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:2606.21352v2 Announce Type: replace Abstract: Understanding the complex topology and hierarchy of urban power grid is crucial for energy prognosis, power flow management, and system resilience analysis. However, detailed grid information remains largely proprietary. This information, nevertheless, is crucial especially for analyzing the last-mile distribution networks connecting individual buildings. This paper addresses this challenge by developing an open-data-driven framework to identify urban power grid topology, from high-voltage transmission down to individual building connections. We integrate public infrastructure data (power-lines, substations, transformers, poles) to map the high and medium-voltage grid skeleton. We then leverage geospatial machine learning on OpenStreetMap building data to cluster loads of building energy demand. Upon the clustering, we develop the physical topology of the final distribution lines linking the clustered buildings and low-voltage distribution grids. Our derived grid topology incorporates physical and geographical constraints like voltage level and road networks, thus leading to reasonable topology and hierarchy of grid networks. We apply the developed framework to the districts of Alna in Oslo, Norway, and Waiheke Island in New Zealand, and we reconstruct the complete grid topology that connects all the buildings, power lines, and electricity infrastructure assets. With the developed framework, we provide a critical tool that facilitates power system analysis, e.g., power flow optimization, cascading failure simulation, and grid resilience against the penetration of distributed renewable generation. This work also opens the opportunity to build energy digital twins that fuse power assets and grid topology, geographic constraints, and fine-grained power demand profiles.
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.
arXiv:2605.09724v2 Announce Type: replace Abstract: Existing accounts of grokking explain the phenomena in terms of mechanistic frameworks such as circuit efficiency or lazy-to-rich transitions. However, despite a known dependence between grokking and model size, how model capacity shapes grokking remains an open question. We give an information-theoretic account of this relationship on the task of modular arithmetic, showing that grokking does not immediately occur when a model becomes large enough to memorise the training set, but rather emerges as the outcome of a competition between two measurable timescales: a memorisation speed $T_{\text{mem}}(P)$ and a generalisation speed $T_{\text{gen}}(P)$, both of which are functions of model parameter count $P$. Adapting the information capacity framework of Morris et al. (2025), we estimate $T_{\text{mem}}(P)$ on random-label data of equivalent complexity and $T_{\text{gen}}(P)$ on the modular task itself, and show that grokking emerges close to the parameter scale where these timescales intersect. The framework also suggests an empirical model for predicting memorisation speed given model capacity and dataset complexity, recovering the previously reported empirical observation that larger models memorise faster. Overall, we motivate the formalisation of different learning timescales as important abstractions to study when explaining how model capacity shapes grokking on algorithmic tasks.
arXiv:2605.08098v2 Announce Type: replace Abstract: Kirigami is an increasingly useful fabrication method to produce shape-programmable metamaterial structures. However, inverse design remains difficult because deployment is nonlinear, and feasible cut layouts must satisfy discrete compatibility rules, avoid overlap, and map one target shape to valid designs. We present RL-Kirigami, an inverse design framework that combines optimal-transport conditional flow matching (OT-CFM) with reinforcement learning to generate compatible ratio fields for compact reconfigurable parallelogram quad kirigami. A marching decoder enforces global geometric compatibility, and Group Relative Policy Optimization (GRPO) aligns the generator with nondifferentiable rewards for silhouette matching, feasibility, and ratio-field regularity. Across procedurally generated target shape instances, a single sample from the pretrained OT-CFM prior reached $94.2\%~\mathrm{sIoU}$ and outperformed solver baselines while reducing forward simulator evaluations from hundreds to $1$. GRPO improved accuracy to $94.91\%~\mathrm{sIoU}$ and, with regularity included, reduced $\mathrm{TV}(\mathbf{x})$ from $0.95$ to $0.81$ while maintaining $94.83\%~\mathrm{sIoU}$. Generated layouts were exported to DXF and laser cut in $50~\mu\mathrm{m}$ polymeric sheets to produce deployable prototypes in $8.0\pm 1.0$ minutes per part. These results support a manufacturing-aware inverse design workflow for deployable kirigami metamaterials under geometric feasibility constraints. Code is available at https://github.com/milad1378yz/RL-Kirigami.
arXiv:2604.23418v2 Announce Type: replace Abstract: Uniform random rotations are useful in fast Johnson--Lindenstrauss embeddings, kernel approximation, communication-efficient learning, and recent AI compression pipelines, but are computationally expensive to generate and apply in high dimensions. A practical alternative repeats Walsh--Hadamard transforms with random sign diagonals. Applying this structured rotation twice has shown empirical benefits, but supporting theory remains limited. We study the approximation quality of the two-stage structured Hadamard rotation. Here $d$ is the dimension of the rotated vector. On the positive side, we prove explicit, nonasymptotic upper bounds of order $\sqrt{\log d/d}$ in both Kolmogorov and Wasserstein-1 distance for corresponding coordinates scaled by $\sqrt d$, uniformly over unit inputs and coordinates. For the input $u=e_1$, both distances also have lower bounds of order $d^{-1/2}$ at every coordinate. On the negative side, we prove an explicit lower bound on the Wasserstein-1 distance between the full vector distributions, showing a substantial discrepancy that does not vanish as $d$ grows for the input $u=e_1$. For the same input, we also prove a matching asymptotic upper bound, showing that the lower-bound scale is sharp. Taken together, the results identify a separation between one-dimensional marginal behavior, where approximation improves with dimension, and the full-vector law, where a nonvanishing Wasserstein-1 discrepancy remains. The marginal bounds control coordinate threshold probabilities and expected scalar Lipschitz losses, including expected averages over coordinates. They do not establish joint-coordinate approximation, and the full-vector separation does not imply failure of a particular algorithm. Connecting these distributional results to performance guarantees for specific algorithms remains open.
arXiv:2604.01730v3 Announce Type: replace Abstract: This paper investigates Koopman operator-based approaches for multivariable control of a two-spool turbofan engine. A physics-based component-level model is developed to generate training data and validate the controllers. A meta-heuristic extended dynamic mode decomposition is adapted, with a cost function designed to accurately capture both spool-speed dynamics and the engine pressure ratio (EPR), enabling the construction of a single Koopman model that can be reused across multiple control strategies. Using the identified time-varying Koopman model, an adaptive Koopman-based model predictive controller (AKMPC) with a disturbance observer is developed and compared with a Koopman-based feedback linearization controller (K-FBLC) and its integrator-augmented version (K-FBLC-I). The Koopman representation further enables nonlinear GTE output limiters, such as rotor-acceleration and turbine-inlet-temperature limits, to be expressed as linear constraints in the AKMPC. The controllers are evaluated for two control configurations of spool speeds and EPR, under both sea-level and varying flight conditions. The results demonstrate that the proposed identification approach enables accurate predictions of both spool speeds and EPR, allowing the Koopman model to be reused flexibly across different control formulations. While all strategies achieve comparable performance in sea-level conditions, the AKMPC demonstrates improved performance under varying flight conditions due to its ability to capture nonlinear dynamics, handle constraints, and compensate for model mismatch. Moreover, the EPR control strategy improves the thrust response. The study highlights the applicability of Koopman-based control and the advantages of the AKMPC framework for robust turbofan engine control.