-based methods provide those guarantees but struggle to adapt in high dimensions. We propose Wahkon, a deep RKHS superposition network that unifies Kolmogorov's superposition principle with RKHS regularization in the smoothing-spline tradition of Wahba. This yields a finite-dimensional deep representer theorem that makes training tractable and provides explicit layerwise complexity control. We show the penalized estimator is exactly the MAP (maximum a posteriori) estimate under a hierarchical Gaussian-process prior, extending the spline/GP duality to deep compositions. Using metric-entropy arguments, we establish minimax-optimal convergence rates under mild smoothness and clarify how depth and width trade off with regularity. Empirically, Wahkon outperforms multilayer perceptrons, Neural Tangent Kernels, and Kolmogorov–Arnold Networks across simulation benchmarks and a single-cell CITE-seq study. By unifying Kolmogorov's superposition principle with RKHS regularization, Wahkon delivers accuracy, interpretability, and statistical rigor in a single framework.

Quantifying regret typically involves repeatedly re-solving a stochastic optimization problem across simulated scenarios. Such an approach is costly: the cost scales with the number of scenarios and the cost of each solve. We propose that regret can instead be measured using the joint moments of the cost vector $c$ and the optimal decision $\pi^*(c)$. Working with the optimal concave and Lipschitz under only a feasible region value function $v(c) = \min_{z\in Z} c^\top z$, we show that regret always decomposes as $\mathrm{Regret} = -\mathrm{Cov}(c,\pi^*(c)) - R(c)$ for a residual $R(c)$. We further show that $R(c)=0$ when $\pi^*$ is affine in $c$, which holds for unconstrained and equality-constrained (e.g., budget-constrained Markowitz) quadratic programs and many, but not all, linear programs. For all cases, we give a distribution-free bound $\mathrm{Regret} \le D\sqrt{\mathrm{tr}(\Sigma_c)}$ that depends only on the radius of the feasible region and the cost covariance. We also derive concentration and asymptotic-normality results for the empirical regret, the latter under an explicit and checkable non-degeneracy condition.

The inflated beta regression model is widely used for modeling continuous proportions with values at the boundaries. Maximum likelihood estimation for these models is well-known for its sensitivity to outliers, which can severely distort inference and lead to misleading conclusions. We propose robust estimators that mitigate the lack of robustness in maximum likelihood-based inference while preserving the simplicity and interpretability of the inflated beta framework. Additionally, an algorithm is introduced to select tuning constants based on the data's robustness requirements. The proposed estimators' asymptotic and robustness properties are studied, and robust Wald-type tests are developed. Simulation studies and a real data application highlight the advantages and practical effectiveness of the proposed robust estimators.

Kernel density estimation is a widely used nonparametric approach to estimate an unknown distribution. Recent work in Bayesian predictive inference has considered stochastic processes formed by specifying the predictive distribution for the next data point given all observed data such that the resulting predictive distributions converge weakly almost surely. We study two kernel based prediction rules: the classic kernel density estimator, and a recursive version previously introduced for online problems. We show that both processes converge weakly almost surely, which opens the door for new Bayesian interpretations of kernel density estimation. Surprisingly, the process based on the classic kernel density estimates converges to a compactly supported measure, while the recursive version converges to a non-compactly supported measure.

Certain recent advances in statistical methodology have promising potential for fruitful use in general biology and the fisheries sciences. This paper reviews and discusses some of the relevant themes, including accurate modelling via focused model selection techniques, dynamic goodness-of-fit testing of processes evolving over time, finding break points for phenomena experiencing changes, prediction uncertainty, and optimal combination of information across diverse sources via confidence distributions. The methods are illustrated for the Hjort liver quality index time series. Its roots lie in the classic Hjort (`Fluctuations in the Great Fisheries of Northern Europe, Viewed in the Light of Biological Research', 1914), where liver quality of the Atlantic cod (Gadus morhua) for 1880–1912 is reported on and studied, along with related factors, making it one of the first teleost time series ever published. Diligent work by Kjesbu et al. (`Making use of Johan Hjort's `unknown' legacy: reconstruction of a 150-year coastal time-series on northeast Arctic cod (Gadus morhua) liver data reveals long-term trends in energy allocation patterns', 2014), involving both archival and calibration efforts, have extended the series both backwards and forwards in time, to 1859–2012, yielding one of the longest time series of marine science. Our study offers a detailed examination of this series and how it relates to and interacts with associated factors, including Kola winter temperatures, length distribution parameters, cod mortality, and a certain index related to availability of food.

