The recent progress in Vision-Language Models (VLMs) has broadened the scope of multimodal applications. However, evaluations often remain limited to functional tasks, neglecting abstract dimensions such as personality traits and human values. To address this gap, we introduce Value-Spectrum, a novel Visual Question Answering (VQA) benchmark aimed at assessing VLMs based on Schwartz's value dimensions that capture core values guiding people's preferences and actions. We designed a VLM agent pipeline to simulate video browsing and constructed a vector database comprising over 50,000 short videos from TikTok, YouTube Shorts, and Instagram Reels. These videos span multiple months and cover diverse topics, including family, health, hobbies, society, technology, etc. Benchmarking on Value-Spectrum highlights notable variations in how VLMs handle value-oriented content. Beyond identifying VLMs' intrinsic preferences, we also explored the ability of VLM agents to adopt specific personas when explicitly prompted, revealing insights into the adaptability of the model in role-playing scenarios. These findings highlight the potential of Value-Spectrum as a comprehensive evaluation set for tracking VLM alignments in value-based tasks and abilities to simulate diverse personas.

In this paper, we leverage the power of latent diffusion models to generate synthetic time series tabular data. Along with the temporal and feature correlations, the heterogeneous nature of the feature in the table has been one of the main obstacles in time series tabular data modeling. We tackle this problem by combining the ideas of the variational auto-encoder (VAE) and the denoising diffusion probabilistic model (DDPM). Our model named as \texttt{TimeAutoDiff} has several key advantages including (1) Generality: the ability to handle the broad spectrum of time series tabular data from single to multi-sequence datasets; (2) Good fidelity and utility guarantees: numerical experiments on six publicly available datasets demonstrating significant improvements over state-of-the-art models in generating time series tabular data, across four metrics measuring fidelity and utility; (3) Fast sampling speed: entire time series data generation as opposed to the sequential data sampling schemes implemented in the existing diffusion-based models, eventually leading to significant improvements in sampling speed, (4) Entity conditional generation: the first implementation of conditional generation of multi-sequence time series tabular data with heterogenous features in the literature, enabling scenario exploration across multiple scientific and engineering domains. Codes are in preparation for release to the public, but available upon request.

Fine-tuning large-scale pre-trained models via transfer learning is an emerging important paradigm for a wide range of downstream tasks, with performance heavily reliant on extensive data. Federated learning (FL), as a distributed framework, provides a secure solution to train models on local datasets while safeguarding raw sensitive data. However, FL networks encounter high communication costs due to the massive parameters of large-scale pre-trained models, necessitating parameter-efficient methods. Notably, parameter efficient fine tuning, such as Low-Rank Adaptation (LoRA), has shown remarkable success in fine-tuning pre-trained models. However, prior research indicates that the fixed parameter budget may be prone to the overfitting or slower convergence. To address this challenge, we propose a Simulated Annealing-based Federated Learning with LoRA tuning (SA-FedLoRA) approach by reducing trainable parameters. Specifically, SA-FedLoRA comprises two stages: initiating and annealing. (1) In the initiating stage, we implement a parameter regularization approach during the early rounds of aggregation, aiming to mitigate client drift and accelerate the convergence for the subsequent tuning. (2) In the annealing stage, we allocate higher parameter budget during the early 'heating' phase and then gradually shrink the budget until the 'cooling' phase. This strategy not only facilitates convergence to the global optimum but also reduces communication costs. Experimental results demonstrate that SA-FedLoRA is an efficient FL, achieving superior performance to FedAvg and significantly reducing communication parameters by up to 93.62%.

The classical non-greedy algorithm (NGA) and the recently proposed proximal alternating minimization method with extrapolation (PAMe) for $L_1$-norm PCA are revisited and their finite-step convergence are studied. It is first shown that NGA can be interpreted as a conditional subgradient or an alternating maximization method. By recognizing it as a conditional subgradient, we prove that the iterative points generated by the algorithm will be constant in finitely many steps under a certain full-rank assumption; such an assumption can be removed when the projection dimension is one. By treating the algorithm as an alternating maximization, we then prove that the objective value will be fixed after at most $\left\lceil\frac{F^{\max}}{\tau_0} \right\rceil$ steps, where the stopping point satisfies certain optimality conditions. Then, a slight modification of NGA with improved convergence properties is analyzed. It is shown that the iterative points generated by the modified algorithm will not change after at most $\left\lceil\frac{2F^{\max}}{\tau} \right\rceil$ steps; furthermore, the stopping point satisfies certain optimality conditions if the proximal parameter $\tau$ is small enough. For PAMe, it is proved that the sign variable will remain constant after finitely many steps and the algorithm can output a point satisfying certain optimality condition, if the parameters are small enough and a full rank assumption is satisfied. Moreover, if there is no proximal term on the projection matrix related subproblem, then the iterative points generated by this modified algorithm will not change after at most $\left\lceil \frac{4F^{\max}}{\tau(1-\gamma)} \right\rceil$ steps and the stopping point also satisfies certain optimality conditions, provided similar assumptions as those for PAMe. The full rank assumption can be removed when the projection dimension is one.

Sparse tensor best rank-1 approximation (BR1Approx), which is a sparsity generalization of the dense tensor BR1Approx, and is a higher-order extension of the sparse matrix BR1Approx, is one of the most important problems in sparse tensor decomposition and related problems arising from statistics and machine learning. By exploiting the multilinearity as well as the sparsity structure of the problem, four approximation algorithms are proposed, which are easily implemented, of low computational complexity, and can serve as initial procedures for iterative algorithms. In addition, theoretically guaranteed worst-case approximation lower bounds are proved for all the algorithms. We provide numerical experiments on synthetic and real data to illustrate the effectiveness of the proposed algorithms.

Low rank tensor learning, such as tensor completion and multilinear multitask learning, has received much attention in recent years. In this paper, we propose higher order matching pursuit for low rank tensor learning problems with a convex or a nonconvex cost function, which is a generalization of the matching pursuit type methods. At each iteration, the main cost of the proposed methods is only to compute a rank-one tensor, which can be done efficiently, making the proposed methods scalable to large scale problems. Moreover, storing the resulting rank-one tensors is of low storage requirement, which can help to break the curse of dimensionality. The linear convergence rate of the proposed methods is established in various circumstances. Along with the main methods, we also provide a method of low computational complexity for approximately computing the rank-one tensors, with provable approximation ratio, which helps to improve the efficiency of the main methods and to analyze the convergence rate. Experimental results on synthetic as well as real datasets verify the efficiency and effectiveness of the proposed methods.