We propose a generalized variant of Frank-Wolfe algorithm for solving a class of sparse/low-rank optimization problems. Our formulation includes Elastic Net, regularized SVMs and phase retrieval as special cases. The proposed Primal-Dual Block Generalized Frank-Wolfe algorithm reduces the per-iteration cost while maintaining linear convergence rate. The per iteration cost of our method depends on the structural complexity of the solution (i.e.

Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the availability of large-scale data from social networks and sensor networks offers an unprecedented opportunity to predict state-changing events at the individual level. Examples of such events include disease transmission, opinion transition in elections, and rumor propagation. Unlike previous research focusing on the collective effects of social systems, this study makes efficient inferences at the individual level. In order to cope with dynamic interactions among a large number of individuals, we introduce the stochastic kinetic model to capture adaptive transition probabilities and propose an efficient variational inference algorithm the complexity of which grows linearly -- rather than exponentially-- with the number of individuals. To validate this method, we have performed epidemic-dynamics experiments on wireless sensor network data collected from more than ten thousand people over three years. The proposed algorithm was used to track disease transmission and predict the probability of infection for each individual. Our results demonstrate that this method is more efficient than sampling while nonetheless achieving high accuracy.

The most advanced diffusion models have recently adopted increasingly deep stacked networks (e.g., U-Net or Transformer) to promote the generative emergence capabilities of vision generation models similar to large language models (LLMs). However, progressively deeper stacked networks will intuitively cause numerical propagation errors and reduce noisy prediction capabilities on generative data, which hinders massively deep scalable training of vision generation models. In this paper, we first uncover the nature that neural networks being able to effectively perform generative denoising lies in the fact that the intrinsic residual unit has consistent dynamic property with the input signal's reverse diffusion process, thus supporting excellent generative abilities. Afterwards, we stand on the shoulders of two common types of deep stacked networks to propose a unified and massively scalable Neural Residual Diffusion Models framework (Neural-RDM for short), which is a simple yet meaningful change to the common architecture of deep generative networks by introducing a series of learnable gated residual parameters that conform to the generative dynamics. Experimental results on various generative tasks show that the proposed neural residual models obtain state-of-the-art scores on image's and video's generative benchmarks. Rigorous theoretical proofs and extensive experiments also demonstrate the advantages of this simple gated residual mechanism consistent with dynamic modeling in improving the fidelity and consistency of generated content and supporting large-scale scalable training.

Differentiable structure learning is a novel line of causal discovery research that transforms the combinatorial optimization of structural models into a continuous optimization problem. However, the field has lacked feasible methods to integrate partial order constraints, a critical prior information typically used in real-world scenarios, into the differentiable structure learning framework. The main difficulty lies in adapting these constraints, typically suited for the space of total orderings, to the continuous optimization context of structure learning in the graph space. To bridge this gap, this paper formalizes a set of equivalent constraints that map partial orders onto graph spaces and introduces a plug-and-play module for their efficient application. This module preserves the equivalent effect of partial order constraints in the graph space, backed by theoretical validations of correctness and completeness. It significantly enhances the quality of recovered structures while maintaining good efficiency, which learns better structures using 90% fewer samples than the data-based method on a real-world dataset. This result, together with a comprehensive evaluation on synthetic cases, demonstrates our method's ability to effectively improve differentiable structure learning with partial orders.

Compressing word embeddings is important for deploying NLP models in memoryconstrained settings. However, understanding what makes compressed embeddings perform well on downstream tasks is challenging--existing measures of compression quality often fail to distinguish between embeddings that perform well and those that do not. We thus propose the eigenspace overlap score as a new measure. We relate the eigenspace overlap score to downstream performance by developing generalization bounds for the compressed embeddings in terms of this score, in the context of linear and logistic regression. We then show that we can lower bound the eigenspace overlap score for a simple uniform quantization compression method, helping to explain the strong empirical performance of this method. Finally, we show that by using the eigenspace overlap score as a selection criterion between embeddings drawn from a representative set we compressed, we can efficiently identify the better performing embedding with up to 2 lower selection error rates than the next best measure of compression quality, and avoid the cost of training a model for each task of interest.

