Papers

Matching is widely used to mimic randomized experiments by forming matched sets in which treated and control units differ only randomly with respect to observed covariates. However, when the study population consists of interconnected units from a single network or a small number of networks, matching solely on observed covariates may produce matched units that are more closely connected in the network than would occur by chance. This increased network proximity within matched sets can induce spurious associations between treatment and outcome when both variables exhibit similar autocorrelation patterns on the network. To reduce spurious associations while preserving the validity of causal comparisons, we propose a new matching method that matches units with similar covariates subject to additional network-proximity constraints. For post-matching inference, we propose a randomization-based procedure for testing the sharp null hypothesis of no causal effect. The inference uses the asymptotic normal approximation and accommodates statistical dependence among test statistics obtained from each matched set without requiring explicit specifications of their correlation structures. We demonstrate the validity and utility of the proposed methods through simulation studies and apply them to the Framingham Heart Study. The matching method and subsequent inference procedure are implemented in the R package netmatchRI.

We consider the estimation of the invariant distribution $\pi$ of a Markov kernel on a discrete state space (or of the mean value $\pi(f)$ of a functional $f$ under $\pi$) when solving the invariance equation is not feasible. Look-ahead estimators exploit the knowledge of the kernel by propagating the empirical occupation measure through $k$ steps of the chain. When the kernel is known, as in Markov chain Monte Carlo, we compare their mean squared error with that of the empirical estimator, for independent or Markovian data, stationary or not. Our main result establishes that, for Markovian data, the one-step estimator always improves on the empirical one asymptotically, and that the improvement grows with $k$ for reversible kernels. A non-reversible counterexample shows that reversibility cannot simply be dropped. In the statistical setting where the kernel belongs to a parametric family with unknown parameter, we introduce plug-in look-ahead estimators, which perform the look-ahead step with an estimated kernel. When the parameter is estimated at the parametric rate, we give a necessary and sufficient condition under which the plug-in look-ahead estimator outperforms the empirical one. The theoretical results are illustrated by extensive simulation studies, which also shed further light on the behaviour of the estimators at hand. Both settings are finally applied to real data arising from geographical mobility problems in the Lyon metropolitan area, France.

Applications such as engineering design often require us to optimize a black-box function, i.e., a system whose inner processing is not analytically known and whose gradients are not available. Practitioners often have a fixed budget for the number of function evaluations and the performance of an optimization algorithm is measured by its simple regret. In this paper, we study the class of "Optimistic Optimization" algorithms for black-box optimization that use a partitioning scheme for the domain. We develop algorithms that learn a good partitioning scheme and use flexible surrogate models such as neural networks in the optimization procedure. For multi-index functions on an $m$-dimensional subspace within $d$ dimensions, our algorithm attains $\tilde{O}(n^{-\beta / d})$ regret, where $\beta = 1 + \frac{d-m}{2m-1}$, as opposed to $\tilde{O}(n^{-1/d})$ for SequOOL, a state-of-the-art optimistic optimization algorithm. We use our approach to improve the quality of Activation-aware Weight Quantization (AWQ) of the OPT-1.3B model, achieving $\sim10\%$ improvement in performance relative to the best possible unquantized model.

Localizing behavior to individual components of a language model is a central goal of mechanistic interpretability. However, scoring components one at a time misses context-dependent effects: a primary component can inhibit the activation of a backup, leading to issues with ranking components. Actual causality studies the structure of such interactions via witnesses: variables that provide contextual information to resolve interaction terms. However, estimation with witnesses typically requires combinatorial enumeration and is infeasible in practice. We introduce the witness-integrated set effect (WISE), a family of causal estimands that build on the witness mechanism while taking expectations over sets of causes and witnesses to remain computationally feasible. Building on this approach, we introduce JuntaLearner, a gradient-based circuit discovery method that learns to rank components by their causal impact across varying-sized sets of components and witnesses. Alongside faithfulness metrics, we introduce measures of necessity and task specificity, and the circuit recognition score (CRS) to summarize each metric across circuit sizes while emphasizing effects achieved by small circuits. Across tasks and models of increasing size, JuntaLearner achieves higher mean CRS compared to attribution baselines on all metrics. Since its cost does not grow with the number of candidate components, JuntaLearner scales to large models while accounting for set-level interactions and avoiding first-order approximations.