Tabular data underpins most high-value prediction problems in science and industry, and TabPFN has driven the foundation model revolution for this modality. Designed with feedback from our users, TabPFN-3 builds on this foundation to scale state-of-the-art performance to datasets with 1M training rows and substantially reduce training and inference time. Pretrained exclusively on synthetic data from our prior, TabPFN-3 dramatically pushes the frontier of tabular prediction and brings substantial gains on time series, relational, and tabular-text data. On the standard tabular benchmark TabArena, a forward pass of TabPFN-3 outperforms all other models, including tuned and ensembled baselines, by a significant margin, and pareto-dominates the speed/performance frontier. On more diverse datasets, TabPFN-3 ranks first on datasets with many classes, and beats 8-hour-tuned gradient-boosted-tree baselines on datasets up to 1M training rows and 200 features. TabPFN-3 introduces test-time compute scaling to tabular foundation models. Our API offering TabPFN-3-Plus (Thinking) exploits this to beat all non-TabPFN models by over 200 Elo on TabArena, rising to 420 Elo on the largest data subset, and outperforms AutoGluon 1.5 extreme while being 10x faster, without using LLMs, real data, internet search or any other model besides TabPFN. TabPFN-3 extends the capabilities of our models, enabling SOTA prediction on relational data (new SOTA foundation model on RelBenchV1) and tabular-text data (SOTA on TabSTAR via TabPFN-3-Plus); and improves existing integrations: a specialized checkpoint, TabPFN-TS-3, ranks 2nd on the time-series benchmark fev-bench, and SHAP-value computation is up to 120x faster. TabPFN-3 achieves this performance while being up to 20x faster than TabPFN-2.5. In addition, a reduced KV cache and row-chunking scale to 1M rows on one H100 with fast inference speed.

Quantum machine learning (QML) aims to accelerate machine learning tasks by exploiting quantum computation. Previous work studied a QML algorithm for selecting sparse subnetworks from large shallow neural networks. Instead of directly solving an optimization problem over a large-scale network, this algorithm constructs a sparse subnetwork by sampling hidden nodes from an optimized probability distribution defined using the ridgelet transform. The quantum algorithm performs this sampling in time $O(D)$ in the data dimension $D$, whereas a naive classical implementation relies on handling exponentially many candidate nodes and hence takes $\exp[O(D)]$ time. In this work, we construct and analyze a quantum-inspired fully classical algorithm for the same sampling task. We show that our algorithm runs in time $O(\operatorname{poly}(D))$, thereby removing the exponential dependence on $D$ from the previous classical approach. Numerical simulations show that the proposed sampler achieves empirical risk comparable to exact sampling from the optimized distribution and substantially lower than sampling from the non-optimized uniform distribution, while also exhibiting exponentially improved runtime scaling compared with the conventional classical implementation. These successful dequantization results show that sparse subnetwork selection via optimized sampling can be achieved classically with polynomial data-dimension scaling on conventional computers without quantum hardware, providing an alternative to the existing quantum algorithm.

