Papers

We consider a process $X^\ve$ solution of a stochastic Volterra equation with an unknown parameter $\theta^\star$ in the drift function. The Volterra kernel is singular near zero, exhibiting a behavior comparable to $K\_0(u)=cu^{\alpha-1} \id{u>0}$ with $\alpha \in (1/2,1)$.It is assumed that the diffusion coefficient is proportional to $\ve \to 0$. Based on discrete observations, with a mesh size $h\to0$, of the Volterra process, we construct a Quasi Maximum Likelihood Estimator. The main step is to assess the error arising in the reconstruction of the path of a semimartingale from the inversion of the Volterra kernel. We show that this error decreases as $h^{1/2}$ regardless of the value of $\alpha$. Then, we can introduce an explicit contrast function, which yields an efficient estimator when $\ve \to 0$.

Collapsibility provides a principled approach for dimension reduction in contingency tables and graphical models. Madigan and Mosurski (1990) pioneered the study of minimal collapsible sets in decomposable models, but existing algorithms for general graphs remain computationally demanding. We show that a model is collapsible onto a target set precisely when that set contains at least one minimal separator between its non-adjacent vertices. This insight motivates the Close Minimal Separator Absorption (CMSA) algorithm, which constructs minimal collapsible sets using only local separator searches at very low costs. Simulations confirm substantial efficiency gains, making collapsibility analysis practical in high-dimensional settings.

Estimating posteriors and the associated model evidences, with desired accuracy and affordable computational cost, is a core issue of Bayesian model updating, and can be of great challenge given expensive-to-evaluate models and posteriors with complex features such as multi-modalities of unequal importance, nonlinear dependencies and high sharpness. Bayesian Quadrature (BQ) equipped with active learning has emerged as a competitive framework for tackling this challenge, as it provides flexible balance between computational cost and accuracy. The performance of a BQ scheme is fundamentally dictated by the acquisition function as it exclusively governs the active generation of integration points. After reexamining one of the most advanced acquisition function from a prospective inference perspective and reformulating the quadrature rules for prediction, four new acquisition functions, inspired by distinct intuitions on expected rewards, are primarily developed, all of which are accompanied by elegant interpretations and highly efficient numerical estimators. Mathematically, these four acquisition functions measure, respectively, the prediction uncertainty of posterior, the contribution to prediction uncertainty of evidence, as well as the expected reduction of prediction uncertainties concerning posterior and evidence, and thus provide flexibility for highly effective design of integration points. These acquisition functions are further extended to the transitional BQ scheme, along with several specific refinements, to tackle the above-mentioned challenges with high efficiency and robustness. Effectiveness of the developments is ultimately demonstrated with extensive benchmark studies and application to an engineering example.

Stepped wedge designs (SWDs) are increasingly used to evaluate longitudinal cluster-level interventions but pose substantial challenges for valid inference. Because crossover times are randomized, intervention effects are intrinsically confounded with secular time trends, while heterogeneity across clusters, complex correlation structures, baseline covariate imbalances, and small numbers of clusters further complicate inference. We propose a unified semiparametric framework for estimating possibly time-varying intervention effects in SWDs. Under a semiparametric model on treatment contrast, we develop a nonstandard semiparametric efficiency theory that accommodates correlated observations within clusters, varying cluster-period sizes, and weakly dependent treatment assignments. The resulting estimator is consistent and asymptotically normal even under misspecified covariance structure and control cluster-period means, and is efficient when both are correctly specified. To enable inference with few clusters, we exploit the permutation structure of treatment assignment to propose a standard error estimator that reflects finite-sample variability, with a leave-one-out correction to reduce plug-in bias. The framework also allows incorporation of effect modification and adjustment for imbalanced precision variables through design-based adjustment or double adjustment that additionally incorporates an outcome-based component. Simulations and application to a public health trial demonstrate the robustness and efficiency of the proposed method relative to standard approaches.