Limited training data diversity constrains generative modeling of 3D human bodies: conservative models remain close to observed examples, whereas exploratory models often violate basic body proportions. We introduce a verifier-guided augmentation framework that uses global and mode-local PCA to generate inexpensive candidates, screens them using correspondence-derived skeletal proportions and body-part geometry, and retrains a diffusion model on accepted candidates. Elastic registration provides both the modal structure used by distributed PCA and the dense anatomical correspondence needed for scalable screening without per-candidate body-model fitting. A blinded human study supports the verifier as a conservative gatekeeper, favoring verifier-accepted over rejected outputs. We evaluate full-pool verifier acceptance separately from the coverage and departure of accepted samples and combine them through EAUC. On 4,498 registered DFAUST surfaces, distributed-PCA augmentation achieves 86.32% acceptance, the highest CP-AUC (0.871), and the highest EAUC (0.752), improving EAUC by 32% over real-only and self-augmented diffusion. These results show that mode-local, verifier-guided proposals broaden diffusion generation while maintaining high agreement with calibrated body measurements.

The LSJM R package provides a series of functions to estimate models based on location-scale linear mixed model and location-scale joint model theory. For longitudinal data, it includes the estimation of location-scale mixed models with subject-specific residual variance that can be time-dependent or distinguish within-visit and between-visits variability. When survival data is considered, implemented joint models handle competing risks as well as semi-competing risks possibly with interval-censored data through the use of a illness-death sub-model. They incorporate flexible dependence structure between the longitudinal marker and the times-to-events through the current value, the slope and/or the residual variability of the marker. Maximum likelihood estimators are obtained using the Marquardt-Levenberg algorithm with stringent convergence criteria. The package also provides several post-fit functions including goodness-of-fit analyses and individual dynamic predictions. Some examples on real data allows to illustrates the use of this package.

Motivated by a real-life problem, namely, inferring genomic regions affected by selection, we studied some properties of a two-step method that performs this task based on the FST. This approach exhibits computational simplicity as an appealing feature. Step one involves fitting a conjugate Bayesian model to find point estimates of FST and selecting the markers to be considered in step two, where they are grouped using such estimates. Subjective priors are frequently used in this problem and large hyperparameters may be encountered; hence, there is interest in addressing their impact. Preliminary analyses suggested that, the number of markers selected in step one tends to zero when the hyperparameters have the same value and tend to infinity, or are different but tend to infinity and their difference tends to zero. Thus, we studied how hyperparameters affect the posterior mean, variance, and predictive density of allele frequencies, and the posterior distribution of FST, formally. Moreover, an empirical approach based on simulated and real data was performed. Our main findings are summarized in two theorems that set the asymptotic behavior of the method, providing a foundation to understand the aforementioned phenomena. As to the empirical studies, the groups created in the second step, the estimated posterior means and the number of selected markers showed high sensitivity to hyperparameters. Albeit the mathematical intractability of the posterior distribution of FST, our results revealed asymptotic properties explaining two features of the method that lacked a formal elucidation.

The rapid build-out of hyperscale computing for artificial-intelligence workloads has made data-center noise a recurring source of community concern in the United States, yet calibrated, standards-grade acoustic data remain scarce. This narrative review synthesizes direct measurements, regulatory and legal records, investigative journalism, and relevant engineering literature to assess what is currently known and identify the measurements needed for credible health inference. Available sources report heterogeneous acoustic values at residences, property lines, and near-source positions, with individual readings from 39 to above 70 dB(A). Because location, metric, duration, instrumentation, and provenance differ, these values are not directly comparable community exposures, do not define a pooled distribution, and do not support an aggregate comparison with nighttime limits. Among cases with spectral detail, all but one reported continuous tonal noise associated with complaints, most often low-frequency content near 70-140 Hz, that A-weighted metrics alone may under-represent. Engineering evidence further suggests that cooling architecture may be a major determinant of facility sound emission; the cited 15-30 dB span is an equipment-level sound-power estimate, not a measured facility- or residential-receptor difference, and remains a hypothesis pending comparative field measurements. We propose a standards-based field-measurement and modeling protocol designed to generate frequency-resolved exposure data at named facilities. Such exposure characterization is a necessary foundation for credible assessment of community health effects and environmental justice implications.

