Open time-series forecasting (TSF) benchmarks cover retail, energy, weather, and traffic, but supply-chain logistics remains underserved. We introduce ISOMORPH, the first public digital twin of a multi-echelon logistics network with fully interpretable, user-configurable parameters and modular topology, demand process, and control rules. The simulator advances a directed routing graph in discrete time: demand arrives at the destination, is served from stock or recorded as backlog, and triggers replenishment through the network. The state vector tracks per-node on-hand inventory with outstanding orders, in-transit shipments, and a smoothed demand estimate, so the dynamics close as a Markov chain on a tractable state space whose transition kernel acts linearly on the empirical distribution of the state. The released data reproduces the bullwhip effect at empirically consistent magnitudes, and three conservation laws encoded in the Markov chain serve as verification tools when users extend the simulator. We release datasets at two catalogue scales ($C=50$ and $C=200$) with six scenario sweeps producing 30 additional rollouts and 20 Latin-hypercube perturbations, exhibiting dynamics absent from fixed TSF benchmarks: variance amplification, cascading bottlenecks, regime shifts, and cross-channel coupling through shared macro shocks. Zero-shot evaluation of four foundation models (Chronos, Moirai, TimesFM, Lag-Llama) shows MASE values exceeding public GIFT-Eval references at low-to-moderate horizons, supporting incorporation into existing benchmarks. The same pairing produces forecast confidence bands via Latin-hypercube perturbation of demand-side knobs, forward UQ from parameter uncertainty unavailable on standard TSF datasets, demonstrating that foundation models can serve as fast surrogates for the digital twin's forward UQ. Code (MIT): https://github.com/tuhinsahai/ISOMORPH.

Calibrated probability outputs of trained classifiers are increasingly used as inputs to downstream regression estimands such as effects, prevalences, or disparities for a latent group observed only on a small labelled subset. A standard practice is to threshold the calibrated score at a confidence cutoff and treat the hard label as the truth. Building on a recent identification result for the underlying moment equation, we develop a calibration-aware diagnostic apparatus for pseudo-labelling pipelines. We derive a closed-form expression for the attenuation bias that confidence thresholding induces in the downstream regression coefficient, and show that the bias can be predicted, before any inference is run, from the residual score variance $V^{*}=\mathbb{E}[\operatorname{Var}(p\mid X)]$ on the unlabelled set after partialling out the downstream controls $X$. We further obtain a sharp sensitivity bound under bounded calibration drift, and identify the boundary $V^{*}=0$, which holds iff $p$ is a deterministic function of $X$; this motivates a structural separation between classifier features $W$ and downstream controls $X\subsetneq W$. Five controlled simulations and a UCI Adult illustration trace the predictions. The contribution is operational: a $(V^{*}, κ)$ decision rule that practitioners can compute from any classifier output to decide whether confidence thresholding is safe.

Single-arm trials are an important study design for evaluating drug efficacy and safety without enrolling patients into a control arm. Although they do not provide the gold-standard evidence of randomized controlled trials, they are increasingly used in clinical development as they offer an efficient, ethical, and practical alternative. A wide variety of approaches can be used to construct control comparators and estimate treatment effects, from fixed comparators informed by clinical knowledge to data-based and model-based patient-level comparators, also known as synthetic controls. Powerful and flexible machine learning models can allow outcome-model-based synthetic controls to overcome key limitations of direct data-based approaches, yield more robust estimates of treatment effects, and provide a principled way to incorporate corrections or encode additional assumptions when external data are not directly comparable. In this work, we argue that outcome-model-based synthetic control arms are an important tool for single-arm trials. We focus on digital twins, personalized predictions of disease progression generated from machine learning models trained on historical datasets, which naturally leverage these flexible approaches. We review doubly robust estimators, present power and sample size formulas, and discuss trade-offs in selecting historical data for training and analysis. We also outline practical considerations for deploying digital twins within the framework of recent FDA draft guidance on the use of artificial intelligence in drug development. Finally, we reanalyze data from trials in amyotrophic lateral sclerosis and Huntington's disease to demonstrate the proposed methods.

Experimental design has emerged as a powerful approach for improving the sample efficiency of A/B testing, yet existing designs rely critically on correctly specified models. We study robust sequential experimental design under model misspecification and develop a unified framework that covers both contextual bandit and dynamic settings. Theoretically, we prove that our design bounds the worst-case mean squared error of the estimated treatment effect. Empirically, we demonstrate the effectiveness of the proposed approach using synthetic and real-world datasets from a leading technology company.

Weak-to-strong (W2S) generalization, in which a strong model is fine-tuned on outputs of a weaker, task-specialized model, has been proposed as an approach to aligning superhuman AI systems. Existing theoretical analyses either fix the student's representations or operate in restricted settings. Whether multi-step SGD can succeed in feature learning while preserving diverse pre-trained capabilities remains open. We study W2S in the setting of reward-model learning with two-layer neural networks. The strong model has pre-trained representations organized into low-dimensional subspaces $V_k$, and is fine-tuned under the supervision of a weak model specialized on task $κ$. We prove that the strong model efficiently learns task $κ$, eliciting its pre-trained knowledge while retaining general capabilities. This establishes W2S generalization in the feature-learning regime, in the sense that the strong model acquires the target feature direction through W2S training, rather than having it given a priori. Moreover, W2S preserves pre-trained off-target features, whereas standard supervised fine-tuning causes catastrophic forgetting when off-target feature directions are correlated with the target's. Numerical experiments on synthetic data confirm our theoretical results.