We study generative modeling on convex domains using flow matching and mirror maps, and identify two fundamental challenges. First, standard log-barrier mirror maps induce heavy-tailed dual distributions, leading to ill-posed dynamics. Second, coupling with Gaussian priors performs poorly when matching heavy-tailed targets. To address these issues, we propose Mirror Flow Matching based on a regularized mirror map that controls dual tail behavior and guarantees finite moments, together with coupling to a Student-$t$ prior that aligns with heavy-tailed targets and stabilizes training. We provide theoretical guarantees, including spatial Lipschitzness and temporal regularity of the velocity field, Wasserstein convergence rates for flow matching with Student-$t$ priors and primal-space guarantees for constrained generation, under $\varepsilon$-accurate learned velocity fields. Empirically, our method outperforms baselines in synthetic convex-domain simulations and achieves competitive sample quality on real-world constrained generative tasks.

The representer theorem is a cornerstone of kernel methods, which aim to estimate latent functions in reproducing kernel Hilbert spaces (RKHSs) in a nonparametric manner. Its significance lies in converting inherently infinite-dimensional optimization problems into finite-dimensional ones over dual coefficients, thereby enabling practical and computationally tractable algorithms. In this paper, we address the problem of estimating the latent triggering kernels–functions that encode the interaction structure between events–for linear multivariate Hawkes processes based on observed event sequences within an RKHS framework. We show that, under the principle of penalized least squares minimization, a novel form of representer theorem emerges: a family of transformed kernels can be defined via a system of simultaneous integral equations, and the optimal estimator of each triggering kernel is expressed as a linear combination of these transformed kernels evaluated at the data points. Remarkably, the dual coefficients are all analytically fixed to unity, obviating the need to solve a costly optimization problem to obtain the dual coefficients. This leads to a highly efficient estimator capable of handling large-scale data more effectively than conventional nonparametric approaches. Empirical evaluations on synthetic datasets reveal that the proposed method attains competitive predictive accuracy while substantially improving computational efficiency over existing state-of-the-art kernel method-based estimators.

The stochastic multi-armed bandit (MAB) problem is one of the most fundamental models in sequential decision-making, with the core challenge being the trade-off between exploration and exploitation. Although algorithms such as Upper Confidence Bound (UCB) and Thompson Sampling, along with their regret theories, are well-established, existing analyses primarily operate from a time-domain and cumulative regret perspective, struggling to characterize the dynamic nature of the learning process. This paper proposes a novel frequency-domain analysis framework, reformulating the bandit process as a signal processing problem. Within this framework, the reward estimate of each arm is viewed as a spectral component, with its uncertainty corresponding to the component's frequency, and the bandit algorithm is interpreted as an adaptive filter. We construct a formal Frequency-Domain Bandit Model and prove the main theorem: the confidence bound term in the UCB algorithm is equivalent in the frequency domain to a time-varying gain applied to uncertain spectral components, a gain inversely proportional to the square root of the visit count. Based on this, we further derive finite-time dynamic bounds concerning the exploration rate decay. This theory not only provides a novel and intuitive physical interpretation for classical algorithms but also lays a rigorous theoretical foundation for designing next-generation algorithms with adaptive parameter adjustment.

Training set sampling methods are used to improve model performance and lower data costs in machine learning problems relevant to chemistry. We introduce Gradient Guided Furthest Point Sampling (GGFPS), a simple extension of Furthest Point Sampling (FPS) that leverages molecular force norms to guide efficient sampling of configurational spaces of molecules. Numerical evidence is presented for a toy system (the Styblinski-Tang function) as well as for molecular dynamics trajectories from the MD17 dataset. Our numerical results indicate superior data efficiency and model robustness when using GGFPS compared to FPS and uniform random sampling (URS), as well as established supervised FPS-style selectors, PCov-FPS and PCov-CUR. Distribution analysis of the MD17 data suggests that FPS systematically under-samples equilibrium geometries, resulting in large test errors for relaxed structures. GGFPS cures this artifact and (i) enables up to twofold reductions in training cost without sacrificing predictive accuracy compared to FPS in the 2-dimensional Styblinski-Tang system, (ii) systematically lowers prediction errors for equilibrium as well as strained structures in MD17, and (iii) systematically decreases prediction error variances across all of the MD17 configuration spaces. These results suggest that gradient-aware sampling methods hold great promise as effective training set selection tools, and that naive use of FPS may result in imbalanced training and inconsistent prediction outcomes.