We propose a data-driven framework for estimating the Bayesian Cramér-Rao bound (CRB) in high-dimensional imaging systems with complex, analytically intractable priors. Direct CRB computation is challenging in this setting due to the need to model the prior score and to form and invert the Bayesian Fisher information matrix in very high dimensions. To address these issues, we first reformulate the inverse problem in the latent space of a pre-trained variational autoencoder, thereby dramatically reducing the dimensionality of the bound estimation problem while preserving the spatial structure of the images. The Bayesian CRB is formed in this latent space and mapped back to the native parameter space using a change-of-variables formula. Second, to learn the latent prior score, we introduce a new sliced score matching objective defined in a Bochner space endowed with an $H^1(\Omega)$ Sobolev norm in space. This "Bochner-space sliced score matching" objective is consistent with standard sliced score matching, but penalizes errors in the spatial gradients of the score, suppressing high-frequency artifacts that otherwise contaminate the resulting CRB estimates. We validate the approach on a stylized quantitative photoacoustic computed tomography (qPACT) breast imaging problem with over one million unknown parameters, using a foundation-model autoencoder derived from Stable Diffusion. The proposed method yields stable, artifact-free Bayesian CRB estimates that reflect the highly non-Gaussian structure of the learned prior and reveal the substantial impact of the prior on the relative performance of competing qPACT design schemes.

Large language models (LLMs) are increasingly used as classifiers, yet they operate as opaque systems whose decisions are difficult to interpret, which complicates their use in regulated domains such as credit scoring or medical diagnosis. We propose an evolutionary framework that iteratively discovers natural language feature definitions (rubrics) for interpretable classification. An LLM generates candidate binary features, evaluates each sample against them, and the resulting vectors can be used to train a transparent classifier such as logistic regression. The feature set evolves over multiple iterations guided by classification errors, per-class activation rates, and feature ablation scores. We evaluate across three benchmarks, including a credit risk dataset representative of regulated domains, comparing single-shot LLM rubrics, evolved rubrics, and direct zero-shot LLM classification. Evolved features improve over single-shot rubrics by +2.9 pp on average and outperform zero-shot LLM classification on two of three tasks, while providing fully auditable decision logic. On the credit risk task, the zero-shot LLM performs at chance (50.7%) with a strong bias toward a single class, whereas evolved features achieve balanced, interpretable predictions. Crucially, this failure is invisible in aggregate accuracy and surfaces only under per-class auditing. Analysis reveals that evolution is most effective when label boundaries cannot be inferred from category names alone or when the LLM lacks reliable domain-specific reasoning.

Aggregated relational data replaces a fully observed network with a compressed version, where survey respondents are asked questions such as “How many of your friends belong to group $G$?”. We consequently only observe a matrix $R = OA$ of the adjacency matrix $A$ with a fixed design $O$. In this paper we understand the effects of this compression on community detection under degree-corrected stochastic block models. First, we give guarantees for when it is possible to recover the full network parameters, and then only just the communities under conditions on a diagonal corrected version of $\mathbb{E}[R]$, which can be used to inform experimental design. Secondly, we show that spectral clustering with single linkage exactly recovers communities when $n\rho_n\gtrsim K^2+K\log n$ when there are $K$ balanced communities under “uniformly spread” or near-orthogonal designs, and characterize more generally how the design influences rates of convergence. We also introduce second-order “friends-of-friends” queries and develop the corresponding theory.