Acquisition differences across sites, scanners, and protocols in dMRI introduce variability that complicates structural connectome analysis. This motivates deep learning models that can represent high-dimensional connectomes in a low-dimensional space while explicitly separating acquisition-related effects from biological variation. Conventional dimensionality reduction methods model all variance as continuous, so acquisition effects often get absorbed into a continuous latent space. Recent hybrid latent-space models combine discrete and continuous components to address this, but typically require manual capacity tuning to ensure the discrete component captures the intended variability. We introduce an unsupervised framework that removes this manual tuning by architecturally annealing encoder outputs before decoding, allowing the model to adaptively balance discrete and continuous latent variables during training. To evaluate it, we curated a dataset of N=7,416 structural connectomes derived from dMRI, spanning ages 2 to 102 and 13 studies with 25 unique acquisition-parameter combinations. Of these, 5,900 are cognitively unimpaired, 877 have mild cognitive impairment (MCI), and 639 have Alzheimer's disease (AD). We compare against a standard VAE, PCA with k-means clustering, and hybrid models that anneal only through the loss function. Our architectural annealing produces stronger site learning (ARI=0.53, p<0.05) than these baselines. Results show that a hybrid continuous-discrete latent space, with architectural rather than loss-based annealing, provides a useful unsupervised mechanism for capturing acquisition variability in dMRI: by jointly modeling smooth and categorical structure, the Joint-VAE recovers clusters aligned with scanner and protocol differences.

NVIDIA GPUs have recently started to be used in computational biology, yet R users lack integrated GPU monitoring tools, forcing reliance on external utilities like nvidia-smi. We introduce CudaMon, an R package providing real-time monitoring of GPU utilization, memory, temperature, and power draw via NVML, along with data export and visualization utilities. Monitoring a GPU-accelerated single-cell RNA-seq pipeline (1M brain cells, RAPIDS workflow) shows that compute-intensive steps (PCA, UMAP, t-SNE) exceed 90% GPU utilization, while data management phases reveal bottlenecks. CudaMon facilitates resource optimization, performance debugging, and reproducibility for GPU-accelerated R workflows.

The football transfer market is a complex, dynamic environment in which clubs compete to acquire players who strengthen their squads. While several frameworks estimate a player's worth, a comprehensive approach that captures both squad optimisation and transfer market dynamics remains limited. In this paper, we propose a quantitative framework for optimising football transfer strategy under budget constraints, integrated with a competitive bidding paradigm. Using data from professional football leagues, we construct player performance and transfer price models using linear mixed-effects frameworks that incorporate player characteristics, recent performance, team context, and league effects. The predicted ratings and estimated transfer prices are then integrated into a weighted multi-criteria constrained optimisation framework that determines a club's transfer activities at the end of the season. Finally, these optimal transfer decisions are embedded within an independent private-value auction model with a random reserve price to analyse market behaviour when multiple teams compete for the same player. We illustrate our approach using the 2018-19 season of the English Premier League to demonstrate its ability to capture transfer-market dynamics.

During thDuring the last few years, the term Mechanistic Interpretability, a specific area, under the umbrella of explainable artificial intelligence (XAI), has been introduced, to explain the decisions made by complex machine learning (ML) models in critical systems like UAV intrusion detection systems (UAVIDS). In this paper, we apply best-practices for data pre-processing and examine a wide range of tree-ensembles, deep neural networks, hybrid stacking models and the latest ensemble neural networks to detect intrusions in UAV, with stratified 10-fold cross validation. With our top-performing model, XGBoost, we proceed to Shapley Additive explanations (SHAP), to analyze the global and local feature importances and understand which features, each attack targets, to mimic normal traffic and where the misclassifications occur. Furthermore a distribution analysis follows, by visually comparing violin plots and the curves of kernel density estimations. With the Westfall-Young permutation test for multiple comparisons, the Bandwidth optimization of the KDEs and the selection of Jensen-Shannon Distance for the test, we discover the true causes of false predictions, observed in Wormhole and Blackhole attacks in UAVIDS-2025. The findings provide robust, reliable and explainable models for UAV intrusion detection, along with statistical insights, which capture and clarify the masked nature of the attacks, regarding the challenge of Density Support Intersection, between these attacks, in this dataset.