Many countries measure poverty based only on income or consumption. However, there is a growing awareness of measuring poverty through multiple dimensions that captures a more reasonable status of poverty. Estimating poverty measure(s) for small geographical areas, commonly referred to as poverty mapping, is challenging due to small or no sample for the small areas. While there is a huge literature available on unidimensional poverty mapping, only a limited effort has been made to address special challenges that arise only in the multidimensional poverty mapping. For example, in multidimensional poverty mapping, a new problem arises involving estimation of relative contributions of different dimensions to overall poverty for small areas. This problem has been grossly ignored in the small area estimation (SAE) literature. We address this issue using a multivariate hierarchical model implemented via a Bayesian method. Moreover, we demonstrate how a multidimensional poverty composite measure can be estimated for small areas. In this paper, we demonstrate our proposed methodology using a survey data specially designed by one of us for multidimensional poverty mapping. This paper adds a new direction to poverty mapping literature.

Weather extremes produce major impacts on society and ecosystems and are likely to change in likelihood and magnitude with climate change. However, very low probability events are hard to characterize statistically using observations or even climate model output because of short records/runs. For precipitation, consideration of such events arises in quantifying Probable Maximum Precipitation (PMP), namely estimating extreme precipitation magnitudes for designing and assessing critical infrastructure. A recent National Academies report on modernizing PMP estimation proposed using very large climate model-based ensembles to estimate extreme quantiles, possibly through machine learning-based ensemble boosting. Here we assess statistical aspects of such an approach for the contiguous United States using a huge ensemble (10560 years) produced by a state-of-the-art emulator (ACE2) trained on ERA5 reanalysis. The results indicate that one can practically estimate very extreme precipitation and temperature quantiles, provided one uses appropriate statistical extreme value techniques. More specifically, the results provide evidence for (1) the use of threshold-exceedance methods with a sufficiently high threshold (necessary for precipitation) for reliable estimation, (2) the robustness of results to variation in extremes by season and storm type, and (3) the sufficiency of the ensemble for well-constrained statistical uncertainty. Our results also show that the emulator produces extremes outside the range of the ERA5 training data. While encouraging for emulators' potential use for quantifying the climatology of extremes, more investigation is needed to assess whether emulators are fit for this purpose. Our focus is on how to use huge ensembles to estimate very extreme statistics; we expect the results to be relevant for future improved emulators.

Based on the multidimensional Leibniz integral rule, we propose a novel unbiased stochastic derivative estimation framework for sample performance functions that are discontinuous in the parameter of interest. In this framework, for general discontinuities, a change of variables followed by the Leibniz integral rule generally yields a multi-run estimator, whereas for indicator-type discontinuities, a suitable transformation of the sample performance leads directly to a single-run estimator. The new framework includes existing likelihood ratio (LR)-based approaches as special cases and applies more broadly. In particular, it encompasses generalized LR (GLR) methods and the new formulation permits us to obtain much milder and simpler sufficient regularity conditions for these estimators to be unbiased, compared with the conditions given in previous papers. We also provide guidance on how to construct efficient single-run estimators in settings where existing methods may require the simulation of multiple sample paths or may be inapplicable. We validate the effectiveness and robustness of the proposed framework through an inventory-price control problem.