Identifying patient subgroups with heterogeneous treatment effects is central to precision medicine, yet existing approaches face a tension. Black-box methods estimate individualized effects well but yield no interpretable subgroups, while tree-based methods produce explicit partitions but are unstable and less accurate in moderate-sample trials. We propose CausalSynthTree, a co-supervised method in which black-box causal estimators guide construction of an interpretable tree. It partitions the covariate space into cells, fits cell-wise conditional average treatment effect models from both observed data and synthetic data labeled by black-box causal teachers, and synthesizes them into a tree through a treatment-effect disparity criterion. Each leaf carries a sparse linear model, so the tree path defines a subgroup and the leaf model shows which covariates modify the effect. Honest inference for leaf-wise effects remains valid despite co-supervised augmentation and data-driven subgroup selection. In simulations it closes much of the gap between the two families. From moderate sample sizes onward it is more accurate than the black-box learners whenever the effect is linear or has a single threshold, and trails them only on a finer partition than the tree it grows. It controls spurious splits and attains nominal coverage throughout. In the ACTG175 HIV trial, where standard interaction tests detect no effect modification, the method reports no subgroups while the competing tree methods report several. In an adjuvant colon cancer trial it reports a borderline covariate in part of the resamples, together with a within-region age gradient that is consistent with an independent test.

Partially observed multivariate time series pose two coupled challenges: recovering missing measurements and forecasting future trajectories when observation patterns are informative. Existing methods often assume ignorable missingness or use the mask only as an auxiliary input. We propose LIFTS (Latent-driven Imputation and Forecasting for partly observed Time Series), a probabilistic framework in which a latent process jointly governs the complete measurement trajectory and observation mask, allowing observation patterns to inform latent-state inference for both forecasting and imputation. LIFTS combines flexible neural-network parameterizations with a forward-backward architecture: the forward pass performs filtering and autoregressive forecasting, while the backward pass performs smoothing and conditional multiple imputation. The model and inference components are trained jointly using a masked energy score and self-masking. We establish forward-backward distributional representations for the general framework and, for an explicit structural subclass, provide full-law identification and consistency guarantees. Simulations and an application to PhysioNet 2019 show that LIFTS provides accurate point predictions, improved distributional accuracy, and well-calibrated predictive intervals; it outperforms competing methods particularly when training data are limited and has substantially faster inference than the diffusion-based baseline.

This study develops a survey-calibrated, path-dependent agent-based microsimulation for evaluating crime and violence reduction policies in Bolivia. A synthetic population is constructed from the 2025 Household Survey and the fourth-quarter 2025 Continuous Employment Survey using official expansion weights and cross-survey donor matching. The model combines heterogeneous agents, place-based risk, criminal adaptation, institutional capacity, community organization, and multiple policy channels. Uncertainty is propagated through adaptive Gaussian-process and tree-ensemble emulators, global sensitivity analysis, tempered ensemble MCMC, and predictive meta-calibration. Simulated portfolios include focused policing, community control, Guardabosques-type incentives, social prevention, environmental interventions, justice reforms, investigation, rehabilitation, and financial-network disruption. Results are interpreted as structural policy scenarios rather than causal forecasts, with explicit attention to displacement, distributional effects, implementation capacity, and multi-objective trade-offs.

Probability-flow ordinary differential equations (PF-ODEs) are widely used as deterministic samplers for score-based diffusion models. Their usual justification is that the Fokker–Planck equation of a diffusion can be rewritten as a continuity equation driven by the score function of the forward diffusion. This identity does not, however, guarantee that the resulting velocity field generates a well-posed flow. We provide theoretical insights into the design of such deterministic samplers for generative models based on diffusions and reflected diffusions. We identify sufficient conditions for a regular Lagrangian PF-ODE flow to exist; reverse sampling and invertibility require two-sided divergence control. For learned scores, sampler stability is controlled by an unweighted velocity error, exposing a mismatch with density-weighted score matching and motivating architectural control of Jacobians, divergence, growth, and compression. Under the manifold hypothesis, positive-time regularization justifies an early-stopped PF-ODE while constants deteriorate near the data endpoint; an explicit sphere example shows that the exact deterministic flow becomes singular as the noise level vanishes even though the diffusion marginals remain well defined. These theoretical insights translate into concrete design principles for stable, invertible, and constraint-preserving diffusion samplers. We illustrate the practical relevance of these design principles using controlled numerical experiments.

