arXiv:2601.07665v2 Announce Type: replace-cross Abstract: We introduce a principled learning to optimize (L2O) framework for solving fixed-point problems involving general nonexpansive mappings. Our idea is to deliberately inject summable perturbations into a standard Krasnosel'skii-Mann iteration to improve its average-case performance over a specific distribution of problems while retaining its convergence guarantees. Under a metric sub-regularity assumption, we prove that the proposed parametrization includes only iterations that locally achieve linear convergence-up to a vanishing bias term-and that it encompasses all iterations that do so at a sufficiently fast rate. We then demonstrate how our framework can be used to augment several widely-used operator splitting methods to accelerate the solution of structured monotone inclusion problems, and validate our approach on a best approximation problem using an L2O-augmented Douglas-Rachford splitting algorithm.
arXiv:2512.08281v3 Announce Type: replace-cross Abstract: Accurate and reliable aircraft landing time prediction is essential for effective resource allocation in air traffic management. However, the inherent uncertainty of aircraft trajectories and traffic flows poses significant challenges to both prediction accuracy and trustworthiness. Therefore, prediction models should not only provide point estimates of aircraft landing times but also the uncertainties associated with these predictions. Furthermore, aircraft trajectories are frequently influenced by the presence of nearby aircraft through air traffic control interventions such as radar vectoring. Consequently, landing time prediction models must account for multi-agent interactions in the airspace. In this work, we propose a probabilistic multi-agent aircraft landing time prediction framework that provides the landing times of multiple aircraft as distributions. We evaluate the proposed framework using an air traffic surveillance dataset collected from the terminal airspace of the Incheon International Airport in South Korea. The results demonstrate that the proposed model achieves higher prediction accuracy than the baselines and quantifies the associated uncertainties of its outcomes. In addition, the model uncovered underlying patterns in air traffic control through its attention scores, thereby enhancing explainability.
arXiv:2511.10383v2 Announce Type: replace-cross Abstract: Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline reinforcement learning from historical data. However, there is limited statistical understanding of the approximation errors inherent in learning policies from offline datasets. We address this by linking reinforcement learning to the Hamilton-Jacobi-Bellman equation and proposing an operator-theoretic algorithm based on a simple dynamic programming recursion. Specifically, we represent our world model in terms of the infinitesimal generator of controlled diffusion processes learned in a reproducing kernel Hilbert space. By integrating statistical learning methods and operator theory, we establish global convergence of the value function under sufficiently small generator-approximation error and derive explicit finite-sample guarantees with bounds tied directly to system properties such as smoothness and stability. Our theoretical and proof-of-concept results indicate that operator-based approaches may hold promise for solving offline reinforcement learning using continuous-time optimal control.
arXiv:2510.07832v2 Announce Type: replace-cross Abstract: Spatial prediction refers to the estimation of unobserved values from spatially distributed observations. Although recent advances have improved the capacity to model diverse observation types, adoption in practice remains limited in industries that demand interpretability. To mitigate this gap, surrogate models that explain black-box predictors provide a promising path toward interpretable decision making. In this study, we propose a graph partitioning problem to construct spatial segments that minimize the sum of within-segment variances of individual predictions. The assignment of data points to segments can be formulated as a mixed-integer quadratic programming problem. While this formulation potentially enables the identification of exact segments, its computational complexity becomes prohibitive as the number of data points increases. Motivated by this challenge, we develop an approximation scheme that leverages the structural properties of graph partitioning. Experimental results demonstrate the computational efficiency of this approximation in identifying spatial segments.
arXiv:2510.00734v2 Announce Type: replace-cross Abstract: Bayesian optimal experimental design provides a principled framework for selecting experimental configurations that maximize obtained information. In this work, we consider settings where the likelihood entropy is independent of the design or can be evaluated explicitly, which applies, e.g. to additive noise models with design-independent or explicitly computable noise entropy. This reduces the problem to maximum entropy estimation, where the nested integral defining the expected information gain collapses into a single integral. Our study is motivated by large-scale inference problems, such as inverse problems, where the computational cost is dominated by expensive likelihood evaluations. Under additive Gaussian noise model, we propose a computational approach in which the evidence density is approximated by a Monte Carlo or quasi-Monte Carlo surrogate, while the differential entropy is evaluated using standard methods without additional likelihood evaluations. We prove that this strategy achieves convergence rates that are comparable to, or better than, state-of-the-art methods for full expected information gain estimation, particularly when the cost of entropy evaluation is negligible. Our approach relies only on mild smoothness of the forward map and avoids stronger technical assumptions required in earlier work. We also present numerical experiments, which confirm some of our theoretical findings.