Stochastic resonance (SR), a phenomenon originally introduced in climate modeling, enhances signal detection by leveraging optimal noise levels within non-linear systems. Traditional SR techniques, mainly based on single-threshold detectors, are limited to signals whose behavior does not depend on time. Often large amounts of noise are needed to detect weak signals, which can distort complex signal characteristics. To address these limitations, this study explores multi-threshold systems and the application of SR in multiscale applications using wavelet transforms. In the multiscale domain signals can be analyzed at different levels of resolution to better understand the underlying dynamics. We propose a double-threshold detection system that integrates two single-threshold detectors to enhance weak signal detection. We evaluate it both in the original data domain and in the multiscale domain using simulated and real-world signals and compare its performance with existing methods. Experimental results demonstrate that, in the original data domain, the proposed double-threshold detector significantly improves weak signal detection compared to conventional single-threshold approaches. Its performance is further improved in the frequency domain, requiring lower noise levels while outperforming existing detection systems. This study advances SR-based detection methodologies by introducing a robust approach to weak signal identification, with potential applications in various disciplines.

Static feature exclusion strategies often fail to prevent bias when hidden dependencies influence the model predictions. To address this issue, we explore a reinforcement learning (RL) framework that integrates bias mitigation and automated feature selection within a single learning process. Unlike traditional heuristic-driven filter or wrapper approaches, our RL agent adaptively selects features using a reward signal that explicitly integrates predictive performance with fairness considerations. This dynamic formulation allows the model to balance generalization, accuracy, and equity throughout the training process, rather than rely exclusively on pre-processing adjustments or post hoc correction mechanisms. In this paper, we describe the construction of a multi-component reward function, the specification of the agents action space over feature subsets, and the integration of this system with ensemble learning. We aim to provide a flexible and generalizable way to select features in environments where predictors are correlated and biases can inadvertently re-emerge.

European grapevine (Vitis vinifera L.) is a climate-sensitive perennial whose flowering and ripening govern yield and quality. Phenological records from monitoring programs are typically collected at irregular intervals, so true transition dates are interval-censored, and many site-years are right-censored. We develop a reproducible workflow that treats phenology as a time-to-event outcome: Status & Intensity observations from the USA-NPN are converted to interval bounds, linked to NASA POWER daily weather, and analyzed with parametric accelerated failure time (AFT) models (Weibull and log-logistic). To avoid outcome-dependent bias from aggregating weather up to the event date, antecedent conditions are summarized in fixed pre-season windows and standardized; quality-control filters ensure adequate within-window data coverage. Applied to flowering and ripening of V.~vinifera, the framework yields interpretable time-ratio effects and publication-ready tables and figures. Warmer pre-season conditions are associated with earlier ripening, whereas flowering responses are modest and uncertain in these data; precipitation plays, at most, a secondary role. The approach demonstrates how interval-censored survival models with exogenous weather windows can extract robust climate signals from citizen-science phenology while preserving observation uncertainty, and it generalizes readily to other species and networks.

This paper presents a hybrid approach to predict the evolution of technological maturity in R and D projects, using the oil and gas sector as an example. Integrating System Dynamics (SD) and Agent Based Modelling (ABM) allows the proposed multi level framework to capture uncertainties in work effort, team size, and project duration, which influence technological progress. While AB SD hybrid models are established in other fields, their use in R and D remains limited. The model combines system level feedback structures governing work phases, rework cycles, and duration with decentralised agents such as team members, tasks, and controllers, whose interactions generate emergent project dynamics. A base case scenario analysed early stage innovation projects with 15 parallel tasks over 156 weeks. A comparative sequential scenario showed an 88 percent reduction in rework duration. A second scenario assessed mixed parallel sequential task structures with varying team sizes. In parallel configurations, increasing team size reduced project duration and improved task completion, with optimal results for teams of four to five members. These findings align with empirical evidence showing that moderate team expansion enhances coordination efficiency without excessive communication overhead. However, larger teams may decrease performance due to communication complexity and management delays. Overall, the model outputs and framework align with expert understanding, supporting their validity as quantitative tools for analysing resource allocation, scheduling efficiency, and technology maturity progression.

