Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels

We analyze prediction error in stochastic dynamical systems with memory, focusing on generalized Langevin equations (GLEs) formulated as stochastic Volterra equations. We establish that, under a strongly convex potential, trajectory discrepancies decay at a rate determined by the decay of the memory kernel and are quantitatively bounded by the estimation error of the kernel in a weighted norm. Our analysis integrates synchronized noise coupling with a Volterra comparison theorem, encompassing both subexponential and exponential kernel classes. For first-order models, we derive moment and perturbation bounds using resolvent estimates in weighted spaces. For second-order models with confining potentials, we prove contraction and stability under kernel perturbations using a hypocoercive Lyapunov-type distance. This framework accommodates non-translation-invariant kernels and white-noise forcing, explicitly linking improved kernel estimation to enhanced trajectory prediction. Numerical examples validate these theoretical findings.

APD-Agents: A Large Language Model-Driven Multi-Agents Collaborative Framework for Automated Page Design

Layout design is a crucial step in developing mobile app pages. However, crafting satisfactory designs is time-intensive for designers: they need to consider which controls and content to present on the page, and then repeatedly adjust their size, position, and style for better aesthetics and structure. Although many design software can now help to perform these repetitive tasks, extensive training is needed to use them effectively. Moreover, collaborative design across app pages demands extra time to align standards and ensure consistent styling. In this work, we propose APD-agents, a large language model (LLM) driven multi-agent framework for automated page design in mobile applications. Our framework contains OrchestratorAgent, SemanticParserAgent, PrimaryLayoutAgent, TemplateRetrievalAgent, and RecursiveComponentAgent. Upon receiving the user's description of the page, the OrchestratorAgent can dynamically can direct other agents to accomplish users' design task. To be specific, the SemanticParserAgent is responsible for converting users' descriptions of page content into structured data. The PrimaryLayoutAgent can generate an initial coarse-grained layout of this page. The TemplateRetrievalAgent can fetch semantically relevant few-shot examples and enhance the quality of layout generation. Besides, a RecursiveComponentAgent can be used to decide how to recursively generate all the fine-grained sub-elements it contains for each element in the layout. Our work fully leverages the automatic collaboration capabilities of large-model-driven multi-agent systems. Experimental results on the RICO dataset show that our APD-agents achieve state-of-the-art performance.

FedCure: Mitigating Participation Bias in Semi-Asynchronous Federated Learning with Non-IID Data

While semi-asynchronous federated learning (SAFL) combines the efficiency of synchronous training with the flexibility of asynchronous updates, it inherently suffers from participation bias, which is further exacerbated by non-IID data distributions. More importantly, hierarchical architecture shifts participation from individual clients to client groups, thereby further intensifying this issue. Despite notable advancements in SAFL research, most existing works still focus on conventional cloud-end architectures while largely overlooking the critical impact of non-IID data on scheduling across the cloud-edge-client hierarchy. To tackle these challenges, we propose FedCure, an innovative semi-asynchronous Federated learning framework that leverages coalition construction and participation-aware scheduling to mitigate participation bias with non-IID data. Specifically, FedCure operates through three key rules: (1) a preference rule that optimizes coalition formation by maximizing collective benefits and establishing theoretically stable partitions to reduce non-IID-induced performance degradation; (2) a scheduling rule that integrates the virtual queue technique with Bayesian-estimated coalition dynamics, mitigating efficiency loss while ensuring mean rate stability; and (3) a resource allocation rule that enhances computational efficiency by optimizing client CPU frequencies based on estimated coalition dynamics while satisfying delay requirements. Comprehensive experiments on four real-world datasets demonstrate that FedCure improves accuracy by up to 5.1x compared with four state-of-the-art baselines, while significantly enhancing efficiency with the lowest coefficient of variation 0.0223 for per-round latency and maintaining long-term balance across diverse scenarios.

Text as Any-Modality for Zero-Shot Classification by Consistent Prompt Tuning

The integration of prompt tuning with multimodal learning has shown significant generalization abilities for various downstream tasks. Despite advancements, existing methods heavily depend on massive modality-specific labeled data (e.g., video, audio, and image), or are customized for a single modality. In this study, we present Text as Any-Modality by Consistent Prompt Tuning (TaAM-CPT), a scalable approach for constructing a general representation model toward unlimited modalities using solely text data. TaAM-CPT comprises modality prompt pools, text construction, and modality-aligned text encoders from pre-trained models, which allows for extending new modalities by simply adding prompt pools and modality-aligned text encoders. To harmonize the learning across different modalities, TaAM-CPT designs intra- and inter-modal learning objectives, which can capture category details within modalities while maintaining semantic consistency across different modalities. Benefiting from its scalable architecture and pre-trained models, TaAM-CPT can be seamlessly extended to accommodate unlimited modalities. Remarkably, without any modality-specific labeled data, TaAM-CPT achieves leading results on diverse datasets spanning various modalities, including video classification, image classification, and audio classification. The code is available at https://github.com/Jinx630/TaAM-CPT.

