Large language model (LLM) based agents are increasingly used to automate financial transactions, yet their reliance on contextual reasoning exposes payment systems to prompt-driven manipulation. The Agent Payments Protocol (AP2) aims to secure agent-led purchases through cryptographically verifiable mandates, but its practical robustness remains underexplored. In this work, we perform an AI red-teaming evaluation of AP2 and identify vulnerabilities arising from indirect and direct prompt injection. We introduce two attack techniques, the Branded Whisper Attack and the Vault Whisper Attack which manipulate product ranking and extract sensitive user data. Using a functional AP2 based shopping agent built with Gemini-2.5-Flash and the Google ADK framework, we experimentally validate that simple adversarial prompts can reliably subvert agent behavior. Our findings reveal critical weaknesses in current agentic payment architectures and highlight the need for stronger isolation and defensive safeguards in LLM-mediated financial systems.

Large Language Model (LLM) serving faces a fundamental tension between stringent latency Service Level Objectives (SLOs) and limited GPU memory capacity. When high request rates exhaust the KV cache budget, existing LLM inference systems often suffer severe head-of-line (HOL) blocking. While prior work explored PCIe-based offloading, these approaches cannot sustain responsiveness under high request rates, often failing to meet tight Time-To-First-Token (TTFT) and Time-Between-Tokens (TBT) SLOs. We present SuperInfer, a high-performance LLM inference system designed for emerging Superchips (e.g., NVIDIA GH200) with tightly coupled GPU-CPU architecture via NVLink-C2C. SuperInfer introduces RotaSched, the first proactive, SLO-aware rotary scheduler that rotates requests to maintain responsiveness on Superchips, and DuplexKV, an optimized rotation engine that enables full-duplex transfer over NVLink-C2C. Evaluations on GH200 using various models and datasets show that SuperInfer improves TTFT SLO attainment rates by up to 74.7% while maintaining comparable TBT and throughput compared to state-of-the-art systems, demonstrating that SLO-aware scheduling and memory co-design unlocks the full potential of Superchips for responsive LLM serving. Code is available in https://github.com/Supercomputing-System-AI-Lab/SuperInfer.

In this paper, we provide a comprehensive theoretical analysis of Stochastic Gradient Descent (SGD) and its momentum variants (Polyak Heavy-Ball and Nesterov) for tracking time-varying optima under strong convexity and smoothness. Our finite-time bounds reveal a sharp decomposition of tracking error into transient, noise-induced, and drift-induced components. This decomposition exposes a fundamental trade-off: while momentum is often used as a gradient-smoothing heuristic, under distribution shift it incurs an explicit drift-amplification penalty that diverges as the momentum parameter $β$ approaches 1, yielding systematic tracking lag. We complement these upper bounds with minimax lower bounds under gradient-variation constraints, proving this momentum-induced tracking penalty is not an analytical artifact but an information-theoretic barrier: in drift-dominated regimes, momentum is unavoidably worse because stale-gradient averaging forces systematic lag. Our results provide theoretical grounding for the empirical instability of momentum in dynamic settings and precisely delineate regime boundaries where vanilla SGD provably outperforms its accelerated counterparts.

Online harassment is a widespread social and public health concern, yet most computational approaches for detecting and addressing harassment focus on publicly visible social media content rather than private messaging environments. Private conversations present unique challenges because harmful interactions often unfold through context-dependent, multi-turn exchanges, while victims may lack timely support during moments of harassment. In this study, we investigate how large language models (LLMs) can support both the detection of and response to online harassment in private messaging. Using a dataset of 80,053 Instagram direct messages donated by 26 adolescents aged 12-18, including youth with suicide risk factors, we first construct a human-labeled dataset of online harassment in private conversations and develop a context-aware cascading LLM classification pipeline. The proposed pipeline outperforms baseline toxicity classifiers trained primarily on public social media data. We then develop a victim-centered response framework that produces context-sensitive and psychologically-grounded AI-generated responses to online harassment messages. Human evaluators perceived the AI-generated responses as significantly more helpful than the original participant responses (95% CI: 0.767--0.815, p < .001), particularly in terms of emotional support and de-escalation. Our findings highlight the potential of context-aware and victim-centered AI systems to provide just-in-time support during harassment in private messaging environments.

Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations, such as simulated annealing or low-rank decompositions, either lack efficiency or fail to capture non-convex kernels. We introduce a differentiable kernel decomposition framework that represents a target spatially-variant, dense, complex kernel using a set of sparse kernel samples. Our approach features (i) a decomposition that enables differentiable optimization of sparse kernels, (ii) a dedicated initialization strategy for non-convex shapes to avoid poor local minima, and (iii) a kernel-space interpolation scheme that extends single-kernel filtering to spatially varying filtering without retraining and additional runtime overhead. Experiments on Gaussian and non-convex kernels show that our method achieves higher fidelity than simulated annealing and significantly lower cost than low-rank decompositions. Our approach provides a practical solution for mobile imaging and real-time rendering, while remaining fully differentiable for integration into broader learning pipelines.

NORi is a machine learning (ML) parameterization of ocean boundary layer turbulence that is physics-based and augmented with neural networks. NORi stands for neural ordinary differential equations (NODEs) Richardson number (Ri) closure. The physical parameterization is controlled by a Richardson number-dependent diffusivity and viscosity. The neural ODEs are trained to capture the entrainment through the base of the boundary layer, which cannot be represented with a local diffusive closure. The parameterization is trained using large-eddy simulations in an "a posteriori" fashion, where parameters are calibrated with a loss function that explicitly depends on the actual time-integrated variables of interest rather than the instantaneous subgrid fluxes, which are inherently noisy. NORi conserves tracers by design, uses realistic nonlinear thermodynamics, and demonstrates excellent prediction and generalization capabilities in capturing entrainment dynamics under different convective strengths, background stratifications, rotation, and wind forcings. NORi is shown to simulate the seasonal evolution of the boundary layer at Ocean Weather Station Papa with similar performance to the state-of-the-art two-equation $k$-$ε$ closure. When implemented in a double-gyre simulation, it is numerically stable for at least 100 years, despite only being trained on two-day horizons, and can be run with time steps as long as one hour. The highly expressive neural networks, combined with a physically rigorous base closure, prove to be a robust paradigm for designing parameterizations for climate models: data required and training cost are drastically reduced, inference performance can be directly optimized as a primary objective, and numerical stability is implicitly promoted through training.

Model Predictive Control (MPC) is a powerful framework for optimal control but can be too slow for low-latency applications. We present a data-driven framework to accelerate MPC by replacing online optimization with a nonparametric policy constructed from offline MPC solutions. Our policy is greedy with respect to a constructed upper bound on the optimal cost-to-go, and can be implemented as a nonparametric lookup rule that is orders of magnitude faster than solving MPC online. Our analysis shows that under sufficient coverage conditions of the offline data, the policy is recursively feasible and admits provable, bounded optimality gap. These conditions establish an explicit trade-off between the amount of data collected and the tightness of the bounds. New solutions can be incorporated straightforwardly without the need for retraining, enabling continual improvement. Our experiments show that this policy is between 100 and 1000 times faster than standard MPC with only a modest hit to optimality, showing potential for real-time control tasks.

This paper presents a high-fidelity evaluation framework for machine learning (ML)-based classification of cyber-attacks and physical faults using electromagnetic transient simulations with digital substation emulation at 4.8 kHz. Twelve ML models, including ensemble algorithms and a multi-layer perceptron (MLP), were trained on labeled time-domain measurements and evaluated in a real-time streaming environment designed for sub-cycle responsiveness. The architecture incorporates a cycle-length smoothing filter and confidence threshold to stabilize decisions. Results show that while several models achieved near-perfect offline accuracies (up to 99.9%), only the MLP sustained robust coverage (98-99%) under streaming, whereas ensembles preserved perfect anomaly precision but abstained frequently (10-49% coverage). These findings demonstrate that offline accuracy alone is an unreliable indicator of field readiness and underscore the need for realistic testing and inference pipelines to ensure dependable classification in inverter-based resources (IBR)-rich networks.