Online Multiple Testing (OMT), a fundamental pillar of sequential statistical inference, traditionally evaluates the False Discovery Rate (FDR) and statistical power in isolation, obscuring the highly asymmetric costs of false positives and false negatives in modern automated pipelines. To unify this evaluation, we introduce $\textit{Weighted Regret}$. Under this metric, we prove the $\textit{Duality of Regret Conservation}$: purely deterministic procedures ensuring strict FDR control inevitably incur an $\Omega(T)$ linear regret penalty, as threshold depletion during signal-sparse cold starts forces massive false negatives. Tailored for exogenous testing streams, we propose Decoupled-OMT (DOMT) as a baseline-agnostic meta-wrapper. By incorporating a history-decoupled, strictly non-negative random perturbation, DOMT rescues purely deterministic baselines from severe threshold depletion. Crucially, it preserves exact asymptotic safety in stationary environments and rigorously bounds finite-sample error inflation during cold-starts. Guaranteeing zero additional false negatives, it yields an order-optimal $\Omega(\sqrt{T})$ regret reduction in bursty environments, with a derived “Cold-Start Tax” characterizing the exact phase transition of algorithmic superiority. Experiments validate that DOMT consistently curtails empirical weighted regret, achieving an order-optimal sublinear mitigation of threshold depletion to navigate the non-stationary Pareto frontier.

Quantization is essential for efficient large language model (LLM) inference, yet the dequantization step-converting low-bit weights back to high-precision for matrix multiplication has become a critical bottleneck on modern AI accelerators. On architectures with decoupled compute units (e.g., Ascend NPUs), dequantization operations can consume more cycles than the matrix multiplication itself, leaving the high-throughput tensor cores underutilized. This paper presents Multi-Scale Dequant (MSD), a quantization framework that removes weight/KV dequantization from the GEMM critical path. Instead of lifting low-bit weights to BF16 precision, MSD decomposes high-precision BF16 activations into multiple low-precision components, each of which can be multiplied directly with quantized weights via native hardware-accelerated GEMM. This approach shifts the computational paradigm from precision conversion to multi-scale approximation, avoiding INT8-to-BF16 weight conversion before GEMM. We instantiate MSD for two weight formats and derive tight error bounds for each. For INT8 weights (W4A16), two-pass INT8 decomposition achieves near 16 effective bits. For MXFP4 weights (W4A16), two-pass MXFP4 decomposition yields near 6.6 effective bits with error bound 1/64 per block surpassing single-pass MXFP8(5.24 bits) while maintaining the same effective GEMM compute time. We further derive closed-form latency and HBM traffic models showing that MSD avoids the Vector-Cube pipeline stall caused by dequantization and reduces KV cache HBM traffic by up to 2.5 times in attention. Numerical simulations on matrix multiplication and Flash Attention kernels confirm that MSD does not degrade accuracy compared to dequantization baselines, and in many settings achieves lower L2 error.

Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space are vacuous in this regime, and recent work has shown that non-vacuous guarantees can be recovered by restricting attention to the part of parameter space that the algorithm actually visits. This survey paper organizes this line of work around three steps: extending PAC-Bayesian theory to random, data-dependent hypothesis sets (arXiv:2404.17442); refining the complexity term with geometric and topological descriptors of the optimization trajectory, including fractal dimensions, alpha-weighted lifetime sums, and positive magnitude (arXiv:2006.09313, arXiv:2302.02766, arXiv:2407.08723); and replacing the resulting information-theoretic terms by stability assumptions (arXiv:2507.06775). We unify these contributions around a single template inequality and a head-to-head comparison of the resulting bounds.

We present a covariance-aware sampler that improves the quality of pixel-space Diffusion Model (DM) sampling in the few-step regime. We hypothesize that in the few-step regime samplers fail because they rely solely on the predicted mean of the reverse distribution, while our solution explicitly models the reverse-process covariance. Our method combines Tweedie's formula to estimate the covariance with an efficient, structured Fourier-space decomposition of the covariance matrix. Implemented as an extension of DDIM, our method requires only a minimal overhead: one extra Jacobian-Vector Product (JVP) per step. We demonstrate that for pixel-based DMs, our method consistently produces superior samples compared to state-of-the-art second order samplers (Heun, DPM-Solver++) and the recent aDDIM sampler, at an identical number of function evaluations (NFE).