Treatment efficacy is traditionally demonstrated on the basis of a single primary outcome. However, clinical decision-making usually requires consideration of multiple outcomes, balancing expected benefits against potential risks. The relative value assigned to these outcomes varies substantially from one patient to another. Given a preference rule over outcome profiles, treatment effects and optimal policies can be defined and estimated. Such a rule is rarely available in practice: it must itself be estimated from pairwise comparisons of outcome profiles, which are costly to collect from clinical experts. We propose an active learning framework that selects which comparisons to query. Standard criteria maximize the information gained on the preference rule itself. We instead target the quantities of interest, and select the query that most reduces uncertainty on the treatment effect and on the optimal policy induced by the learned rule. Under a Gaussian process model of the preference rule, we derive a closed-form approximation of this criterion. On semi-synthetic data built from a Parkinson's disease cohort with 13 clinical outcomes, our criterion achieves lower treatment effect estimation error and lower policy regret than existing criteria at equal query budget.

Whether a mortality model needs a Makeham term, the constant representing background mortality, is commonly decided with a likelihood-ratio test. The constant cannot be negative, so testing its absence places it on a boundary, where the usual chi-squared calibration fails. Assuming independent Poisson death counts and standard regularity conditions, we show that when the constant is the only parameter on a boundary the statistic converges to an equal mixture of a point mass at zero and a chi-squared distribution with one degree of freedom: at the 5% level the critical value is 2.71, not 3.84. We state conditions under which the correction holds for Makeham models, verify them for Gompertz–Makeham and gamma-Gompertz–Makeham, and quantify the information about the constant, which fixes the local power, the smallest detectable term, and the loss of detectability as the age window narrows. When a gamma-frailty variance is estimated at a true value of zero, the limit is no longer a chi-squared mixture and the correction rejects too often. Monte Carlo experiments show the conventional cutoff rejecting at half the nominal level, a correctly calibrated test missing a term at its detection threshold in most samples, and excess rejections persisting as exposure grows.

The dynamics of cells, organisms, and fluids are often modeled as probability distributions evolving over time. Reconstructing and extrapolating this evolution from unpaired snapshots requires assumptions about the underlying process. Wasserstein gradient flows are a common choice, but they cannot describe conservative or periodic dynamics. Lagrangian mechanics in Wasserstein space covers both, but existing methods for learning it are simulation-based: they run a numerical solver at every training step, which makes training expensive. We propose Double-Stitch, a simulation-free method that learns these mechanics by penalizing the residual of the equation of motion along a learned population path. We derive this equation from a Clebsch variational principle that does not require gradient velocities, and show that the residual vanishes exactly when the equation holds. We test Double-Stitch on synthetic, single-cell and ocean vortex datasets and find that it matches or outperforms gradient-flow methods and simulation-based WLM on most tasks, while training $4$-$14$ times faster than WLM. We provide a JAX implementation of Double-Stitch at https://github.com/BasisResearch/stitching.

Policy-gradient methods are central to modern reinforcement learning, including LLM post-training. When they struggle, the usual suspects are exploration, credit assignment and action-sampling noise. Classification has none of them. A classifier is a policy whose expected reward, its expected accuracy, is the probability it assigns to the correct label, and because that label is known, the policy gradient is exact and smooth. Yet exact policy gradient loses to cross-entropy, even on expected accuracy. The exact gradient is myopic: it values an update only by what it buys now, but each update also sets where the next one starts, so an update's value depends on how much learning remains. Viewed this way, cross-entropy is patient accuracy, the total error an example would pay if its log-odds rose at unit speed forever, while exact policy gradient is the zero-horizon limit. Truncating this total at the learning that remains yields the horizon loss, a one-line change that moves from cross-entropy toward exact policy gradient as training runs out. In a simple allocation model, it provably escapes the trap that catches each endpoint. On MNIST and on ImageNet with ResNet-50, ResNet-101 and ViT-S/16, the horizon loss improves top-1 accuracy over cross-entropy at a flat learning rate, and the gain grows with label noise.

