Zerui Tao

Chao Li, Junhua Zeng, Zerui Tao et al. · tsinghua

Recent works put much effort into tensor network structure search (TN-SS), aiming to select suitable tensor network (TN) structures, involving the TN-ranks, formats, and so on, for the decomposition or learning tasks. In this paper, we consider a practical variant of TN-SS, dubbed TN permutation search (TN-PS), in which we search for good mappings from tensor modes onto TN vertices (core tensors) for compact TN representations. We conduct a theoretical investigation of TN-PS and propose a practically-efficient algorithm to resolve the problem. Theoretically, we prove the counting and metric properties of search spaces of TN-PS, analyzing for the first time the impact of TN structures on these unique properties. Numerically, we propose a novel meta-heuristic algorithm, in which the searching is done by randomly sampling in a neighborhood established in our theory, and then recurrently updating the neighborhood until convergence. Numerical results demonstrate that the new algorithm can reduce the required model size of TNs in extensive benchmarks, implying the improvement in the expressive power of TNs. Furthermore, the computational cost for the new algorithm is significantly less than that in~\cite{li2020evolutionary}.

Zerui Tao, Qibin Zhao

Low-rank tensor decomposition (TD) is usually effective on clean, fully observed data, but it often degrades under severe missingness or noise. Low-rankness is itself a useful but limited structural prior, and additional handcrafted priors (e.g., sparsity or smoothness) still fall short of capturing the rich statistics of real-world data. To compensate for this weak inductive bias under heavy corruption, one would like to inject a learned, data-driven prior; however, the state-of-the-art diffusion models are not readily compatible with current TD and tractable posterior inference. To address these challenges, we introduce DiffBCP, a hybrid-prior Bayesian CP decomposition framework that couples a cumulative shrinkage process prior over the CP factors for automatic rank selection with an off-the-shelf pre-trained diffusion model as an implicit data prior on the reconstructed tensor. To make posterior inference tractable despite the coupling among the likelihood, low-rank constraint, and diffusion prior, we develop a split Gibbs sampler: CP factors admit conjugate updates, while the diffusion block is sampled via low-rank-guided denoising. A noise-adaptive coupling schedule further reduces sensitivity to hand-tuned annealing. Experiments on image inpainting and denoising, including high-resolution out-of-distribution images, show consistent gains over Bayesian, nonlinear, and plug-and-play TD baselines.

Wenjing lu, Zerui Tao, Dongping Zhang et al.

CLIP delivers strong zero-shot classification but remains highly vulnerable to adversarial attacks. Previous work of adversarial fine-tuning largely focuses on matching the predicted logits between clean and adversarial examples, which overlooks uncertainty calibration and may degrade the zero-shot generalization. A common expectation in reliable uncertainty estimation is that predictive uncertainty should increase as inputs become more difficult or shift away from the training distribution. However, we frequently observe the opposite in the adversarial setting: perturbations not only degrade accuracy but also suppress uncertainty, leading to severe miscalibration and unreliable over-confidence. This overlooked phenomenon highlights a critical reliability gap beyond robustness. To bridge this gap, we propose a novel adversarial fine-tuning objective for CLIP considering both prediction accuracy and uncertainty alignments. By reparameterizing the output of CLIP as the concentration parameter of a Dirichlet distribution, we propose a unified representation that captures relative semantic structure and the magnitude of predictive confidence. Our objective aligns these distributions holistically under perturbations, moving beyond single-logit anchoring and restoring calibrated uncertainty. Experiments on multiple zero-shot classification benchmarks demonstrate that our approach effectively restores calibrated uncertainty and achieves competitive adversarial robustness while maintaining clean accuracy.

Chao Li, Zerui Tao, Yuchen Cong et al.

Matrix product operator Born machines (MPO-BMs) are tractable tensor-network models for probabilistic modeling, but their efficient approximation capability remains unclear. We characterize this boundary from both negative and positive perspectives. First, we prove that KL approximation is NP-hard for MPO-BMs in the continuous setting, ruling out universal efficient approximation in the worst case. Second, for score-based variational inference, we show that, under a locality and spectral-gap conditions on the loss-induced Hamiltonian, structured targets (e.g., path-graph Markov random fields) admit MPO-BM approximations with polynomial bond dimension and provable KL guarantees. Third, under the same locality structure, we prove that polynomially many score queries suffice to estimate the induced Hamiltonian and obtain such guarantees. Our results provide a theoretical characterization of when MPO-BMs are fundamentally hard to approximate and when they become efficiently learnable.