Reinforcement learning (RL) for large language models (LLMs) is dominated by the cost of rollout generation, which has motivated the use of low-precision rollouts (e.g., FP8) paired with a BF16 trainer to improve throughput and reduce memory pressure. This introduces a rollout-training mismatch that biases the policy gradient and can cause training to collapse outright on reasoning benchmarks. We show that the mismatch is non-stationary and acts as a double-edged sword: early in training it provides a stochastic exploration bonus, exposing the gradient to trajectories the trainer would otherwise under-sample, but the same perturbation transitions into a destabilizing source of bias as the policy concentrates. To solve this, we propose Adaptive Importance Sampling (AIS), a correction framework that adjusts the strength of its intervention on a per-batch basis. AIS combines three real-time diagnostics, namely weight reliability, divergence severity, and variance amplification, into a single mixing coefficient that interpolates between the uncorrected and fully importance-weighted gradients, suppressing the destabilizing component of the mismatch while preserving its exploratory benefit. We integrate AIS into GRPO and evaluate it on the diffusion-based LLaDA-8B-Instruct and the autoregressive Qwen3-8B and Qwen3.5-9B across mathematical reasoning and planning benchmarks. AIS matches the BF16 baseline on most tasks while retaining the 1.5 to 2.76x rollout speedup of FP8.

Valiant's 1984 paper is widely credited with introducing the PAC learning model, but it, in fact, introduced a different model: unlike PAC learning, the learner receives only positives, may issue membership queries, and must output a hypothesis with no false positives. Prior work characterized variants, including the case without queries. We revisit Valiant's original model and ask: *Which classes are learnable in it?* For every finite domain, including Valiant's Boolean-hypercube setting, we show that a class is learnable if and only if every realizable positive sample can be certified by a poly-size adaptive query-compression scheme. This is a new variant of sample compression where the learner certifies samples via a short interaction with the membership oracle. Our characterization shows that learnability in Valiant's model is strictly sandwiched between learnability in the PAC model and the variant of Valiant's model without membership queries. This is one of the rare cases where introducing membership queries changes the set of learnable classes, and not just the sample or computational complexity. Next, we study the natural extension of the model to arbitrary domains. While we do not obtain an exact characterization, our techniques readily generalize and show that the same strict sandwiching persists. Finally, we show that $d$-dimensional halfspaces, which are not learnable without queries, are learnable with queries: we give a $\mathrm{poly}(d) \tilde{O}(1/\epsilon)$ sample and $\mathrm{poly}(d) \mathrm{polylog}(1/\epsilon)$ query algorithm, and prove that at least $\Omega(d)$ samples or queries are necessary. To our knowledge, this is the first algorithm for halfspaces in Valiant's model. Together, these results uncover a surprisingly rich theory behind Valiant's original notion of learnability and introduce ideas that may be of independent interest in learning theory.

This paper develops a macroscopic, activity-based model of urban active mobility using nonintrusive sensor data. It introduces attendance functions to describe spatio-temporal travel patterns between activities and formulates the disaggregation of aggregated counts as a statistical inference problem. Counts are modeled as Poisson variables, and unknown subpopulation sizes are estimated via maximum likelihood, with theoretical guarantees and an efficient EM algorithm for computation. Grounded in a microscopic stochastic model, the framework offers a scalable and privacy-preserving approach to analyzing urban soft mobility dynamics.