Generative Artificial Intelligence (GenAI) represents a rapidly expanding digital infrastructure whose energy demand and associated CO2 emissions are emerging as a new category of climate risk. This study introduces G-TRACE (GenAI Transformative Carbon Estimator), a cross-modal, region-aware framework that quantifies training- and inference-related emissions across modalities and deployment geographies. Using real-world analytics and microscopic simulation, G-TRACE measures energy use and carbon intensity per output type (text, image, video) and reveals how decentralized inference amplifies small per-query energy costs into system-level impacts. Through the Ghibli-style image generation trend (2024-2025), we estimate 4,309 MWh of energy consumption and 2,068 tCO2 emissions, illustrating how viral participation inflates individual digital actions into tonne-scale consequences. Building on these findings, we propose the AI Sustainability Pyramid, a seven-level governance model linking carbon accounting metrics (L1-L7) with operational readiness, optimization, and stewardship. This framework translates quantitative emission metrics into actionable policy guidance for sustainable AI deployment. The study contributes to the quantitative assessment of emerging digital infrastructures as a novel category of climate risk, supporting adaptive governance for sustainable technology deployment. By situating GenAI within climate-risk frameworks, the work advances data-driven methods for aligning technological innovation with global decarbonization and resilience objectives.

Vine copulas offer flexible multivariate dependence modeling and have become widely used in machine learning. Yet, structure learning remains a key challenge. Early heuristics, such as Dissmann's greedy algorithm, are still considered the gold standard but are often suboptimal. We propose random search algorithms and a statistical framework based on model confidence sets, to improve structure selection, provide theoretical guarantees on selection probabilities and excess risk, as well as serve as a foundation for ensembling. Empirical results on real-world data sets show that our methods consistently outperform state-of-the-art approaches.

Understanding the dynamics of feature learning in neural networks (NNs) remains a significant challenge. The work of (Mousavi-Hosseini et al., 2023) analyzes a multiple index teacher-student setting and shows that a two-layer student attains a low-rank structure in its first-layer weights when trained with stochastic gradient descent (SGD) and a strong regularizer. This structural property is known to reduce sample complexity of generalization. Indeed, in a second step, the same authors establish algorithm-specific learning guarantees under additional assumptions. In this paper, we focus exclusively on the structure discovery aspect and study it under weaker assumptions, more specifically: we allow (a) NNs of arbitrary size and depth, (b) with all parameters trainable, (c) under any smooth loss function, (d) tiny regularization, and (e) trained by any method that attains a second-order stationary point (SOSP), e.g.\ perturbed gradient descent (PGD). At the core of our approach is a key $\textit{derandomization}$ lemma, which states that optimizing the function $\mathbb{E}_{\mathbf{x}} \left[g_θ(\mathbf{W}\mathbf{x} + \mathbf{b})\right]$ converges to a point where $\mathbf{W} = \mathbf{0}$, under mild conditions. The fundamental nature of this lemma directly explains structure discovery and has immediate applications in other domains including an end-to-end approximation for MAXCUT, and computing Johnson-Lindenstrauss embeddings.

Large language models (LLMs) are often modified after release through post-processing such as post-training or quantization, which makes it challenging to determine whether one model is derived from another. Existing provenance detection methods have two main limitations: (1) they embed signals into the base model before release, which is infeasible for already published models, or (2) they compare outputs across models using hand-crafted or random prompts, which are not robust to post-processing. In this work, we propose LLMPrint, a novel detection framework that constructs fingerprints by exploiting LLMs' inherent vulnerability to prompt injection. Our key insight is that by optimizing fingerprint prompts to enforce consistent token preferences, we can obtain fingerprints that are both unique to the base model and robust to post-processing. We further develop a unified verification procedure that applies to both gray-box and black-box settings, with statistical guarantees. We evaluate LLMPrint on five base models and around 700 post-trained or quantized variants. Our results show that LLMPrint achieves high true positive rates while keeping false positive rates near zero. The code is publicly available at https://github.com/hifi-hyp/ACL-LLMPrint.