Guang Lin, Zerui Tao, Jianhai Zhang et al.

Diffusion model (DM) based adversarial purification (AP) has proven to be a powerful defense method that can remove adversarial perturbations and generate a purified example without threats. In principle, the pre-trained DMs can only ensure that purified examples conform to the same distribution of the training data, but it may inadvertently compromise the semantic information of input examples, leading to misclassification of purified examples. Recent advancements introduce guided diffusion techniques to preserve semantic information while removing the perturbations. However, these guidances often rely on distance measures between purified examples and diffused examples, which can also preserve perturbations in purified examples. To further unleash the robustness power of DM-based AP, we propose an adversarial guided diffusion model (AGDM) by introducing a novel adversarial guidance that contains sufficient semantic information but does not explicitly involve adversarial perturbations. The guidance is modeled by an auxiliary neural network obtained with adversarial training, considering the distance in the latent representations rather than at the pixel-level values. Extensive experiments are conducted on CIFAR-10, CIFAR-100 and ImageNet to demonstrate that our method is effective for simultaneously maintaining semantic information and removing the adversarial perturbations. In addition, comprehensive comparisons show that our method significantly enhances the robustness of existing DM-based AP, with an average robust accuracy improved by up to 7.30% on CIFAR-10.

Zerui Tao, Toshihisa Tanaka, Qibin Zhao

In numerous applications, binary reactions or event counts are observed and stored within high-order tensors. Tensor decompositions (TDs) serve as a powerful tool to handle such high-dimensional and sparse data. However, many traditional TDs are explicitly or implicitly designed based on the Gaussian distribution, which is unsuitable for discrete data. Moreover, most TDs rely on predefined multi-linear structures, such as CP and Tucker formats. Therefore, they may not be effective enough to handle complex real-world datasets. To address these issues, we propose ENTED, an \underline{E}fficient \underline{N}onparametric \underline{TE}nsor \underline{D}ecomposition for binary and count tensors. Specifically, we first employ a nonparametric Gaussian process (GP) to replace traditional multi-linear structures. Next, we utilize the \pg augmentation which provides a unified framework to establish conjugate models for binary and count distributions. Finally, to address the computational issue of GPs, we enhance the model by incorporating sparse orthogonal variational inference of inducing points, which offers a more effective covariance approximation within GPs and stochastic natural gradient updates for nonparametric models. We evaluate our model on several real-world tensor completion tasks, considering binary and count datasets. The results manifest both better performance and computational advantages of the proposed model.

Zerui Tao, Toshihisa Tanaka, Qibin Zhao

Tensor decompositions play a crucial role in numerous applications related to multi-way data analysis. By employing a Bayesian framework with sparsity-inducing priors, Bayesian Tensor Ring (BTR) factorization offers probabilistic estimates and an effective approach for automatically adapting the tensor ring rank during the learning process. However, previous BTR method employs an Automatic Relevance Determination (ARD) prior, which can lead to sub-optimal solutions. Besides, it solely focuses on continuous data, whereas many applications involve discrete data. More importantly, it relies on the Coordinate-Ascent Variational Inference (CAVI) algorithm, which is inadequate for handling large tensors with extensive observations. These limitations greatly limit its application scales and scopes, making it suitable only for small-scale problems, such as image/video completion. To address these issues, we propose a novel BTR model that incorporates a nonparametric Multiplicative Gamma Process (MGP) prior, known for its superior accuracy in identifying latent structures. To handle discrete data, we introduce the Pólya-Gamma augmentation for closed-form updates. Furthermore, we develop an efficient Gibbs sampler for consistent posterior simulation, which reduces the computational complexity of previous VI algorithm by two orders, and an online EM algorithm that is scalable to extremely large tensors. To showcase the advantages of our model, we conduct extensive experiments on both simulation data and real-world applications.

Haixu Liu, Penghao Jiang, Zerui Tao et al.