We thank all the reviewers for their thoughtful feedback. We will clarify these points. R2 and R3 had concerns about the amount of content we deferred to the appendix. In Appendix B.4, we discuss a variant of the embedding reconstruction error applicable to R2 asked about our question answering results in Section 2.3. We use the DrQA model [5], as described in Section 4. R3: R3 asked about the intuition for the proof of Theorem 2. We leverage the Davis-Kahan sin(Θ) theorem, which R3 proposed an idea to use non-uniform quantization to further improve the performance of quantized embeddings.

This paper presents a new mechanism for producing sanitized statistical summaries that achieve differential privacy, called the K-Norm Gradient Mechanism, or KNG. This new approach maintains the strong flexibility of the exponential mechanism, while achieving the powerful utility performance of objective perturbation. KNG starts with an inherent objective function (often an empirical risk), and promotes summaries that are close to minimizing the objective by weighting according to how far the gradient of the objective function is from zero. Working with the gradient instead of the original objective function allows for additional flexibility as one can penalize using different norms. We show that, unlike the exponential mechanism, the noise added by KNG is asymptotically negligible compared to the statistical error for many problems. In addition to theoretical guarantees on privacy and utility, we confirm the utility of KNG empirically in the settings of linear and quantile regression through simulations.

In this technical supplement, we provide detailed insights and additional results to support our main paper. Section A.1 outlines the generation process of the SynRS3D dataset, including the tools and plugins used. It also covers the licenses for these plugins. Section A.3 elaborates on the evaluation metrics for different tasks, including the proposed F Section A.4 describes the experimental setup and the selection of hyperparameters for the RS3DAda method. Section A.5 presents the ablation study results and analysis for the RS3DAda method. Section A.6 provides supplementary experimental results combining SynRS3D and real data scenarios, complementing Section 5.2 of the main paper. Section A.9 highlights the performance of models trained on the SynRS3D dataset using RS3DAda in the critical application of disaster mapping in remote sensing. A.1 Detailed Generation Workflow of SynRS3D The generation workflow of SynRS3D involves several key steps, from initializing sensor and sunlight parameters to generating the layout, geometry, and textures of the scene. This comprehensive process ensures that the generated SynRS3D mimics real-world remote sensing scenarios with high fidelity. The main steps of the workflow are as follows: Initialization: Set up the sensor and sunlight parameters using uniform and normal distributions to simulate various conditions. Layout Generation: Define the grid and terrain parameters to create diverse urban and natural environments. Texture Generation: Use advanced models like GPT-4 [1] and Stable Diffusion [18] to generate realistic textures for different categories of land cover.

Global semantic 3D understanding from single-view high-resolution remote sensing (RS) imagery is crucial for Earth observation (EO). However, this task faces significant challenges due to the high costs of annotations and data collection, as well as geographically restricted data availability. To address these challenges, synthetic data offer a promising solution by being unrestricted and automatically annotatable, thus enabling the provision of large and diverse datasets. We develop a specialized synthetic data generation pipeline for EO and introduce SynRS3D, the largest synthetic RS dataset. SynRS3D comprises 69,667 high-resolution optical images that cover six different city styles worldwide and feature eight land cover types, precise height information, and building change masks. To further enhance its utility, we develop a novel multi-task unsupervised domain adaptation (UDA) method, RS3DAda, coupled with our synthetic dataset, which facilitates the RS-specific transition from synthetic to real scenarios for land cover mapping and height estimation tasks, ultimately enabling global monocular 3D semantic understanding based on synthetic data. Extensive experiments on various real-world datasets demonstrate the adaptability and effectiveness of our synthetic dataset and the proposed RS3DAda method. SynRS3D and related codes are available at https://github.com/JTRNEO/SynRS3D.

Visible-Infrared Person Re-identification (VI-ReID) is a challenging cross-modal retrieval task due to significant modality differences, primarily resulting from the absence of color information in the infrared modality. The development of large foundation models like Large Language Models (LLMs) and Vision Language Models (VLMs) motivates us to explore a feasible solution to empower VI-ReID with off-the-shelf large foundation models. To this end, we propose a novel Textenhanced VI-ReID framework driven by Large Foundation Models (TVI-LFM). The core idea is to enrich the representation of the infrared modality with textual descriptions automatically generated by VLMs. Specifically, we incorporate a pre-trained VLM to extract textual features from texts generated by VLM and augmented by LLM, and incrementally fine-tune the text encoder to minimize the domain gap between generated texts and original visual modalities. Meanwhile, to enhance the infrared modality with extracted textual representations, we leverage modality alignment capabilities of VLMs and VLM-generated feature-level filters.