We develop a Bayesian framework for learning nonlinear operators between infinite-dimensional spaces. Given a map $g_0:\mathcal{X}\to\mathcal{Y}$ between separable Hilbert spaces, we study the recovery of $g_0$ from $n\in\mathbb{N}$ noisy input-output pairs $(\boldsymbol{X},\boldsymbol{Z})=(X_i,Z_i)_{i=1}^n$ with $Z_i= g_0 (X_i ) + E_i$. Here the $X_i\in\mathcal{X}$ are randomly drawn 'design' points in a compact subset of $\mathcal X$, and the $E_i$ are assumed to be i.i.d. draws from a Gaussian white noise process indexed by $\mathcal{Y}$. For any 'operator-valued' prior $\mathbb{P}_G$ supported on the space of continuous operators, we show existence of the posterior $\mathbb P_{G|(\boldsymbol{X},\boldsymbol{Z})}$ as a regular conditional distribution, and provide a characterization of its Radon-Nikodym derivative. For Gaussian priors, we establish algebraic (in the sample size $n$) convergence rates for the posterior mean towards the ground truth; this corresponds to a ridge regularized kernel estimator. Moreover, we show that the posterior mean is minimax optimal (up to logarithmic factors) over hyperrectangles when the smoothness of the prior matches that of the ground truth. To illustrate the applicability of our analysis, we derive explicit learning rates for the Darcy flow solution operator.

Many machine learning methods aim to approximate the lower-dimensional manifold on which the data lives. A desirable feature of such methods is that they should capture the epistemic uncertainty of this learned manifold. One model that achieves this is the Gaussian Process Latent Variable Model, in which a Gaussian Process (GP) mapping from the latent space provides an estimate of the uncertainty of the manifold. However, the effectiveness of this uncertainty estimation is limited by the mean-field variational approximation between the GP inducing points and the latent variables. In this work, we apply Amortized Structured Stochastic Variational Inference to allow the variational posterior for the latent space to be conditionally dependent on the value of the inducing points. We demonstrate that this more flexible variational posterior improves several metrics relating to the reconstruction of points on the data manifold.

Stationarity rewards memory, but after a change the same history can mislead. We ask when forgetting should be permitted. E-process-authorized Thompson sampling (e-ATS) gives each arm full-history and discounted Beta states. An anytime-valid e-process first authorizes the discounted state, then a reversible relevance score controls its influence. Before authorization, e-ATS exactly follows optimistic Thompson sampling (OTS). Under a Beta-Bernoulli prior-predictive stationary model, e-ATS's probability of ever departing from OTS is at most the chosen $\alpha_E$, without fitted thresholds. Relative to e-ATS, removing authorization increased mean normalized dynamic pseudo-regret by $38.4\%$ on the registered suite but reduced it by $7.5\%$ on the literature-derived replay suite. Therefore, evidence controls when adaptation begins, not whether it always helps.

Neural network loss landscapes have many symmetries, which are preserved by gradient flow but broken by finite-stepsize stochastic gradient descent (SGD). A canonical example of such a symmetry is scale in homogeneous networks: one can scale up the parameters in one layer and down in the next without changing the network output. Previous work has documented cases in which SGD breaks this symmetry in favor of balancing gradient noise or minimizing fluctuations. Here, we show that the solution geometry of undercomplete linear autoencoders instead selects a preferred sign for scale drift: on the PCA solution manifold, SGD favors large decoder weights. This directed scale drift occurs on a slow timescale, and its dynamics admit an analytically-tractable effective description. However, it cannot continue indefinitely: increasing scale eventually drives the dynamics towards a finite-stepsize stability boundary. The resulting solutions are sharper than a balanced baseline in the sense of the maximum eigenvalue of the loss Hessian, but different sharpness measures can move in opposing directions. Thus, undercomplete autoencoders give a concrete illustration of how loss geometry can convert residual gradient noise into directed motion along a manifold of functionally-equivalent solutions.