arXiv:2505.22193v2 Announce Type: replace-cross Abstract: Quantum Diffusion Models (QDMs) are an emerging paradigm in Generative AI that aims to use quantum properties to improve the performances of their classical counterparts. However, existing algorithms are not easily scalable due to the limitations of near-term quantum devices. Following our previous work on QDMs, here we propose and implement two physics-inspired protocols. In the first, we use the formalism of quantum stochastic walks, showing that a specific interplay of quantum and classical dynamics in the forward process produces statistically more robust models generating sets of MNIST images with lower Fr\'echet Inception Distance (FID) than using totally classical dynamics. In the second approach, we realize an algorithm to generate images by exploiting the intrinsic noise of real IBM quantum hardware with only four qubits. Our work could be a starting point to pave the way for new scenarios for large-scale algorithms in quantum Generative AI, where quantum noise is neither mitigated nor corrected, but instead exploited as a useful resource.
arXiv:2412.06534v5 Announce Type: replace-cross Abstract: Understanding the internal mechanisms of deep neural networks remains a central challenge in machine learning. In computer vision, one promising yet only preliminarily explored approach is feature inversion via inverse networks, which reconstructs images from intermediate representations using trained inverse networks. In this study, we revisit feature inversion via inverse networks, introducing a novel, modular variant that enables a computationally more efficient application of the technique while, in some cases, producing semantically more coherent image reconstructions. We apply our method to large-scale transformer-based vision models, specifically Detection Transformer, Vision Transformer, Swin Transformer, and Data-Efficient Image Transformer, analyzing the resulting reconstructions across network depth. Our main analysis compares Detection Transformer and Vision Transformer, which exhibit the most informative differences among the evaluated architectures. At the same time, results for Swin Transformer and Data-Efficient Image Transformer support the broader applicability of our framework. Our findings reveal gradual representational changes across transformer layers as a shared characteristic of Detection Transformer and Vision Transformer, as well as systematic differences in how they preserve contextual shape and fine-grained image details, and in their robustness to color perturbations. These findings deepen understanding of transformer-based vision models and demonstrate the utility of modular feature inversion as an interpretability tool.
arXiv:2407.16407v3 Announce Type: replace-cross Abstract: This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are unknown, while only a control penalty function and constraints are provided. To this end, we embed state probability densities into a reproducing kernel Hilbert space (RKHS) to leverage recent advances in operator regression, thereby identifying Markov transition operators associated with controlled diffusion processes. This operator learning approach integrates naturally with convex operator-theoretic Hamilton-Jacobi-Bellman recursions that scale linearly with state dimensionality, effectively solving a wide range of nonlinear optimal control problems. Numerical results demonstrate its ability to address diverse nonlinear control tasks, including the depth regulation of an autonomous underwater vehicle.
arXiv:2609.35545v2 Announce Type: replace Abstract: Epidemic policy planning often requires coordination between geographical regions, taking into account mobility-driven spillovers and how to make use of limited resources. Existing methods either lack action-conditioned models of coupled dynamics or cannot guarantee per-period feasibility. We present EpiMind, a graph world model framework for constrained epidemic policy planning across regions. A graph-factored recurrent state-space model generates joint policy-conditioned rollouts from regional latent beliefs, while graph-temporal ADMM optimizes regional interventions, enforces shared-resource feasibility through projection, and evaluates temporal specifications under the learned model. EpiMind reduces admission RMSE by 29% relative to graph-free dynamics modeling, plans within 1-5% of the best feasible constant policy with guaranteed shared-budget feasibility, and outperforms all deployable baselines across three resource budgets in real-context evaluation. These results demonstrate that graph-structured policy imagination with explicit constrained coordination supports effective epidemic interventions from learned dynamics.