We propose a simple yet effective use of LLM-powered AI tools to improve causal estimation. In double machine learning, the accuracy of causal estimates of the effect of a treatment on an outcome in the presence of a high-dimensional confounder depends on the performance of estimators of conditional expectation functions. We show that predictions made by generative models trained on historical data can be used to improve the performance of these estimators relative to approaches that solely rely on adjusting for embeddings extracted from these models. We argue that the historical knowledge and reasoning capacities associated with these generative models can help overcome curse-of-dimensionality problems in causal inference problems. We consider a case study using a small dataset of online jewelry auctions, and demonstrate that inclusion of LLM-generated guesses as predictors can improve efficiency in estimation.

In recent years, there has been growing research interest in addressing treatment hierarchy questions within network meta-analysis (NMA). In NMAs involving many treatments, the number of possible hierarchy questions becomes prohibitively large. To manage this complexity, previous work has recommended pre-selecting specific hierarchy questions of interest (e.g., “among options A, B, C, D, E, do treatments A and B have the two best effects in terms of improving outcome X?") and calculating the empirical probabilities of the answers being true given the data. In contrast, we propose an efficient and scalable algorithmic approach that eliminates the need for pre-specification by systematically generating a comprehensive catalog of highly credible treatment hierarchy questions, specifically, those with empirical probabilities exceeding a chosen threshold (e.g., 95%). This enables decision-makers to extract all meaningful insights supported by the data. An additional algorithm trims redundant insights from the output to facilitate interpretation. We define and address six broad types of binary hierarchy questions (i.e., those with true/false answers), covering standard hierarchy questions answered using existing ranking metrics - pairwise comparisons and (cumulative) ranking probabilities - as well as many other complex hierarchy questions. We have implemented our methods in an R package and illustrate their application using real NMA datasets on diabetes and depression interventions. Beyond NMA, our approach is relevant to any decision problem concerning three or more treatment options.

In many scientific domains, clustering aims to reveal interpretable latent structure that reflects relevant subpopulations or processes. Widely used Bayesian mixture models for model-based clustering often produce overlapping or redundant components because priors on cluster locations are specified independently, hindering interpretability. To mitigate this, repulsive priors have been proposed to encourage well-separated components, yet existing approaches face both computational and theoretical challenges. We introduce a fully tractable Bayesian repulsive mixture model by assigning a projection Determinantal Point Process (DPP) prior to the component locations. Projection DPPs induce strong repulsion and allow exact sampling, enabling parsimonious and interpretable posterior clustering. Leveraging their analytical tractability, we derive closed-form posterior and predictive distributions. These results, in turn, enable two efficient inference algorithms: a conditional Gibbs sampler and the first fully implementable marginal sampler for DPP-based mixtures. We also provide strong frequentist guarantees, including posterior consistency for density estimation, elimination of redundant components, and contraction of the mixing measure. Simulation studies confirm superior mixing and clustering performance compared to alternatives in misspecified settings. Finally, we demonstrate the utility of our method on event-related potential functional data, where it uncovers interpretable neuro-cognitive subgroups. Our results support the projection DPP mixtures as a theoretically sound and practically effective solution for Bayesian clustering.

Causal inference in spatial domains faces two intertwined challenges: (1) unmeasured spatial factors, such as weather, air pollution, or mobility, that confound treatment and outcome, and (2) interference from nearby treatments that violate standard no-interference assumptions. While existing methods typically address one by assuming away the other, we show they are deeply connected: interference reveals structure in the latent confounder. Leveraging this insight, we propose the Spatial Deconfounder, a two-stage method that reconstructs a substitute confounder from local treatment vectors using a conditional variational autoencoder (C-VAE) with a spatial prior, then estimates causal effects with a flexible outcome model. We show that this enables nonparametric identification of direct and spillover effects under weak assumptions–without multiple treatment types or a known latent-field model. Empirically, we extend SpaCE, a benchmark suite for spatial confounding, to include treatment interference, and show that the Spatial Deconfounder consistently improves effect estimation across real-world environmental health and social science datasets. By turning local interference into a multi-cause proxy for latent spatial confounding, our framework advances robust causal inference for spatial data.