Deep tabular generative models are benchmarked on datasets with tens of thousands of rows; clinical datasets have hundreds. We preregistered and ran a size-ladder benchmark to find where the two regimes diverge: 8 public datasets subsampled from 200 to 20,000 training rows, seven generators (independent marginals, Gaussian copula, SMOTE, unconditional SMOTE, CTGAN, TVAE, TabDDPM) with a fixed 20-trial tuning budget and 5 evaluation seeds, plus 4 natively small clinical datasets at true size, for 2,220 committed runs in total. The primary metric is the AUROC of fixed classifiers trained on synthetic and tested on real data. In 23 of 24 (dataset, deep model) pairs no deep model ever beats the best trivial baseline by more than seed noise, at any training size we measured. The best baseline wins 40 of 49 (dataset, size) cells. Our preregistered prediction that the deep models' ranking would be unstable at small sizes is falsified: mean Kendall tau between adjacent rungs below 5,000 rows is 0.806, above our 0.8 threshold, and stability is highest at the smallest sizes rather than lowest. One caveat bounds all of this: in 81% of cells the gap between the top two methods is smaller than the variation between seeds. Finally, method rankings on natively small clinical datasets agree only moderately with rankings on subsampled large ones (mean tau 0.57 to 0.64), which questions whether a subsampled large dataset can stand in for a small one. All 2,220 result files, the preregistration and its hash, and the code that regenerates every figure and number from those files are public.

We introduce AREX, a training-free sampler for pretrained flow matching models that uses the target mean and covariance to capture an analytically tractable part of the sampling dynamics. We show that the velocity field of the moment-matched Gaussian target is the $L^2$-optimal affine approximation to the marginal velocity field. This motivates decomposition of the learned dynamics into an affine component over the whole sampling path, determined by the first two target moments, and a neural residual term. AREX keeps the affine component and integrates it using an explicit matrix-valued propagator. In turn, we only require to integrate over the residual term. This differs from scalar exponential integrators, which analytically handle only isotropic linear dynamics. Across image and text-to-image generation tasks, AREX consistently improves sample fidelity in the few-step sampling regime without retraining the underlying model.

The analysis of large data panels is important in econometrics and beyond. Prediction and inference methods for such data typically rely on simplifying model assumptions for the covariance structure of errors. One convenient assumption is what we call groupwise sphericity: that errors are uncorrelated across individuals and have constant variance within certain groups. While theoretically useful, in large panels groupwise sphericity is often too restrictive to apply in practice. We therefore develop new quantitative inference tools to test whether deviations from this model assumption are practically relevant. Our approach covers both large-dimensional data matrices and regression panels, in a regime where the cross-sectional dimension is proportional to the sample size. The theory is based on the analysis of extreme eigenvalues of the empirical covariance matrix and uses recent advances in random matrix theory. Numerical experiments demonstrate accurate size control and good power in finite samples.