LLM-enabled AI workflows increasingly produce outputs through iterative generate-evaluate-revise loops. Each iteration can improve the candidate, but it also creates a release decision: when to stop and output the current result? This raises a statistical challenge because deployment-time evaluator scores are adaptively generated and repeatedly monitored, yet the likelihood models or exchangeability assumptions typically used for calibration are unavailable. We propose an always-valid release wrapper for existing generator-evaluator pipelines. The wrapper builds a hard-negative reference pool of high-scoring failures, calibrates deployment-time evaluator scores against this pool, and accumulates the resulting evidence with an e-process. This separates two roles: the reference pool turns black-box scores into conservative evidence, while the e-process provides validity under optional stopping. In theory, we show that a conservative reference pool yields finite-sample control of the probability of releasing on infeasible tasks, that is, tasks for which the given workflow is not capable of producing a reliable solution. We also characterize conditions under which the same conservative rule still achieves nontrivial release on feasible tasks. In an MBPP+ coding-agent case study, the wrapper reduces premature incorrect release relative to baseline stopping rules while still releasing on tasks for which the workflow repeatedly accumulates moderate supporting evidence.

We propose Coreset-Induced Conditional Velocity Flow Matching (CCVFM), a generative model that augments hierarchical rectified flow with a data-informed source distribution. Hierarchical flow matching models the full conditional velocity law in velocity space, but its inner flow is asked to transport isotropic Gaussian noise to a multimodal target velocity distribution from scratch. Our key observation is that this inner source can be replaced by a closed-form surrogate built from a coreset of the target. CCVFM first compresses the target into weighted atoms using an entropic Sinkhorn coreset and lifts them to a Gaussian mixture. The induced conditional velocity law is then a closed-form Gaussian mixture that can be sampled without a learned neural sampler. A lightweight correction flow, trained from this exact surrogate source, then refines the remaining surrogate-to-target residual rather than learning an entire noise-to-data map. We prove that the surrogate transport cost equals the target--surrogate Wasserstein gap under an explicit compression assumption, whereas the noise-source analogue has a dimension-scale lower bound. We further characterize the conditional second moment of the direct surrogate-source training target and show that its source-dependent excess is small when the surrogate conditional law is close to the true conditional velocity law in mean and covariance. Empirically, on MNIST, CIFAR-10, ImageNet-32, and CelebA-HQ, the proposed method reaches competitive few-step generation under matched architectures.

Estimating the covariance of asset returns, i.e., the risk model, is a key component of financial portfolio construction and evaluation. Most risk modeling approaches produce a factor model that decomposes the asset variability into two components: the first attributed to a small number of factors that are common among the assets and the second attributed to the idiosyncratic behavior of each asset. Third-party providers typically provide risk models to investors, and while these models are typically of high quality, they may fail to capture important information, e.g., changing market regimes and transient factors. To overcome these limitations, we propose a systematic method based on maximum likelihood estimation to enhance an existing factor model by both refining the given model and adding new statistical factors. Our approach relies only on the observed sequence of realized returns and on the choice of two hyperparameters: the number of additional factors and the half-life parameter that determines the weights assigned to returns in the log-likelihood objective. Importantly, our methodology applies to the situation where asset returns may be missing, making it suitable for typical equity datasets. We demonstrate our approach on the Barra short-term US risk model, a high-quality risk model used in practice, for a universe of US high-capitalization equities. We show that the proposed extension captures structure in the returns that is missed by the original model.

Density estimation in high-dimensional settings is an important and challenging statistical problem.Traditional methods based on kernel smoothing are inefficient in high dimensions due to the difficulties in specifying appropriate location-adaptive kernels. In this work, we introduce pre-training, a key idea behind many cutting-edge AI technologies, to the context of non-parametric density estimation. By establishing a pre-trained neural network that can recommend an appropriate location-adaptive kernel for each sample point, efficient density estimation with adaptive kernels is achieved in high dimensions. A wide range of numerical experiments show that this strategy is highly effective for improving density-estimation accuracy, when the target distribution is close to the distribution family for pre-training. When the target distribution is substantially different from the pre-training distribution family, the benefit from the proposed pre-training strategy may be diluted, but can be reactivated by an additional fine-tuning procedure.

Determinantal point processes (DPPs) have emerged as a kernelized alternative to vanilla independent sampling for generating efficient minibatches, coresets and other parsimonious representations of large-scale datasets. While theoretical foundations and promising empirical performance have been demonstrated, there are two challenges for current proposals for DPP-based coresets or minibatches. The first is the need for families of DPPs with certain key variance reduction properties, usually constructed in a continuous setting, of which there are few known examples. The second is the need for an ad-hoc construction of a discrete DPP defined on a given dataset, that inherits such variance reduction. In this work, we contribute to the programme of establishing DPPs as a subsampling toolbox for ML by advancing on these two fronts. First, we propose new DPPs on the Euclidean space based on wavelets, with provably better accuracy guarantees than the best known rates. Second, we introduce a general method to convert such continuous DPPs, which are more amenable to proving analytical statements, into discrete kernels, which are pertinent for subsampling tasks such as minibatch and coreset constructions. This conversion mechanism simultaneously preserves the desired variance decay and reveals a low-rank decomposition of the discrete kernel, which makes sampling the corresponding DPP computationally inexpensive. En route, we enlarge the class of ML tasks amenable to improvements via DPP-based minibatches and coresets to include objective functions with arbitrarily low regularity, and rate guarantees that explicitly adapt to this regularity.