Large language models (LLMs) now play a central role in code generation, yet they continue to hallucinate, frequently inventing non-existent libraries. Such library hallucinations are not just benign errors: they can mislead developers, break builds, and expose systems to supply chain threats such as slopsquatting. Despite growing awareness of these risks, there is limited understanding of how library hallucinations manifest under realistic usage conditions. To fill this gap, we present the first systematic study of how user-level prompt variations influence library hallucinations in LLM-generated code. Across seven diverse LLMs, we analyse library name hallucinations (invalid imports) and library member hallucinations (invalid calls from valid libraries), examining the effects of realistic developer language and controlled user mistakes, including misspellings and fabricated libraries or members. Our findings expose systemic vulnerabilities: one-character misspellings trigger hallucinations in up to 26% of tasks; fabricated library names are accepted in up to 99%; and time-based prompts induce hallucinations in up to 85%. Grounded in the highest-risk prompts identified in our study, we introduce LibHalluBench, a benchmark that enables a systematic and reproducible evaluation of these library hallucinations. Our findings underscore the fragility of LLMs to natural prompt variation and highlight the urgent need for safeguards against library-related hallucinations and their downstream risks.

This paper proposes two algorithms for estimating square Wasserstein distance matrices from a small number of entries. These matrices are used to compute manifold learning embeddings like multidimensional scaling (MDS) or Isomap, but contrary to Euclidean distance matrices, are extremely costly to compute. We analyze matrix completion from upper triangular samples and Nyström completion in which $\mathcal{O}(d\log(d))$ columns of the distance matrices are computed where $d$ is the desired embedding dimension, prove stability of MDS under Nyström completion, and show that it can outperform matrix completion for a fixed budget of sample distances. Finally, we show that classification of the OrganCMNIST dataset from the MedMNIST benchmark is stable on data embedded from the Nyström estimation of the distance matrix even when only 10\% of the columns are computed.

Incorporating natural language input has the potential to improve the capabilities of biomedical data discovery interfaces. However, user interface elements and visualizations are still powerful tools for interacting with data. In our prototype system, YAC, Yet Another Chatbot, we integrate natural language and interactive visualizations. YAC uses a tool-calling multi-agent system to generate declarative output, which is interpreted to render linked interactive visualizations and apply data filters. We also include adjustment widgets, which allow users to directly modify the structured output. Structured text is also generated to clarify user intent, notify users of system boundaries, and explain aspects of the data with live data element links. We conducted a user study with domain experts to surface areas where YAC can be improved. Furthermore we reflect on the capabilities and design of this system with an analysis of its technical dimensions.

Domestic Violence (DV) is a pervasive public health problem characterized by patterns of coercive and abusive behavior within intimate relationships. With the rise of social media as a key outlet for DV victims to disclose their experiences, online self-disclosure has emerged as a critical yet underexplored avenue for support-seeking. In addition, existing research lacks a comprehensive and nuanced understanding of DV self-disclosure, support provisions, and their connections. To address these gaps, this study proposes a novel computational framework for modeling DV support-seeking behavior alongside community support mechanisms. The framework consists of four key components: self-disclosure detection, post clustering, topic summarization, and support extraction and mapping. We implement and evaluate the framework with data collected from relevant social media communities. Our findings not only advance existing knowledge on DV self-disclosure and online support provisions but also enable victim-centered digital interventions.