We study best-policy identification for finite-horizon risk-sensitive reinforcement learning under the entropic risk measure. Recent work established a constant gap in the exponential horizon dependence between lower and upper bounds on the number of samples required to identify an approximately optimal policy. Precisely, known lower bounds scale in $\Omega(e^{|\beta| H})$ where $H$ is the horizon of the MDP, while the state-of-the-art upper bound achieves at best $O(e^{2|\beta| H})$ (arXiv:2506.00286v2) using a generative model. We show that this extra exponential factor can be traced to overly loose concentration control for exponential utilities. To close this open gap, we revisit the analysis of this problem through a forward-model based algorithm building on KL-based exploration bonuses that we adapt to the entropic criterion. The improvement we get is due to two main novel technical innovations. We leverage the smoothness properties of the exponential utility to derive sharper concentration bounds, and we propose a new stopping rule that exploits further this tightness to obtain a sample complexity that matches the lower bound.

In statistics permutations typically arise in the context of rank plots for two-dimensional data. Such plots can also be interpreted as discrete copulas. In discrete mathematics, typically in the context of the description of large (non-random) objects, two-dimensional copulas appear as limits of permutations and are then known as permutons if the topology refers to the convergence of pattern frequencies. We obtain a functional central limit theorem for such pattern frequencies in the context of two-dimensional random samples. The result serves as the basis for nonparametric goodness-of-fit tests, for two-sample tests, and for tests of symmetry. This includes a suitable variant of the bootstrap for obtaining critical values. Pattern-based procedures are also of interest in a parametric context. We consider two examples, the Farlie-Gumbel-Morgenstern class and a family of delay copulas. We discuss implementation aspects of the resulting procedures and we provide a simulation study that supplements the theoretical results in the nonparametric case.

With the growing application of spatial predictive modeling in ecology, the question of how to appropriately evaluate the resulting maps has gained increasing attention. While there is consensus that map accuracy is ideally estimated using an independent probability sample of the prediction area, there is still no agreement on the most appropriate way to conduct an evaluation for the common case when such a sample is not available. Cross-validation, which involves multiple train-test splits, is commonly applied not only to estimate final model accuracy but also to guide model tuning and selection. Many different spatial and non-spatial approaches to cross-validation have been proposed, and approaches in both groups have faced substantial criticism. It has been shown that random cross-validation methods are suitable when the training points are randomly distributed in the prediction area, while spatial cross-validation is better suited towards extrapolation situations. In practice, however, there is a continuum and most cases are between those two extremes. To address this gap, we advocate for a new category of cross-validation methods to account for this: prediction-domain adaptive evaluation. Methods in this category flexibly adapt to the prediction situation, yielding most reliable estimates of map accuracy across different scenarios. To ground this perspective empirically, we reproduce a simulation study that was used in earlier research and systematically compare different evaluation methods and discuss their purpose.

We introduce a family of synthetic languages with hierarchical structure – generated by a broadcast process on trees – for which the role of context length and reasoning in autoregressive generation can be analyzed precisely. At the heart of our analytic approach is an \emph{exact $k$-gram ansatz} in place of transformers with context length $k$, a substitution we then validate empirically. Using this ansatz we derive explicit asymptotic predictions for distributional statistics of the sequences produced by a trained model, instantiated in two settings. For the Ising broadcast process (a soft-constrained language), we prove that the variance of the generated sum scales log-linearly in the context depth and its kurtosis converges to that of a Gaussian – both deviating from the true language for any sublinear context. For the coloring broadcast process (a hard-constrained language) in the freezing regime, bounded-context autoregression produces sequences that, with high probability, are inconsistent with any valid coloring of the underlying tree. Together these results imply an $\Omega(n)$ lower bound on the context length required to faithfully sample length-$n$ sequences. In contrast, we prove that an autoregressive reasoning model with only $\Theta(\log n)$ working memory can sample exactly from the true language – an exponential improvement. We confirm both the lower-bound predictions and the reasoning-based upper bound empirically with transformers trained on the synthetic language; the trained models track our asymptotic predictions quantitatively across a wide range of context sizes.

