This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to separate them by using similar ideas as RPCA? Is there any benefit in treating the manifold as a whole as opposed to treating each local region independently? We answer these two questions affirmatively by proposing and analyzing an optimization framework that separates the sparse component from the manifold under noisy data. Theoretical error bounds are provided when the tangent spaces of the manifold satisfy certain incoherence conditions. We also provide a near optimal choice of the tuning parameters for the proposed optimization formulation with the help of a new curvature estimation method. The efficacy of our method is demonstrated on both synthetic and real datasets.

The state-of-the-art approximate nearest neighbor search (ANNS) algorithm builds a large proximity graph on the dataset and performs a greedy beam search, which may bring many unnecessary explorations. We develop a novel framework, namely corssing sparse proximity graph (CSPG), based on random partitioning of the dataset. It produces a smaller sparse proximity graph for each partition and routing vectors that bind all the partitions. An efficient two-staged approach is designed for exploring CSPG, with fast approaching and cross-partition expansion. We theoretically prove that CSPG can accelerate the existing graph-based ANNS algorithms by reducing unnecessary explorations. In addition, we conduct extensive experiments on benchmark datasets. The experimental results confirm that the existing graph-based methods can be significantly outperformed by incorporating CSPG, achieving 1.5x to 2x speedups of QPS in almost all recalls.

Datasets play a pivotal role in training visual models, facilitating the development of abstract understandings of visual features through diverse image samples and multidimensional attributes. However, in the realm of aesthetic evaluation of artistic images, datasets remain relatively scarce. Existing painting datasets are often characterized by limited scoring dimensions and insufficient annotations, thereby constraining the advancement and application of automatic aesthetic evaluation methods in the domain of painting. To bridge this gap, we introduce the Aesthetics Paintings and Drawings Dataset (APDD), the first comprehensive collection of paintings encompassing 24 distinct artistic categories and 10 aesthetic attributes. Building upon the initial release of APDDv1[Jin et al., 2024], our ongoing research has identified opportunities for enhancement in data scale and annotation precision. Consequently, APDDv2 boasts an expanded image corpus and improved annotation quality, featuring detailed language comments to better cater to the needs of both researchers and practitioners seeking high-quality painting datasets. Furthermore, we present an updated version of the Art Assessment Network for Specific Painting Styles, denoted as ArtCLIP. Experimental validation demonstrates the superior performance of this revised model in the realm of aesthetic evaluation, surpassing its predecessor in accuracy and efficacy.

This paper focuses on the problem of computing an ǫ-optimal policy in a discounted Markov Decision Process (MDP) provided that we can access the reward and transition function through a generative model. We propose an algorithm that is initially agnostic to the MDP but that can leverage the specific MDP structure, expressed in terms of variances of the rewards and next-state value function, and gaps in the optimal action-value function to reduce the sample complexity needed to find a good policy, precisely highlighting the contribution of each state-action pair to the final sample complexity. A key feature of our analysis is that it removes all horizon dependencies in the sample complexity of suboptimal actions except for the intrinsic scaling of the value function and a constant additive term.

Table 1: Averaged samples to reach the reward threshold on Mujoco-V1. Rebuttal-Figure 1: LA-MCTS on Walker2d Table. 2 in the main paper uses Mujoco-V2. We sincerely thank reviewers R1, R2, R3 for their constructive feedbacks. We redo the experiment on Mujoco-V1 in Table. 1. LA-MCTS shows This is when a plateau of regret happens. We will clarify it in the paper.

The predict-then-optimize framework is fundamental in many practical settings: predict the unknown parameters of an optimization problem, and then solve the problem using the predicted values of the parameters. A natural loss function in this environment is to consider the cost of the decisions induced by the predicted parameters, in contrast to the prediction error of the parameters. This loss function was recently introduced [7] and christened Smart Predict-then-Optimize (SPO) loss. Since the SPO loss is nonconvex and noncontinuous, standard results for deriving generalization bounds do not apply. In this work, we provide an assortment of generalization bounds for the SPO loss function. In particular, we derive bounds based on the Natarajan dimension that, in the case of a polyhedral feasible region, scale at most logarithmically in the number of extreme points, but, in the case of a general convex set, have poor dependence on the dimension. By exploiting the structure of the SPO loss function and an additional strong convexity assumption on the feasible region, we can dramatically improve the dependence on the dimension via an analysis and corresponding bounds that are akin to the margin guarantees in classification problems.

Designing computationally efficient network architectures remains an ongoing necessity in computer vision. In this paper, we adapt Mamba, a state-space language model, into VMamba, a vision backbone with linear time complexity. At the core of VMamba is a stack of Visual State-Space (VSS) blocks with the 2D Selective Scan (SS2D) module. By traversing along four scanning routes, SS2D bridges the gap between the ordered nature of 1D selective scan and the non-sequential structure of 2D vision data, which facilitates the collection of contextual information from various sources and perspectives. Based on the VSS blocks, we develop a family of VMamba architectures and accelerate them through a succession of architectural and implementation enhancements. Extensive experiments demonstrate VMamba's promising performance across diverse visual perception tasks, highlighting its superior input scaling efficiency compared to existing benchmark models.

Consistent losses are well-motivated theoretically, yet for large n, such as in information retrieval and structured prediction tasks, their optimization may be computationally infeasible.

Generative Adversarial Networks (GANs) enjoy great success at image generation, but have proven difficult to train in the domain of natural language. Challenges with gradient estimation, optimization instability, and mode collapse have lead practitioners to resort to maximum likelihood pre-training, followed by small amounts of adversarial fine-tuning. The benefits of GAN fine-tuning for language generation are unclear, as the resulting models produce comparable or worse samples than traditional language models. We show it is in fact possible to train a language GAN from scratch -- without maximum likelihood pre-training. We combine existing techniques such as large batch sizes, dense rewards and discriminator regularization to stabilize and improve language GANs. The resulting model, ScratchGAN, performs comparably to maximum likelihood training on EMNLP2017 News and WikiText-103 corpora according to quality and diversity metrics.

We introduce the CRONOS algorithm for convex optimization of two-layer neural networks. CRONOS is the first algorithm capable of scaling to high-dimensional datasets such as ImageNet, which are ubiquitous in modern deep learning. This significantly improves upon prior work, which has been restricted to downsampled versions of MNIST and CIFAR-10. Taking CRONOS as a primitive, we then develop a new algorithm called CRONOS-AM, which combines CRONOS with alternating minimization, to obtain an algorithm capable of training multilayer networks with arbitrary architectures. Our theoretical analysis proves that CRONOS converges to the global minimum of the convex reformulation under mild assumptions.