Many social science questions ask how linguistic properties causally affect an audience's attitudes and behaviors. Because text properties are often interlinked (e.g., angry reviews use profane language), we must control for possible latent confounding to isolate causal effects. Recent literature proposes adapting large language models (LLMs) to learn latent representations of text that successfully predict both treatment and the outcome. However, because the treatment is a component of the text, these deep learning methods risk learning representations that actually encode the treatment itself, inducing overlap bias. Rather than depending on post-hoc adjustments, we introduce a new experimental design that handles latent confounding, avoids the overlap issue, and unbiasedly estimates treatment effects. We apply this design in an experiment evaluating the persuasiveness of expressing humility in political communication. Methodologically, we demonstrate that LLM-based methods perform worse than even simple bag-of-words models using our real text and outcomes from our experiment. Substantively, we isolate the causal effect of expressing humility on the perceived persuasiveness of political statements, offering new insights on communication effects for social media platforms, policy makers, and social scientists.

Changepoint localization aims to provide confidence sets for a changepoint (if one exists). Existing methods either relying on strong parametric assumptions or providing only asymptotic guarantees or focusing on a particular kind of change(e.g., change in the mean) rather than the entire distributional change. A method (possibly the first) to achieve distribution-free changepoint localization with finite-sample validity was recently introduced by \cite{dandapanthula2025conformal}. However, while they proved finite sample coverage, there was no analysis of set size. In this work, we provide rigorous theoretical guarantees for their algorithm. We also show the consistency of a point estimator for change, and derive its convergence rate without distributional assumptions. Along that line, we also construct a distribution-free consistent test to assess whether a particular time point is a changepoint or not. Thus, our work provides unified distribution-free guarantees for changepoint detection, localization, and testing. In addition, we present various finite sample and asymptotic properties of the conformal $p$-value in the distribution change setup, which provides a theoretical foundation for many applications of the conformal $p$-value. As an application of these properties, we construct distribution-free consistent tests for exchangeability against distribution-change alternatives and a new, computationally tractable method of optimizing the powers of conformal tests. We run detailed simulation studies to corroborate the performance of our methods and theoretical results. Together, our contributions offer a comprehensive and theoretically principled approach to distribution-free changepoint inference, broadening both the scope and credibility of conformal methods in modern changepoint analysis.

In this growing age of data and technology, large black-box models are becoming the norm due to their ability to handle vast amounts of data and learn incredibly complex input-output relationships. The deficiency of these methods, however, is their inability to explain the prediction process, making them untrustworthy and their use precarious in high-stakes situations. SHapley Additive exPlanations (SHAP) analysis is an explainable AI method growing in popularity for its ability to explain model predictions in terms of the original features. For each sample and feature in the data set, we associate a SHAP value that quantifies the contribution of that feature to the prediction of that sample. Clustering these SHAP values can provide insight into the data by grouping samples that not only received the same prediction, but received the same prediction for similar reasons. In doing so, we map the various pathways through which distinct samples arrive at the same prediction. To showcase this methodology, we present a simulated experiment in addition to a case study in Alzheimer's disease using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. We also present a novel generalization of the waterfall plot for multi-classification.