The Trapped Gyro-Landau Fluid (TGLF) model provides fast, accurate predictions of turbulent transport in tokamaks, but whole device simulations requiring thousands of evaluations remain computationally expensive. Neural network (NN) surrogates offer accelerated inference with fully differentiable approximations that enable gradient-based coupling but typically require large training datasets to capture transport flux variations across plasma conditions, creating significant training burden and limiting applicability to expensive gyrokinetic simulations. We propose TGLF-WINN (Wavenumber-Informed Neural Network) with three key innovations: (1) principled feature engineering that reduces target prediction range, simplifying the learning task; (2) physics-guided wavenumber-resolved regularization to improve generalization under sparse data; and (3) Bayesian Active Learning (BAL) to strategically select training samples based on model uncertainty, reducing data requirements while maintaining accuracy. Feature tuning and wavenumber regularization together deliver a 12.5% relative RMSLE reduction over TGLF-NN on the full dataset; under sparse, unfiltered training (approximately 1/9 the full size) they yield an order-of-magnitude smaller RMSLE degradation than TGLF-NN, with the wavenumber-informed regularization imposing a physics-guided constraint on per-mode fluxes. Adding Bayesian Active Learning, TGLF-WINN matches TGLF-NN's full-data offline accuracy using only 25% of the training data, within 2.8% of TGLF-NN's full-data baseline and 4.3% of our own full-data result. A downstream flux-matching workflow further shows practicality: the NN surrogate gives a 45x speedup over TGLF with comparable reconstruction accuracy.

We mathematically analyze and numerically study an actor-critic machine learning algorithm for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) partial differential equations from stochastic control theory. The architecture of the critic (the estimator for the value function) is structured so that the boundary condition is always perfectly satisfied (rather than being included in the training loss) and utilizes a biased gradient which reduces computational cost. The actor (the estimator for the optimal control) is trained by minimizing the integral of the Hamiltonian over the domain, where the Hamiltonian is estimated using the critic. We show that the training dynamics of the actor and critic neural networks converge in a Sobolev-type space to a certain infinite-dimensional ordinary differential equation (ODE) as the number of hidden units in the actor and critic $\rightarrow \infty$. Further, under a convexity-like assumption on the Hamiltonian, we prove that any fixed point of this limit ODE is a solution of the original stochastic control problem. This provides an important guarantee for the algorithm's performance in light of the fact that finite-width neural networks may only converge to a local minimizers (and not optimal solutions) due to the non-convexity of their loss functions. In our numerical studies, we demonstrate that the algorithm can solve stochastic control problems accurately in up to 200 dimensions. In particular, we construct a series of increasingly complex stochastic control problems with known analytic solutions and study the algorithm's numerical performance on them. These problems range from a linear-quadratic regulator equation to highly challenging equations with non-convex Hamiltonians, allowing us to identify and analyze the strengths and limitations of this neural actor-critic method for solving HJB equations.

This study investigates the feasibility and performance of federated learning (FL) for multi-label ICD code classification using clinical notes from the MIMIC-IV dataset. Unlike previous approaches that rely on centralized training or fine-tuned large language models, we propose a lightweight and scalable pipeline combining frozen text embeddings with simple multilayer perceptron (MLP) classifiers. This design offers a privacy-preserving and deployment-efficient alternative for clinical NLP applications, particularly suited to distributed healthcare settings. Extensive experiments across both centralized and federated configurations were conducted, testing six publicly available embedding models from Massive Text Embedding Benchmark leaderboard and three MLP classifier architectures under two medical coding (ICD-9 and ICD-10). Additionally, ablation studies over ten random stratified splits assess performance stability. Results show that embedding quality substantially outweighs classifier complexity in determining predictive performance, and that federated learning can closely match centralized results in idealized conditions. While the models are orders of magnitude smaller than state-of-the-art architectures and achieved competitive micro and macro F1 scores, limitations remain including the lack of end-to-end training and the simplified FL assumptions. Nevertheless, this work demonstrates a viable way toward scalable, privacy-conscious medical coding systems and offers a step toward for future research into federated, domain-adaptive clinical AI.