arXiv:2609.33521v2 Announce Type: replace Abstract: Trust evaluation plays a critical role in cybersecurity by supporting risk mitigation and decision-making. A variety of trust evaluation methods have been proposed, with learning-based approaches offering high accuracy and automation. However, they often require substantial ground truth, suffer from low training efficiency, lack support for basic trust properties, and provide limited explainability. Large Language Models (LLMs) offer a compelling alternative due to their strong zero-/few-shot reasoning abilities and broad knowledge. To this end, we propose LLM4Trust, the first benchmark framework that systematically explores the capabilities of LLMs for trust evaluation. We first construct diverse trust graphs to model five basic trust properties and design corresponding property understanding tasks. We then assess the ability of eight representative LLMs to understand these properties under nine prompt methods. Based on this exploration, we identify the most effective LLM-prompt combinations and apply them to five real-world datasets for validating LLMs' trust evaluation capability. During this process, we propose two strategies to extract key information from large-scale trust graphs, addressing the context window limitations of LLMs. Extensive experiments show that LLMs can effectively understand basic trust properties and have great potential for real-world trust evaluation, particularly under limited supervision. However, they remain vulnerable to attacks targeting trust graphs and demonstration examples used in few-shot prompting, and incur high inference costs. Accordingly, we propose a defense mechanism and batch inference to improve the robustness and efficiency of LLM-based trust evaluation. The source code of LLM4Trust is available at https://github.com/Jieerbobo/LLM4Trust
arXiv:2608.01032v2 Announce Type: replace Abstract: Training error is what we can observe on a training set; test error is the quantity we care about. We study squared-error linear regression in a deterministic $(d+1)$-dimensional single-spike model. Each training vector has spike coordinate $\sqrt{\gamma}$, $\gamma>1$, and equal-norm, mutually orthogonal nuisance components. Training labels are $1$. Fresh test points are centered Gaussian with covariance $\operatorname{diag}(\gamma,1,\ldots,1)$ and noise-free label $x[1]/\sqrt{\gamma}$. We compute the exact train--test tradeoff for linear predictors in the training span. When the spike direction is unknown, allowing all linear predictors does not improve this tradeoff, on average or in the worst case over directions consistent with the data. There is a range of training-set sizes where every span predictor that generalizes well must fit the training data worse than the zero predictor. We call this benign misfitting, or the fourth quadrant. At its sharpest, test error tends to zero while training error diverges, with both zero-predictor errors normalized to one. The best span predictor begins to generalize when $n\gg d/\gamma^2$, while interpolation needs $n\gg d/\gamma$. In the intervening window $d/\gamma^2\ll n\ll d/\gamma$, useful span prediction lies beyond interpolation: training predictions overshoot the labels. One-pass stochastic gradient descent with a large constant learning rate attains small test error throughout this window, matching the best span predictor up to a logarithmic factor, while leaving large empirical training error. Finally, the nuisance component responsible for the training misfit also controls adversarial sensitivity.
arXiv:2607.22724v2 Announce Type: replace Abstract: Group-based policy optimization has been increasingly used to train large language model (LLM) agents from sparse outcome rewards by comparing trajectories or steps within a group. However, on difficult long-horizon agentic tasks, we found this comparison suffers from a sampling imbalance: repeated or low-effect actions dominate the high-probability region of the policy, leaving useful state-changing actions under-sampled. This imbalance produces many all-failed rollout groups, where the relative advantages within such a group provide no direction for updating the policy. Consequently, the sampling imbalance and the all-failed groups collapse into a self-perpetuating credit trap: failure-dominated sampling yields no learning signal, allowing repeated low-effect actions to persist. To break this trap, we propose Coverage-conditioned Group Policy Optimization (CovGPO), which uses first-visit observation coverage only when all samples in a group receive zero outcome reward. Specifically, within such groups, CovGPO assigns higher relative advantages to state-exploring actions without corrupting the original reward signal, as reaching new observations is a prerequisite for task success. Experiments on two challenging agentic benchmarks, ALFWorld and WebShop, show that CovGPO consistently improves over group-based baselines, with particularly large gains on hard tasks.
arXiv:2606.25001v2 公告类型：替换 摘要：机器遗忘（MU）通常通过输出遗忘来评判，例如遗忘集上的低准确率或成员推断能力的降低。然而，如果输出层面的成功可以与表征空间中不符合重新训练结果的残留同时存在，那么当前评估究竟在验证哪一种遗忘？我们通过与重新训练一致的表征遗忘来研究这一问题，将一组重新训练的模型（即不使用待遗忘数据、从头训练的模型）作为理想遗忘的可操作参考分布。针对多种遗忘方法、数据集和模型，我们的理论分析与实证结果表明，标准的输出层面评估可能系统性地高估机器遗忘的成功程度。在这一更严格的视角下，当前方法往往在输出层看似已完成遗忘，但相对于重新训练仍呈现结构性失配。它们在待遗忘样本上与重新训练部分对齐，在保留样本上则表现出更强的不一致性，并且往往留下沿重新训练相关方向局部分布的残余差异，而非弥散于整个表征空间。这种结构性失配的特征包括遗忘与保留之间的不对称性、方向性失配，以及沿重新训练相关方向集中的残留。在许多情况下，这些差异超出了独立重新训练的变异范围，并带来在重新学习攻击中恢复信息的风险。总体而言，结果表明，当前对 MU 的评估往往针对的是表面遗忘，而非与重新训练一致的遗忘。更广泛地说，重新训练揭示了输出遗忘所掩盖的内容。
arXiv:2606.07627v4 Announce Type: replace Abstract: When a learned representation is reused for a new task, which of its structure should survive? A task is a small category, a change of task is a functor $J$, and the invariants of a trained representation form a functor $F$. The left Kan extension $\operatorname{Lan}_JF$ is the invariant that the source and the change of task force on the target: by its universal property, every comparison of the source with an observed target invariant factors through it. The transfer discrepancy is the largest distance, over the target objects, between this extension and the observed invariant. For persistent homology the extension is a cokernel over comma categories, and a functorial version of the discrepancy, which also compares the maps between target objects, is $1$-Lipschitz under interleavings. On finite samples the discrepancy is a bottleneck distance, computed without approximation. For data glued from two pieces whose exclusive parts lie farther apart than the filtration scale, a Mayer-Vietoris sequence identifies what extending homology loses, while extending chains loses nothing. For a merge of labelled point clouds, the degree-zero discrepancy vanishes if and only if some $1$-Lipschitz classifier has a margin above the filtration scale at every sample point. In experiments on sampled manifolds, trained encoders and pretrained image models, every exact prediction holds on every sample. The discrepancy of truncated invariants recovers a hidden merge of separated parts far above chance and tells the intended target of a merge from a permuted control, but across pretrained models it does not track the accuracy of a linear probe.