Predicting plant species composition in specific spatiotemporal contexts plays an important role in biodiversity management and conservation, as well as in improving species identification tools. Our work utilizes 88,987 plant survey records conducted in specific spatiotemporal contexts across Europe. We also use the corresponding satellite images, time series data, climate time series, and other rasterized environmental data such as land cover, human footprint, bioclimatic, and soil variables as training data to train the model to predict the outcomes of 4,716 plant surveys. We propose a feature construction and result correction method based on the graph structure. Through comparative experiments, we select the best-performing backbone networks for feature extraction in both temporal and image modalities. In this process, we built a backbone network based on the Swin-Transformer Block for extracting temporal Cubes features. We then design a hierarchical cross-attention mechanism capable of robustly fusing features from multiple modalities. During training, we adopt a 10-fold cross-fusion method based on fine-tuning and use a Threshold Top-K method for post-processing. Ablation experiments demonstrate the improvements in model performance brought by our proposed solution pipeline.

Peng Wang, Li Shen, Zerui Tao et al.

Averaging iterations of Stochastic Gradient Descent (SGD) have achieved empirical success in training deep learning models, such as Stochastic Weight Averaging (SWA), Exponential Moving Average (EMA), and LAtest Weight Averaging (LAWA). Especially, with a finite weight averaging method, LAWA can attain faster convergence and better generalization. However, its theoretical explanation is still less explored since there are fundamental differences between finite and infinite settings. In this work, we first generalize SGD and LAWA as Finite Weight Averaging (FWA) and explain their advantages compared to SGD from the perspective of optimization and generalization. A key challenge is the inapplicability of traditional methods in the sense of expectation or optimal values for infinite-dimensional settings in analyzing FWA's convergence. Second, the cumulative gradients introduced by FWA introduce additional confusion to the generalization analysis, especially making it more difficult to discuss them under different assumptions. Extending the final iteration convergence analysis to the FWA, this paper, under a convexity assumption, establishes a convergence bound $\mathcal{O}(\log\left(\frac{T}{k}\right)/\sqrt{T})$, where $k\in[1, T/2]$ is a constant representing the last $k$ iterations. Compared to SGD with $\mathcal{O}(\log(T)/\sqrt{T})$, we prove theoretically that FWA has a faster convergence rate and explain the effect of the number of average points. In the generalization analysis, we find a recursive representation for bounding the cumulative gradient using mathematical induction. We provide bounds for constant and decay learning rates and the convex and non-convex cases to show the good generalization performance of FWA. Finally, experimental results on several benchmarks verify our theoretical results.

Guang Lin, Duc Thien Nguyen, Zerui Tao et al.

Deep neural networks are known to be vulnerable to well-designed adversarial attacks. Although numerous defense strategies have been proposed, many are tailored to the specific attacks or tasks and often fail to generalize across diverse scenarios. In this paper, we propose Tensor Network Purification (TNP), a novel model-free adversarial purification method by a specially designed tensor network decomposition algorithm. TNP depends neither on the pre-trained generative model nor the specific dataset, resulting in strong robustness across diverse adversarial scenarios. To this end, the key challenge lies in relaxing Gaussian-noise assumptions of classical decompositions and accommodating the unknown distribution of adversarial perturbations. Unlike the low-rank representation of classical decompositions, TNP aims to reconstruct the unobserved clean examples from an adversarial example. Specifically, TNP leverages progressive downsampling and introduces a novel adversarial optimization objective to address the challenge of minimizing reconstruction error but without inadvertently restoring adversarial perturbations. Extensive experiments conducted on CIFAR-10, CIFAR-100, and ImageNet demonstrate that our method generalizes effectively across various norm threats, attack types, and tasks, providing a versatile and promising adversarial purification technique.

Peng Wang, Shengchao Hu, Zerui Tao et al.

Weight averaging has become a standard technique for enhancing model performance. However, methods such as Stochastic Weight Averaging (SWA) and Latest Weight Averaging (LAWA) often require manually designed procedures to sample from the training trajectory, and the results depend heavily on hyperparameter tuning. To minimize human effort, this paper proposes a simple yet efficient algorithm called Selective Weight Averaging (SeWA), which adaptively selects checkpoints during the final stages of training for averaging. Based on SeWA, we show that only a few points are needed to achieve better generalization and faster convergence. Theoretically, solving the discrete subset selection problem is inherently challenging. To address this, we transform it into a continuous probabilistic optimization framework and employ the Gumbel-Softmax estimator to learn the non-differentiable mask for each checkpoint. Further, we theoretically derive the SeWA's stability-based generalization bounds, which are sharper than that of SGD under both convex and non-convex assumptions. Finally, solid extended experiments in various domains, including behavior cloning, image classification, and text classification, further validate the effectiveness of our approach.