Modern industrial systems are often subject to multiple failure modes, and their conditions are monitored by multiple sensors, generating multiple time-series signals. Additionally, time-to-failure data are commonly available. Accurately predicting a system's remaining useful life (RUL) requires effectively leveraging multi-sensor time-series data alongside multi-mode failure event data. In most existing models, failure modes and RUL prediction are performed independently, ignoring the inherent relationship between these two tasks. Some models integrate multiple failure modes and event prediction using black-box machine learning approaches, which lack statistical rigor and cannot characterize the inherent uncertainty in the model and data. This paper introduces a unified approach to jointly model the multi-sensor time-series data and failure time concerning multiple failure modes. This proposed model integrate a Cox proportional hazards model, a Convolved Multi-output Gaussian Process, and multinomial failure mode distributions in a hierarchical Bayesian framework with corresponding priors, enabling accurate prediction with robust uncertainty quantification. Posterior distributions are effectively obtained by Variational Bayes, and prediction is performed with Monte Carlo sampling. The advantages of the proposed model is validated through extensive numerical and case studies with jet-engine dataset.

Reliable link adaptation is critical for efficient wireless communications in dynamic fading environments. However, reinforcement learning (RL) solutions often suffer from unstable convergence due to poorly conditioned policy gradients, hindering their practical application. We propose the quantum-preconditioned policy gradient (QPPG) algorithm, which leverages Fisher-information-based preconditioning to stabilise and accelerate policy updates. Evaluations in Rayleigh fading scenarios show that QPPG achieves faster convergence, a 28.6% increase in average throughput, and a 43.8% decrease in average transmit power compared to classical methods. This work introduces quantum-geometric conditioning to link adaptation, marking a significant advance in developing robust, quantum-inspired reinforcement learning for future 6G networks, thereby enhancing communication reliability and energy efficiency.

Reliable automatic seizure detection from long-term electroencephalography (EEG) remains an unsolved challenge, as current models often fail to generalize across patients or clinical settings. Manual EEG review still is the standard of care, highlighting the need for robust models and standardized evaluation. The current literature often reports high efficacy, yet these models frequently fail when deployed to unseen patient populations. To rigorously assess this generalization gap, we conducted a large-scale empirical study evaluating 28 state-of-the-art algorithmic architectures, ranging from classical feature engineering to modern Deep Learning. These algorithms were collected by organizing a competition. A strictly held-out private dataset of continuous EEG recordings from 65 subjects, totaling 4,360 hours of data, was utilized to evaluate algorithm performance. Expert neurophysiologists annotated these recordings, establishing the ground truth for seizure events. Algorithms were evaluated using event-based metrics from the SzCORE framework, including sensitivity, precision, F1-score, and false positive rate per day. Results revealed significant performance variability among state-of-the-art approaches, with the top F1 score of 32% (sensitivity 37%, precision 29%), highlighting the persistent difficulty of this task. Analysis uncovered a discordance between peak performance and population-level stability. The algorithms achieving the highest aggregate F1-scores did not achieve the most consistent ranking across subjects. This independent evaluation exposed a notable gap between self-reported efficacies and hold-out performance, underscoring the critical need for standardized, rigorous benchmarking. The evaluation infrastructure transitions into a continuously open benchmarking platform, fostering reproducible research and accelerating robust seizure detection algorithm development.

In this article, we consider the infinite-horizon reach-avoid (RA) and stabilize-avoid (SA) zero-sum game problems for general nonlinear continuous-time systems, where the goal is to find the set of states that can be controlled to reach or stabilize to a target set, without violating constraints even under the worst-case disturbance. Based on the Hamilton-Jacobi reachability method, we address the RA problem by designing a new Lipschitz continuous RA value function, whose zero sublevel set exactly characterizes the RA set. We establish that the associated Bellman backup operator is contractive and that the RA value function is the unique viscosity solution of a Hamilton-Jacobi variational inequality. Finally, we develop a two-step framework for the SA problem by integrating our RA strategies with a recently proposed Robust Control Lyapunov-Value Function, thereby ensuring both target reachability and long-term stability. We numerically verify our RA and SA frameworks on a 3D Dubins car system to demonstrate the efficacy of the proposed approach.

