We consider the noisy matrix sensing problem in the over-parameterization setting, where the estimated rank $r$ is larger than the true rank $r_\star$. Specifically, our main objective is to recover a matrix $ X_\star \in \mathbb{R}^{n_1 \times n_2} $ with rank $ r_\star $ from noisy measurements using an over-parameterized factorized form $ LR^\top $, where $ L \in \mathbb{R}^{n_1 \times r}, \, R \in \mathbb{R}^{n_2 \times r} $ and $ \min\{n_1, n_2\} \ge r > r_\star $, with the true rank $ r_\star $ being unknown. Recently, preconditioning methods have been proposed to accelerate the convergence of matrix sensing problem compared to vanilla gradient descent, incorporating preconditioning terms $ (L^\top L + \lambda I)^{-1} $ and $ (R^\top R + \lambda I)^{-1} $ into the original gradient. However, these methods require careful tuning of the damping parameter $\lambda$ and are sensitive to initial points and step size. To address these limitations, we propose the alternating preconditioned gradient descent (APGD) algorithm, which alternately updates the two factor matrices, eliminating the need for the damping parameter and enabling faster convergence with larger step sizes. We theoretically prove that APGD achieves near-optimal error convergence at a linear rate, starting from arbitrary random initializations. Through extensive experiments, we validate our theoretical results and demonstrate that APGD outperforms other methods, achieving the fastest convergence rate. Notably, both our theoretical analysis and experimental results illustrate that APGD does not rely on the initialization procedure, making it more practical and versatile.

Lifelong person re-identification (LReID) exhibits a contradictory relationship between intra-domain discrimination and inter-domain gaps when learning from continuous data. Intra-domain discrimination focuses on individual nuances (e.g. clothing type, accessories, etc.), while inter-domain gaps emphasize domain consistency. Achieving a trade-off between maximizing intra-domain discrimination and minimizing inter-domain gaps is a crucial challenge for improving LReID performance. Most existing methods aim to reduce inter-domain gaps through knowledge distillation to maintain domain consistency. However, they often ignore intra-domain discrimination. To address this challenge, we propose a novel domain consistency representation learning (DCR) model that explores global and attribute-wise representations as a bridge to balance intra-domain discrimination and inter-domain gaps. At the intra-domain level, we explore the complementary relationship between global and attribute-wise representations to improve discrimination among similar identities. Excessive learning intra-domain discrimination can lead to catastrophic forgetting. We further develop an attribute-oriented anti-forgetting (AF) strategy that explores attribute-wise representations to enhance inter-domain consistency, and propose a knowledge consolidation (KC) strategy to facilitate knowledge transfer. Extensive experiments show that our DCR model achieves superior performance compared to state-of-the-art LReID methods. Our code will be available soon.

Lifelong Person Re-Identification (LReID) aims to continuously learn from successive data streams, matching individuals across multiple cameras. The key challenge for LReID is how to effectively preserve old knowledge while incrementally learning new information, which is caused by task-level domain gaps and limited old task datasets. Existing methods based on CNN backbone are insufficient to explore the representation of each instance from different perspectives, limiting model performance on limited old task datasets and new task datasets. Unlike these methods, we propose a Diverse Representations Embedding (DRE) framework that first explores a pure transformer for LReID. The proposed DRE preserves old knowledge while adapting to new information based on instance-level and task-level layout. Concretely, an Adaptive Constraint Module (ACM) is proposed to implement integration and push away operations between multiple overlapping representations generated by transformer-based backbone, obtaining rich and discriminative representations for each instance to improve adaptive ability of LReID. Based on the processed diverse representations, we propose Knowledge Update (KU) and Knowledge Preservation (KP) strategies at the task-level layout by introducing the adjustment model and the learner model. KU strategy enhances the adaptive learning ability of learner models for new information under the adjustment model prior, and KP strategy preserves old knowledge operated by representation-level alignment and logit-level supervision in limited old task datasets while guaranteeing the adaptive learning information capacity of the LReID model. Compared to state-of-the-art methods, our method achieves significantly improved performance in holistic, large-scale, and occluded datasets.

This paper considers the problem of recovering a tensor with an underlying low-tubal-rank structure from a small number of corrupted linear measurements. Traditional approaches tackling such a problem require the computation of tensor Singular Value Decomposition (t-SVD), that is a computationally intensive process, rendering them impractical for dealing with large-scale tensors. Aim to address this challenge, we propose an efficient and effective low-tubal-rank tensor recovery method based on a factorization procedure akin to the Burer-Monteiro (BM) method. Precisely, our fundamental approach involves decomposing a large tensor into two smaller factor tensors, followed by solving the problem through factorized gradient descent (FGD). This strategy eliminates the need for t-SVD computation, thereby reducing computational costs and storage requirements. We provide rigorous theoretical analysis to ensure the convergence of FGD under both noise-free and noisy situations. Additionally, it is worth noting that our method does not require the precise estimation of the tensor tubal-rank. Even in cases where the tubal-rank is slightly overestimated, our approach continues to demonstrate robust performance. A series of experiments have been carried out to demonstrate that, as compared to other popular ones, our approach exhibits superior performance in multiple scenarios, in terms of the faster computational speed and the smaller convergence error.

We propose residual denoising diffusion models (RDDM), a novel dual diffusion process that decouples the traditional single denoising diffusion process into residual diffusion and noise diffusion. This dual diffusion framework expands the denoising-based diffusion models, initially uninterpretable for image restoration, into a unified and interpretable model for both image generation and restoration by introducing residuals. Specifically, our residual diffusion represents directional diffusion from the target image to the degraded input image and explicitly guides the reverse generation process for image restoration, while noise diffusion represents random perturbations in the diffusion process. The residual prioritizes certainty, while the noise emphasizes diversity, enabling RDDM to effectively unify tasks with varying certainty or diversity requirements, such as image generation and restoration. We demonstrate that our sampling process is consistent with that of DDPM and DDIM through coefficient transformation, and propose a partially path-independent generation process to better understand the reverse process. Notably, our RDDM enables a generic UNet, trained with only an $\ell _1$ loss and a batch size of 1, to compete with state-of-the-art image restoration methods. We provide code and pre-trained models to encourage further exploration, application, and development of our innovative framework (https://github.com/nachifur/RDDM).

Reviewing plays an important role when learning knowledge. The knowledge acquisition at a certain time point may be strongly inspired with the help of previous experience. Thus the knowledge growing procedure should show strong relationship along the temporal dimension. In our research, we find that during the network training, the evolution of feature map follows temporal sequence property. A proper temporal supervision may further improve the network training performance. Inspired by this observation, we propose Temporal Supervised Knowledge Distillation (TSKD). Specifically, we extract the spatiotemporal features in the different training phases of student by convolutional Long Short-term memory network (Conv-LSTM). Then, we train the student net through a dynamic target, rather than static teacher network features. This process realizes the refinement of old knowledge in student network, and utilizes it to assist current learning. Extensive experiments verify the effectiveness and advantages of our method over existing knowledge distillation methods, including various network architectures and different tasks (image classification and object detection) .