Zerui Tao, Yuhta Takida, Naoki Murata et al.

Parameter-Efficient Fine-Tuning (PEFT) of text-to-image models has become an increasingly popular technique with many applications. Among the various PEFT methods, Low-Rank Adaptation (LoRA) and its variants have gained significant attention due to their effectiveness, enabling users to fine-tune models with limited computational resources. However, the approximation gap between the low-rank assumption and desired fine-tuning weights prevents the simultaneous acquisition of ultra-parameter-efficiency and better performance. To reduce this gap and further improve the power of LoRA, we propose a new PEFT method that combines two classes of adaptations, namely, transform and residual adaptations. In specific, we first apply a full-rank and dense transform to the pre-trained weight. This learnable transform is expected to align the pre-trained weight as closely as possible to the desired weight, thereby reducing the rank of the residual weight. Then, the residual part can be effectively approximated by more compact and parameter-efficient structures, with a smaller approximation error. To achieve ultra-parameter-efficiency in practice, we design highly flexible and effective tensor decompositions for both the transform and residual adaptations. Additionally, popular PEFT methods such as DoRA can be summarized under this transform plus residual adaptation scheme. Experiments are conducted on fine-tuning Stable Diffusion models in subject-driven and controllable generation. The results manifest that our method can achieve better performances and parameter efficiency compared to LoRA and several baselines.

Haixu Liu, Penghao Jiang, Zerui Tao

As the volume of digital image data increases, the effectiveness of image classification intensifies. This study introduces a robust multi-label classification system designed to assign multiple labels to a single image, addressing the complexity of images that may be associated with multiple categories (ranging from 1 to 19, excluding 12). We propose a multi-modal classifier that merges advanced image recognition algorithms with Natural Language Processing (NLP) models, incorporating a fusion module to integrate these distinct modalities. The purpose of integrating textual data is to enhance the accuracy of label prediction by providing contextual understanding that visual analysis alone cannot fully capture. Our proposed classification model combines Convolutional Neural Networks (CNN) for image processing with NLP techniques for analyzing textual description (i.e., captions). This approach includes rigorous training and validation phases, with each model component verified and analyzed through ablation experiments. Preliminary results demonstrate the classifier's accuracy and efficiency, highlighting its potential as an automatic image-labeling system.

Haixu Liu, Zerui Tao, Wenzhen Dong et al.

This paper provides a novel 3D medical image segmentation model structure called nnY-Net. This name comes from the fact that our model adds a cross-attention module at the bottom of the U-net structure to form a Y structure. We integrate the advantages of the two latest SOTA models, MedNeXt and SwinUNETR, and use Swin Transformer as the encoder and ConvNeXt as the decoder to innovatively design the Swin-NeXt structure. Our model uses the lowest-level feature map of the encoder as Key and Value and uses patient features such as pathology and treatment information as Query to calculate the attention weights in a Cross Attention module. Moreover, we simplify some pre- and post-processing as well as data enhancement methods in 3D image segmentation based on the dynUnet and nnU-net frameworks. We integrate our proposed Swin-NeXt with Cross-Attention framework into this framework. Last, we construct a DiceFocalCELoss to improve the training efficiency for the uneven data convergence of voxel classification.

Haixu Liu, Zerui Tao, Naihui Zhang et al.

Label noise refers to incorrect labels in a dataset caused by human errors or collection defects, which is common in real-world applications and can significantly reduce the accuracy of models. This report explores how to estimate noise transition matrices and construct deep learning classifiers that are robust against label noise. In cases where the transition matrix is known, we apply forward correction and importance reweighting methods to correct the impact of label noise using the transition matrix. When the transition matrix is unknown or inaccurate, we use the anchor point assumption and T-Revision series methods to estimate or correct the noise matrix. In this study, we further improved the T-Revision method by developing T-Revision-Alpha and T-Revision-Softmax to enhance stability and robustness. Additionally, we designed and implemented two baseline classifiers, a Multi-Layer Perceptron (MLP) and ResNet-18, based on the cross-entropy loss function. We compared the performance of these methods on predicting clean labels and estimating transition matrices using the FashionMINIST dataset with known noise transition matrices. For the CIFAR-10 dataset, where the noise transition matrix is unknown, we estimated the noise matrix and evaluated the ability of the methods to predict clean labels.