Anomaly Detection (AD) defines the task of identifying observations or events that deviate from typical - or normal - patterns, a critical capability in IT security for recognizing incidents such as system misconfigurations, malware infections, or cyberattacks. In enterprise environments like SAP HANA Cloud systems, this task often involves monitoring high-dimensional, multivariate time series (MTS) derived from telemetry and log data. With the advent of quantum machine learning offering efficient calculations in high-dimensional latent spaces, many avenues open for dealing with such complex data. One approach is the Quantum Autoencoder (QAE), an emerging and promising method with potential for application in both data compression and AD. However, prior applications of QAEs to time series AD have been restricted to univariate data, limiting their relevance for real-world enterprise systems. In this work, we introduce a novel QAE-based framework designed specifically for MTS AD towards enterprise scale. We theoretically develop and experimentally validate the architecture, demonstrating that our QAE achieves performance competitive with neural-network-based autoencoders while requiring fewer trainable parameters. We evaluate our model on datasets that closely reflect SAP system telemetry and show that the proposed QAE is a viable and efficient alternative for semisupervised AD in real-world enterprise settings.

Crowd movement simulation is crucial for pedestrian safety management and facility design. Data-driven models offer the potential to improve realism and predictive accuracy, but most are developed for a single scenario, limiting their flexibility. We propose a data-driven crowd simulation model that incorporates refined visual-information extraction and explicit exit cues, aiming to improve flexibility across multiple scenarios by more effectively capturing core navigational features. The model is tested on four fundamental modules (bottleneck, corridor, corner, and T-junction) and further evaluated in a composite scenario using a modular approach. Results show that our model performs well across these scenarios, aligning with pedestrian movement in real-world experiments, and outperforms the classical knowledge-driven model in these scenarios. The research outcomes can provide inspiration for the development of data-driven crowd simulation models and advance the application of data-driven approaches.

A computational method for the synthesis of time-optimal feedback control laws for linear nilpotent systems is proposed. The method is based on the use of the bang-bang theorem, which leads to a characterization of the time-optimal trajectory as a parameter-dependent polynomial system for the control switching sequence. A deflated Newton's method is then applied to exhaust all the real roots of the polynomial system. The root-finding procedure is informed by the Hermite quadratic form, which provides a sharp estimate on the number of real roots to be found. In the second part of the paper, the polynomial systems are sampled and solved to generate a synthetic dataset for the construction of a time-optimal deep neural network -- interpreted as a binary classifier -- via supervised learning. Numerical tests in integrators of increasing dimension assess the accuracy, robustness, and real-time-control capabilities of the approximate control law.

Given an unnormalized probability density $π\propto\mathrm{e}^{-V}$, estimating its normalizing constant $Z=\int_{\mathbb{R}^d}\mathrm{e}^{-V(x)}\mathrm{d}x$ or free energy $F=-\log Z$ is a crucial problem in Bayesian statistics, statistical mechanics, and machine learning. It is challenging especially in high dimensions or when $π$ is multimodal. To mitigate the high variance of conventional importance sampling estimators, annealing-based methods such as Jarzynski equality and annealed importance sampling are commonly adopted, yet their quantitative complexity guarantees remain largely unexplored. We take a first step toward a non-asymptotic analysis of annealed importance sampling. In particular, we derive an oracle complexity of $\widetilde{O}\left(\frac{dβ^2{\mathcal{A}}^2}{\varepsilon^4}\right)$ for estimating $Z$ within $\varepsilon$ relative error with high probability, where $β$ is the smoothness of $V$ and $\mathcal{A}$ denotes the action of a curve of probability measures interpolating $π$ and a tractable reference distribution. Our analysis, leveraging Girsanov's theorem and optimal transport, does not explicitly require isoperimetric assumptions on the target distribution. Finally, to tackle the large action of the widely used geometric interpolation, we propose a new algorithm based on reverse diffusion samplers, establish a framework for analyzing its complexity, and empirically demonstrate its efficiency in tackling multimodality.