DaringFed: A Dynamic Bayesian Persuasion Pricing for Online Federated Learning under Two-sided Incomplete Information

Online Federated Learning (OFL) is a real-time learning paradigm that sequentially executes parameter aggregation immediately for each random arriving client. To motivate clients to participate in OFL, it is crucial to offer appropriate incentives to offset the training resource consumption. However, the design of incentive mechanisms in OFL is constrained by the dynamic variability of Two-sided Incomplete Information (TII) concerning resources, where the server is unaware of the clients' dynamically changing computational resources, while clients lack knowledge of the real-time communication resources allocated by the server. To incentivize clients to participate in training by offering dynamic rewards to each arriving client, we design a novel Dynamic Bayesian persuasion pricing for online Federated learning (DaringFed) under TII. Specifically, we begin by formulating the interaction between the server and clients as a dynamic signaling and pricing allocation problem within a Bayesian persuasion game, and then demonstrate the existence of a unique Bayesian persuasion Nash equilibrium. By deriving the optimal design of DaringFed under one-sided incomplete information, we further analyze the approximate optimal design of DaringFed with a specific bound under TII. Finally, extensive evaluation conducted on real datasets demonstrate that DaringFed optimizes accuracy and converges speed by 16.99%, while experiments with synthetic datasets validate the convergence of estimate unknown values and the effectiveness of DaringFed in improving the server's utility by up to 12.6%.

Bi-Lipschitz Ansatz for Anti-Symmetric Functions

Motivated by applications for simulating quantum many body functions, we propose a new universal ansatz for approximating anti-symmetric functions. The main advantage of this ansatz over previous alternatives is that it is bi-Lipschitz with respect to a naturally defined metric. As a result, we are able to obtain quantitative approximation results for approximation of Lipschitz continuous antisymmetric functions. Moreover, we provide preliminary experimental evidence to the improved performance of this ansatz for learning antisymmetric functions.

Multi-Label Test-Time Adaptation with Bound Entropy Minimization

Mainstream test-time adaptation (TTA) techniques endeavor to mitigate distribution shifts via entropy minimization for multi-class classification, inherently increasing the probability of the most confident class. However, when encountering multi-label instances, the primary challenge stems from the varying number of labels per image, and prioritizing only the highest probability class inevitably undermines the adaptation of other positive labels. To address this issue, we investigate TTA within multi-label scenario (ML--TTA), developing Bound Entropy Minimization (BEM) objective to simultaneously increase the confidence of multiple top predicted labels. Specifically, to determine the number of labels for each augmented view, we retrieve a paired caption with yielded textual labels for that view. These labels are allocated to both the view and caption, called weak label set and strong label set with the same size k. Following this, the proposed BEM considers the highest top-k predicted labels from view and caption as a single entity, respectively, learning both view and caption prompts concurrently. By binding top-k predicted labels, BEM overcomes the limitation of vanilla entropy minimization, which exclusively optimizes the most confident class. Across the MSCOCO, VOC, and NUSWIDE multi-label datasets, our ML--TTA framework equipped with BEM exhibits superior performance compared to the latest SOTA methods, across various model architectures, prompt initialization, and varying label scenarios. The code is available at https://github.com/Jinx630/ML-TTA.

Controllable Satellite-to-Street-View Synthesis with Precise Pose Alignment and Zero-Shot Environmental Control

Generating street-view images from satellite imagery is a challenging task, particularly in maintaining accurate pose alignment and incorporating diverse environmental conditions. While diffusion models have shown promise in generative tasks, their ability to maintain strict pose alignment throughout the diffusion process is limited. In this paper, we propose a novel Iterative Homography Adjustment (IHA) scheme applied during the denoising process, which effectively addresses pose misalignment and ensures spatial consistency in the generated street-view images. Additionally, currently, available datasets for satellite-to-street-view generation are limited in their diversity of illumination and weather conditions, thereby restricting the generalizability of the generated outputs. To mitigate this, we introduce a text-guided illumination and weather-controlled sampling strategy that enables fine-grained control over the environmental factors. Extensive quantitative and qualitative evaluations demonstrate that our approach significantly improves pose accuracy and enhances the diversity and realism of generated street-view images, setting a new benchmark for satellite-to-street-view generation tasks.

Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectives

The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence behavior in both finite-dimensional and mean-field settings. In particular, for finite-dimensional quadratic min-max games, we obtain long-time convergence in near quasi-static regimes through the hypocoercivity method. For mean-field GDA dynamics, we investigate convergence under a finite-scale ratio using a mixed synchronous-reflection coupling technique.

A Unified Blockwise Measurement Design for Learning Quantum Channels and Lindbladians via Low-Rank Matrix Sensing

Quantum superoperator learning is a pivotal task in quantum information science, enabling accurate reconstruction of unknown quantum operations from measurement data. We propose a robust approach based on the matrix sensing techniques for quantum superoperator learning that extends beyond the positive semidefinite case, encompassing both quantum channels and Lindbladians. We first introduce a randomized measurement design using a near-optimal number of measurements. By leveraging the restricted isometry property (RIP), we provide theoretical guarantees for the identifiability and recovery of low-rank superoperators in the presence of noise. Additionally, we propose a blockwise measurement design that restricts the tomography to the sub-blocks, significantly enhancing performance while maintaining a comparable scale of measurements. We also provide a performance guarantee for this setup. Our approach employs alternating least squares (ALS) with acceleration for optimization in matrix sensing. Numerical experiments validate the efficiency and scalability of the proposed methods.