Traditional transfer learning typically reuses large pre-trained networks by freezing some of their weights and adding task-specific layers. While this approach is computationally efficient, it limits the model's ability to adapt to domain-specific features and can still lead to overfitting with very limited data. To address these limitations, we propose Structured Output Regularization (SOR), a simple yet effective framework that freezes the internal network structures (e.g., convolutional filters) while using a combination of group lasso and $L_1$ penalties. This framework tailors the model to specific data with minimal additional parameters and is easily applicable to various network components, such as convolutional filters or various blocks in neural networks enabling broad applicability for transfer learning tasks. We evaluate SOR on three few shot medical imaging classification tasks and we achieve competitive results using DenseNet121, and EfficientNetB4 bases compared to established benchmarks.

Complex, high-dimensional data is ubiquitous across many scientific disciplines, including machine learning, biology, and the social sciences. One of the primary methods of visualizing these datasets is with two-dimensional scatter plots that visually capture some properties of the data. Because visually determining the accuracy of these plots is challenging, researchers often use quality metrics to measure the projection's accuracy and faithfulness to the original data. One of the most commonly employed metrics, normalized stress, is sensitive to uniform scaling (stretching, shrinking) of the projection, despite this act not meaningfully changing anything about the projection. Another quality metric, the Kullback–Leibler (KL) divergence used in the popular t-Distributed Stochastic Neighbor Embedding (t-SNE) technique, is also susceptible to this scale sensitivity. We investigate the effect of scaling on stress and KL divergence analytically and empirically by showing just how much the values change and how this affects dimension reduction technique evaluations. We introduce a simple technique to make both metrics scale-invariant and show that it accurately captures expected behavior on a small benchmark.

Safety alignment of large language models currently faces a central challenge: existing alignment techniques often prioritize mitigating responses to harmful prompts at the expense of overcautious behavior, leading models to incorrectly refuse benign requests. A key goal of safe alignment is therefore to improve safety while simultaneously minimizing false refusals. In this work, we introduce Energy Landscape Steering (ELS), a novel, fine-tuning free framework designed to resolve this challenge through dynamic, inference-time intervention. We train a lightweight external Energy-Based Model (EBM) to assign high energy to undesirable states (false refusal or jailbreak) and low energy to desirable states (helpful response or safe reject). During inference, the EBM maps the LLM's internal activations to an energy landscape, and we use the gradient of the energy function to steer the hidden states toward low-energy regions in real time. This dynamically guides the model toward desirable behavior without modifying its parameters. By decoupling behavioral control from the model's core knowledge, ELS provides a flexible and computationally efficient solution. Extensive experiments across diverse models demonstrate its effectiveness, raising compliance on the ORB-H benchmark from 57.3 percent to 82.6 percent while maintaining baseline safety performance. Our work establishes a promising paradigm for building LLMs that simultaneously achieve high safety and low false refusal rates.

We construct a neural network to perform regression on the local dark-matter density field given line-of-sight peculiar velocities of dark-matter halos, biased tracers of the dark matter field. Our architecture combines a convolutional U-Net with a point-cloud DeepSets. This combination enables efficient use of small-scale information and improves reconstruction quality relative to a U-Net-only approach. Specifically, our hybrid network recovers both clustering amplitudes and phases better than the U-Net on small scales.

Diffusion language models (DLMs) enable parallel, order-agnostic generation with iterative refinement, offering a flexible alternative to autoregressive large language models (LLMs). However, adapting reinforcement learning (RL) fine-tuning to DLMs remains an open challenge because of the intractable likelihood. Pioneering work such as diffu-GRPO estimated token-level likelihoods via one-step unmasking. While computationally efficient, this approach is severely biased. A more principled foundation lies in sequence-level likelihoods, where the evidence lower bound (ELBO) serves as a surrogate. Yet, despite this clean mathematical connection, ELBO-based methods have seen limited adoption due to the prohibitive cost of likelihood evaluation. In this work, we revisit ELBO estimation and disentangle its sources of variance. This decomposition motivates reducing variance through fast, deterministic integral approximations along a few pivotal dimensions. Building on this insight, we introduce Group Diffusion Policy Optimization (GDPO), a new RL algorithm tailored for DLMs. GDPO leverages simple yet effective Semi-deterministic Monte Carlo schemes to mitigate the variance explosion of ELBO estimators under vanilla double Monte Carlo sampling, yielding a provably lower-variance estimator under tight evaluation budgets. Empirically, GDPO achieves consistent gains over pretrained checkpoints and outperforms diffu-GRPO, one of the state-of-the-art baselines, on the majority of math, reasoning, and coding benchmarks.