arXiv:2605.21282v3 Announce Type: replace Abstract: Combining entropy regularisation with mirror descent in online off-policy reinforcement learning requires expressive policies with efficient sampling and explicit entropy control. Gaussian policies struggle to represent multimodal targets, whereas generative policies often require iterative sampling or lack tractable entropy estimates. We introduce Stochastic MeanFlow Policies (SMFP), a one-step generative policy class that combines MeanFlow-based noise-to-action mappings with Gaussian reparameterisation. The latent mapping captures diverse action modes, while a learnable conditional Gaussian scale provides an analytic entropy lower bound. We use this bound to regulate stochasticity alongside direct value guidance and advantage-weighted MeanFlow regression, enabling entropy-regularised mirror-descent learning with one-step policies. Across seven MuJoCo benchmarks, SMFP achieves strong performance against Gaussian and generative baselines with single-step inference. Additional experiments demonstrate multimodal action modelling and effective exploration in sparse-reward navigation.
arXiv:2605.20482v2 Announce Type: replace Abstract: Quadratic constraints (QCs) are widely used to characterize nonlinearities and uncertainties, but generic analytical characterizations can be conservative on bounded domains. This paper develops a framework for constructing verified quadratic characterizations of scalar relations in the two-dimensional real plane. Candidate quadratic inequalities are locally generated by solving convex quadratic programs using samples from the relation and exterior sample points. They are then verified globally using sum-of-squares certificates over an exact semialgebraic description or, in the case of nonpolynomial relations, over relaxed polynomial descriptions. The resulting verified constraints define a sound overapproximation of the scalar relations over the considered domains. These constraints are directly compatible with existing analysis frameworks based on QCs and pointwise integral quadratic constraints (IQCs) for static nonlinearities and uncertainties, and they can also be embedded in QC-based semidefinite programs for reachability and safety analysis of feedforward neural networks. For smooth activations such as $\tanh$, the method yields domain-dependent quadratic characterizations that constitute an alternative to generic sector- or slope-based descriptions. For ReLU networks, we give methods to reduce conservatism in QC-based reachability analysis of feedforward networks by exploiting dependencies between neurons and tighter local bounds. Numerical examples demonstrate improved reachability results for smooth activations, reduced conservatism for ReLU networks, and applicability beyond neural networks through an example involving saturation.
arXiv:2605.13088v2 Announce Type: replace Abstract: Dynamical modelling in pharmacometrics, systems biology, and epidemiology often involves subjects with related but distinct dynamics, observed through temporally sparse and irregular measurements. Classical nonlinear mixed-effects ODE models represent this heterogeneity but rely on parametric vector fields, making them vulnerable to structural misspecification. Existing nonparametric ODE methods typically assume shared dynamics rather than an explicit mixed-effect hierarchy. We propose MEGPODE, a Bayesian nonparametric mixed-effect ODE model that decomposes each subject's vector field into a shared population component and a subject-specific deviation, both endowed with Gaussian process priors. To avoid repeated ODE solves during training, we represent latent trajectories with state-space GP priors and penalize discrepancies between their derivatives and the vector fields on a finite time grid. A single variational objective enables approximate joint inference over trajectories and vector fields, accounting for state uncertainty and dependence between population and subject-specific dynamics. Across heterogeneous oscillatory and biomedical ODE benchmarks, MEGPODE improves population-field recovery and subject-level trajectory prediction relative to strong baselines.
arXiv:2605.11471v2 Announce Type: replace Abstract: Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, yet their approximation capabilities remain poorly understood in theory. In this paper, we characterize these capabilities from both negative and positive perspectives. As a negative result, we prove that constructing a polynomial-bond MPO-BM approximation to an arbitrary continuous target with bounded KL error is NP-hard. On the positive side, for score-based variational inference, we prove that targets satisfying a log-Sobolev inequality admit polynomial-bond MPO-BM approximations with provable KL guarantees when the loss-induced Hamiltonian is local and has a constant spectral gap. Furthermore, under the same conditions, we construct local importance-sampling estimators and prove that polynomially many local score queries suffice to preserve the KL guarantees.