Flow Language Models (FLMs) are a recently introduced class of language models which adapt continuous flow matching for one-hot encoded token sequences. Their denoisers have a special structure absent from generic continuous diffusion models: each block of the denoising mean is a posterior marginal distribution over the clean token at that position. Standard DDPM-style samplers collapse these marginals to a single conditional-mean endpoint and bridge toward this simplex-valued point, which is generally not a valid one-hot sequence. We argue that the natural sampler for an FLM is instead posterior-predictive. At each reverse step, we sample a clean one-hot endpoint from the factorized posterior defined by the FLM token marginals, and then sample the next continuous state from the analytic Ornstein–Uhlenbeck bridge conditioned on that endpoint. The method is training-free, uses the same model evaluations as standard sampling, and gives a principled interface for token-level decoding controls such as temperature scaling and nucleus truncation. We show that, under exact posterior marginals, the endpoint approximation error is exactly the conditional multi-information among token positions. The induced one-step bridge kernel preserves all token-wise posterior-predictive marginals and loses only the residual cross-position dependence. Finally, we prove a Girsanov path-space comparison showing that the marginal-conditioned bridge has a no-larger denoising-error term than the frozen conditional-mean bridge, with strict improvement whenever intermediate coordinate-wise bridge observations reveal additional information about the clean token. Experiments with FLMs show that the sampler improves the quality–diversity tradeoff. Code is available at: github.com/imbirik/mcb.

Camera traps have become an important tool in ecological research, enabling large-scale, noninvasive monitoring of wildlife populations and behavior. By automatically recording animals as they pass within view, these devices generate massive image datasets with minimal field effort. This data richness introduces a new bottleneck when translating the images into usable information due to time and effort required for human annotation. Artificial intelligence (AI) has recently been integrated into the workflow to improve efficiency. However, the data procured from AI approaches are of a different nature, necessitating new statistical methods. We develop a new Bayesian hierarchical data-fusion model that combines the strengths of human annotations and AI predictions. The benefits of our approach are an ability to provide uncertainty quantification as well as improved inference and predictive power, which we demonstrate through simulation. We apply our model to an AI analysis of the body condition of white-tailed deer (Odocoileus virginianus) from camera trap images from North Carolina to study the relationship between health and their environment. Our analysis derived novel ecological inference compared to a more traditional approach using the same data. We find that bucks in rut have higher (healthier) body condition than other deer and that green, open habitats are correlated with high body condition.

Estimation of the extreme value index under right censoring is a fundamental problem in extreme value theory, with important applications in finance, insurance, and reliability. Classical integral estimators for Pareto-type tails typically require that the asymptotic proportion of uncensored observations in the tail is larger than one half, corresponding to the weak censoring regime. This restriction excludes many practically relevant situations involving strong censoring, where the proportion of uncensored observations is smaller than or equal to one half, and reflects the absence of a uniformly valid Gaussian approximation for the associated tail empirical process. To overcome this limitation, we introduce a weighted and truncated Nelson–Aalen tail empirical process and construct a class of integral estimators indexed by a tuning parameter larger than one. This approach restores a tractable asymptotic structure over the entire censoring range, from very weak to very strong censoring. Under standard regular variation conditions, we establish a uniform Gaussian approximation and derive consistency and asymptotic normality without imposing restrictions on the censoring level. A key ingredient of the analysis is a linearization of the estimator as a functional of the underlying process. Simulation studies and real data applications demonstrate improved stability and accuracy, particularly under moderate and strong censoring. In particular, the analysis of insurance loss data, representing weak censoring, and Australian AIDS survival data, representing strong censoring, illustrates the practical relevance of the proposed methodology across contrasting censoring regimes.