Recent work has generalized several results concerning the well-understood spiked Wigner matrix model of a low-rank signal matrix corrupted by additive i.i.d. Gaussian noise to the inhomogeneous case, where the noise has a variance profile. In particular, for the special case where the variance profile has a block structure, a series of results identified an effective spectral algorithm for detecting and estimating the signal, identified the threshold signal strength required for that algorithm to succeed, and proved information-theoretic lower bounds that, for some special signal distributions, match the above threshold. We complement these results by studying the computational optimality of this spectral algorithm. Namely, we show that, for a much broader range of signal distributions, whenever the spectral algorithm cannot detect a low-rank signal, then neither can any low-degree polynomial algorithm. This gives the first evidence for a computational hardness conjecture of Guionnet, Ko, Krzakala, and Zdeborová (2023). With similar techniques, we also prove sharp information-theoretic lower bounds for a class of signal distributions not treated by prior work. Unlike all of the above results on inhomogeneous models, our results do not assume that the variance profile has a block structure, and suggest that the same spectral algorithm might remain optimal for quite general profiles. We include a numerical study of this claim for an example of a smoothly-varying rather than piecewise-constant profile. Our proofs involve analyzing the graph sums of a matrix, which also appear in free and traffic probability, but we require new bounds on these quantities that are tighter than existing ones for non-negative matrices, which may be of independent interest.

Reinforcement Learning with Verifiable Rewards (RLVR), which uses simple binary feedback to post-train large language models, has found significant empirical success. However, a principled understanding of why it works is lacking. This paper builds a theoretical foundation for RLVR by analyzing its training process at both the full-response (trajectory) and token levels. Central to our analysis is a new quantity called the Gradient Gap, which formalizes the direction of improvement from low-reward to high-reward regions of the response space. We prove that convergence critically depends on aligning the update direction with this Gradient Gap. Moreover, we derive a sharp step-size threshold based on the magnitude of the Gradient Gap: below it, learning converges, whereas above it, performance collapses. Our theory further predicts how the critical step size must scale with response length and the success rate, thereby explaining why practical heuristics such as length normalization improve stability and showing that, with a fixed learning rate, the success rate can stagnate strictly below $100\%$. Importantly, our theory holds flexibly for any policy-gradient algorithm and so characterizes the dynamics of popular approaches such as REINFORCE and GRPO. We validate these predictions through controlled bandit simulations and language model experiments on post-training Qwen2.5-Math-7B with GRPO.

Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to $n!$ such representations for graphs with $n$ nodes is only partially mitigated by using permutation-equivariant learning architectures. Despite their computational efficiency, existing graph diffusion models struggle to distinguish certain graph families and their spectra, unless graph data are augmented with ad hoc features. This shortcoming stems from enforcing the inductive bias within the learning architecture. In this work, we leverage random matrix theory to analytically extract the spectral properties of the diffusion process, allowing us to push most of the inductive bias from the architecture into the dynamics. Building on this, we introduce the Dyson Diffusion Model, which employs Dyson's Brownian motion to capture the spectral dynamics of an Ornstein-Uhlenbeck process on the adjacency matrix. Furthermore, conditioned on the spectral dynamics, we formulate a Lie group diffusion, appropriately modeling the remaining degrees of freedom. Strikingly, the resulting learning problem becomes permutation invariant at the Lie algebra level. We demonstrate that the Dyson Diffusion Model learns graph spectra accurately and outperforms existing graph diffusion models.