K-fold cross-validation (CV) is widely used as evidence of out-of-sample performance, although folds are neither independent experiments nor equally informative under heterogeneous data. Cross Upper-Bound Validation (CUBV) replaces point-wise CV accuracy by conservative upper bounds on true risk. Here we generalise CUBV through a single exponential framework in which the moment-generating function of the generalisation gap is controlled by a cumulant envelope gamma(lambda). This yields a family of risk bounds covering Hoeffding-, Bernstein-, dependency-aware, PAC-Bayesian, and heterogeneous source-fusion settings. For K-fold CV, dependence between fold-wise gaps is modelled through a joint sub-Gaussian proxy matrix. Under equicorrelation, this gives an effective number of folds, Keff = K/[1+(K-1)rho], showing that increasing K does not necessarily increase statistical evidence when folds are strongly dependent. The framework is also extended to posterior distributions over predictors and weighted multi-source fusion, where weights are selected by minimising an upper bound on future risk rather than empirical error alone. Experiments with trained linear classifiers on heterogeneous multimodal Gaussian mixtures compare K-fold CV with full-sample resubstitution plus risk correction. Bounds are evaluated by coverage and tightness. In low-dimensional small-sample settings, K-fold partitioning can increase uncertainty because individual folds under-represent minority modes, while corrected resubstitution can remain valid and tighter; this effect disappears as sample size increases. Overall, gamma-CUBV separates observed performance, uncertainty, dependence, model complexity, and confidence into explicit terms, providing a unified route from CV scores to risk statements and a principled validation criterion for heterogeneous small-sample applications such as neuroimaging.

Consistency models (CMs) have become a leading approach for generating high-quality samples in few steps. However, adding steps can improve or degrade sample quality in ways that are highly sensitive to the schedule and that existing theory does not fully explain. To provide accuracy guarantees and guide CM sampler design, we analyze multistep CM sampling as a composition of noising and approximate denoising operators. Under explicit, verifiable stability assumptions, we derive a non-asymptotic error bound that separates contraction of the initialization error from accumulation of approximation error. The bound assigns distinct roles to the schedule: large early noise levels drive contraction, while small late noise levels control the residual bias. As a corollary, we obtain explicit constants for strongly log-concave and semi-log-concave targets. We further establish a complementary guarantee whose assumptions, one-step accuracy and stability, can be estimated for a given trained model. Experiments show that the contraction and approximation profiles entering our bounds can be reliably measured and closely match the predicted functional forms. Together, these results provide a meaningful convergence theory for multi-step CMs and a practical route to sampler design.

Flow- and diffusion-based generative models have recently emerged as flexible and highly efficient forecasting models for dynamical systems. When combined with inference-time guidance, they offer a promising route to high-dimensional non-Gaussian data assimilation (DA), the problem of combining forecasts with observations to estimate latent system states. Existing filters, however, condition on a fixed history and assimilate only the most recent observation, leaving them unable to revise past states when new observations arrive. Estimates then stay tethered to a history that later observations may contradict, and errors accumulate over the assimilation run. To this end, we introduce **DAWIS**, a unified DA method covering filtering, fixed-lag smoothing, and block smoothing within a single framework. DAWIS replaces the single flow time of a state-level prior with a multitask stochastic interpolant over a window of consecutive states, assigning a separate flow time to each. An assimilation cycle inverts the window to a vector of per-state turning points and regenerates it under observation guidance, with the turning points controlling how strongly each state is held fixed, revised, or generated from scratch. The same construction can also absorb the forecast into the assimilation cycle, removing the need for a separate forecasting model. Experiments on challenging nonlinear systems show that DAWIS improves on both filtering and smoothing baselines under sparse, noisy, and nonlinear observations. The code for DAWIS is available at https://github.com/Erik-Wikingsson/DAWIS

Existing machine learning weather forecasting models typically generate forecasts through autoregressive rollouts at a fixed temporal resolution. While highly efficient for long-range prediction, this formulation can suffer from severe error accumulation when used with shorter time steps and does not explicitly encode the locality and temporal continuity of atmospheric dynamics. To address these limitations, we introduce **SDECast**, a Neural Stochastic Differential Equation (SDE) framework for continuous-time probabilistic weather forecasting. SDECast extends SDE Matching to learn stochastic dynamics directly in physical space, without requiring repeated SDE simulation during training. On a simulated geophysical flow, we show that SDECast recovers meaningful drift dynamics and faithfully reproduces the underlying continuous-time behavior. We then demonstrate its scalability to global weather forecasting at hourly resolution, where SDECast produces skillful probabilistic forecasts for lead times of up to five days.