Most anomaly detection systems output scores rather than calibrated decisions, leaving practitioners to choose thresholds heuristically and without clear statistical interpretation. Conformal anomaly detection addresses this limitation by converting anomaly scores into calibrated p-values that are valid under the statistical assumption of data exchangeability, with a growing literature extending this idea beyond that setting. We present nonconform, a Python package for applying conformal anomaly detection within existing machine-learning workflows, and use it as the basis for an implementation-grounded introduction to the field. The package integrates with scikit-learn, PyOD, and custom anomaly detectors, and provides a unified interface for calibration, p-value generation, and false discovery rate control. It supports several conformalization strategies, ranging from simple split-conformal calibration to more data-efficient and shift-aware extensions. Through a progression from foundational concepts to advanced conformalization strategies, complemented by code examples, the paper connects the statistical ideas behind conformal anomaly detection to their practical use in nonconform. Empirical results demonstrate that the implemented methods enable statistically principled anomaly detection. Together, the package and exposition aim to make core conformal anomaly detection workflows more accessible and reproducible in experimental and production-oriented settings.

In this paper, we establish last-iterate convergence rates for off-policy actor–critic methods in reinforcement learning. In particular, under a single-loop, single-timescale implementation and a broad class of policy updates, including approximate policy iteration and natural policy gradient methods, we prove the first $\tilde{\mathcal{O}}(\epsilon^{-2})$ sample complexity guarantee for finding an $\epsilon$-optimal policy under minimal assumptions, namely, the existence of a policy that induces an irreducible Markov chain. This stands in stark contrast to the existing literature, where an $\tilde{\mathcal{O}}(\epsilon^{-2})$ sample complexity is achieved only through nested-loop updates and/or under strong, algorithm-dependent assumptions on the policies, such as uniform mixing and uniform exploration. Technically, to address the challenges posed by the coupled update equations arising from the single-loop implementation, as well as the potentially unbounded iterates induced by off-policy learning, our analysis is based on a coupled Lyapunov drift framework. Specifically, we establish a geometric convergence rate for the actor and an $\tilde{\mathcal{O}}(1/T)$ convergence rate for the critic, and combine the two Lyapunov drift inequalities through a cross-domination property. We believe this analytical framework is of independent interest and may be applicable to other coupled iterative algorithms with unbounded

Computer-use agents are increasingly capable of operating on real operating systems, but this capability has also increased the risks posed by prompt injection, indirect instructions, and visual attacks. Existing defenses typically rely on analyzing the prompt or each potentially malicious input with a second large model at inference time, which can limit coverage or increase deployment cost. We propose ProjGuard, an alternative based on behavioral trajectory monitoring. At each step, we derive a lightweight scalar risk signal from the agent's accumulated interaction history and evaluate, online, whether execution is beginning to drift toward an unsafe region. This enables early warnings before the trajectory reaches a potentially harmful action. When an alert is raised, we selectively activate an auxiliary vision-language model to propose a corrected next step and steer execution back toward task completion. Experiments on OS-Harm show that monitoring with on-demand correction reduces the unsafe rate from 16 percent to 3 percent while improving task completion from 59 percent to 65 percent. We further evaluate transfer to RiosWorld, where the method remains competitive, reaching 4 percent unsafe and 64 percent completion. Overall, these results support a hierarchical safety strategy in which always-on monitoring anticipates deviations and activates correction only when needed.

Understanding how deep neural networks learn useful internal representations from data remains a central open problem in the theory of deep learning. We introduce Neural Low-Degree Filtering (Neural LoFi), a stylized limit of gradient-based training in which hierarchical feature learning becomes an explicit iterative spectral procedure. In this limit, the dynamics at each layer decouple: given the current representation, the next layer selects directions with maximal accessible low-degree correlation to the label. This yields a tractable surrogate mechanism for deep learning, together with a natural kernel-space interpretation. Neural LoFi provides a mathematically explicit framework for studying multi-layer feature learning beyond the lazy regime. It predicts how representations are selected layer by layer, explains how emergence of concepts arises with given sample complexity, and gives a concrete mechanism by which depth progressively constructs new features from old ones through low-degree compositionality. We complement the theory with mechanistic experiments on fully connected and convolutional architectures, showing that Neural LoFi improves over lazy random-feature baselines, recovers meaningful structured filters, and predicts representations aligned with early gradient-descent feature discovery with real datasets.