We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging a global decay bound on the coefficients in the Chebyshev expansion of any Lipschitz function, we sharpen prior work, proving that accurate recovery in the Wasserstein distance is possible with more noise than previously known. Our result immediately yields a number of applications: 1) We give a simple "linear query" algorithm for constructing a differentially private synthetic data distribution with Wasserstein-$1$ error $\tilde{O}(1/n)$ based on a dataset of $n$ points in $[-1,1]$. This bound is optimal up to log factors, and matches a recent result of Boedihardjo, Strohmer, and Vershynin [Probab. Theory. Rel., 2024], which uses a more complex "superregular random walk" method. 2) We give an $\tilde{O}(n^2/ε)$ time algorithm for the linear algebraic problem of estimating the spectral density of an $n\times n$ symmetric matrix up to $ε$ error in the Wasserstein distance. Our result accelerates prior methods from Chen et al. [ICML 2021] and Braverman et al. [STOC 2022]. 3) We tighten an analysis of Vinayak, Kong, Valiant, and Kakade [ICML 2019] on the maximum likelihood estimator for the statistical problem of "Learning Populations of Parameters'', extending the parameter regime in which sample optimal results can be obtained. Beyond these main results, we provide an extension of our bound to estimating distributions in $d > 1$ dimensions. We hope that these bounds will find applications more broadly to problems involving distribution recovery from noisy moment information.

Many real-world decision problems require solving, again and again, combinatorial optimization instances drawn from a common distribution. A recent line of structured learning methods exploits this regularity by learning policies that pair a statistical model with a tractable combinatorial oracle, instead of solving each instance independently. Training such policies is notoriously difficult, however: the resulting empirical risk is piecewise constant in the model parameters, which hinders gradient-based optimization, and only a few theoretical guarantees have been provided so far. We address this issue by analyzing smoothed (perturbed) policies: adding controlled random perturbations to the direction used by the linear oracle yields a differentiable surrogate risk and improves generalization. Our main contribution is a generalization bound that decomposes the excess risk into $(\mathit{i})$ perturbation bias, $(\mathit{ii})$ statistical estimation error, and $(\mathit{iii})$ optimization error. The perturbation bias is controlled by the \emph{fan-crossing probability}, a new geometric quantity measuring the likelihood that a perturbation changes the oracle solution. We introduce two complementary conditions to bound it--the \emph{Uniformly Bounded Density} (UBD) property, yielding a sharp ${O}(λ)$ bias, and the weaker \emph{Uniform Weak moment} (UW) property, yielding a sub-linear bound--both capturing the geometric interaction between the statistical model and the normal fan of the feasible polytope. The statistical estimation error is controlled via a uniform deviation bound over the policy class, with rate ${O}(1/(λ\sqrt{n}))$ that scales inversely in the smoothing parameter. Concerning the optimization error, we exploit kernel Sum-of-Squares methods to mitigate the curse of dimensionality of global optimization.

Safe motion planning in uncertain, time-varying environments is challenging because the safe region can change unpredictably across planning steps, often causing a loss of recursive feasibility. In this work, we present a Probabilistic Recursively Feasible Model Predictive Control (PRF-MPC) framework that guarantees recursive feasibility with a specified probability. We introduce properties that an ideal predictor should satisfy to ensure distributional consistency, and use these properties to derive closed-form expressions for the means and covariances of trajectories predicted at future time steps. Building on this analysis, we construct safety constraints that ensure, with high probability, that the current safe set is contained within the safe sets at future time steps, thereby probabilistically guaranteeing recursive feasibility. Simulation results on a lane-change scenario demonstrate that the proposed method significantly improves recursive feasibility.