Deyu Meng

AAAI Conference 2026 Conference Paper

DynamicEarth: How Far Are We from Open-Vocabulary Change Detection?

• Kaiyu Li
• Xiangyong Cao
• Yupeng Deng
• Chao Pang
• Zepeng Xin
• Hui Qiao
• Tieliang Gong
• Deyu Meng

Monitoring Earth's evolving land covers requires methods capable of detecting changes across a wide range of categories and contexts. Existing change detection methods are hindered by their dependency on predefined classes, reducing their effectiveness in open-world applications. To address this issue, we introduce open-vocabulary change detection (OVCD), a novel task that bridges vision and language to detect changes across any category. Considering the lack of high-quality data and annotation, we propose two training-free frameworks, M-C-I and I-M-C, which leverage and integrate off-the-shelf foundation models for the OVCD task. The insight behind the M-C-I~framework is to discover all potential changes and then classify these changes, while the insight of I-M-C~framework is to identify all targets of interest and then determine whether their states have changed. Based on these two frameworks, we instantiate to obtain several methods, e.g., SAM-DINOv2-SegEarth-OV, Grounding-DINO-SAM2-DINO, etc. Extensive evaluations on 4 benchmark datasets demonstrate the superior generalization and robustness of our OVCD methods over existing supervised and unsupervised methods. To support continued exploration, we release DynamicEarth, a dedicated codebase designed to advance research and application of OVCD.

IJCAI Conference 2025 Conference Paper

Beyond Low-rankness: Guaranteed Matrix Recovery via Modified Nuclear Norm

• Jiangjun Peng
• Yisi Luo
• Xiangyong Cao
• Shuang Xu
• Deyu Meng

The nuclear norm (NN) has been widely explored in matrix recovery problems, such as Robust PCA and matrix completion, leveraging the inherent global low-rank structure of the data. In this study, we introduce a new modified nuclear norm (MNN) framework, where the MNN family norms are defined by adopting suitable transformations and performing the NN on the transformed matrix. The MNN framework offers two main advantages: (1) it jointly captures both local information and global low-rankness without requiring trade-off parameter tuning; (2) under mild assumptions on the transformation, we provide theoretical recovery guarantees for both Robust PCA and MC tasks—an achievement not shared by existing methods that combine local and global information. Thanks to its general and flexible design, MNN can accommodate various proven transformations, enabling a unified and effective approach to structured low-rank recovery. Extensive experiments demonstrate the effectiveness of our method. Code and supplementary material are available at https: //github. com/andrew-pengjj/modified_nuclear_norm.

AAAI Conference 2025 Conference Paper

Deep Rank-One Tensor Functional Factorization for Multi-Dimensional Data Recovery

• Yanyi Li
• Xi Zhang
• Yisi Luo
• Deyu Meng

Many real-world data are inherently multi-dimensional, e.g., color images, videos, and hyperspectral images. How to effectively and compactly represent these multi-dimensional data within a unified framework is an important pursuit. Previous methods focus on tensor factorizations, convolutional networks, or diffusion models for multi-dimensional data representation, which may not fully utilize inherent data structures and may lead to redundant parameters. In this work, we propose a Deep Rank-One Tensor Functional Factorization (DRO-TFF), which internally utilizes more comprehensive data priors facilitated by much fewer parameters. Concretely, our DRO-TFF consists of three organically integrated blocks: compact rank-one factorizations in the spatial domain, a deep transform to capture underlying low-dimensional structures, and smooth factors parameterized by implicit neural representations. Through a series of theoretical analysis, we show the rich data priors encoded in the DRO-TFF structure, e.g., Lipschitz smoothness and low-rankness. Extensive experiments on multi-dimensional data recovery problems, such as image and video inpainting, image denoising, and hyperspectral mixed noise removal, showcase the effectiveness of the proposed method.

TMLR Journal 2025 Journal Article

Diversity-Enhanced and Classification-Aware Prompt Learning for Few-Shot Learning via Stable Diffusion

• Gaoqin Chang
• Jun Shu
• Xiang Yuan
• Deyu Meng

Recent text-to-image generative models have exhibited an impressive ability to generate fairly realistic images from some text prompts. In this work, we explore to leverage off-the-shelf text-to-image generative models to train non-specific downstream few-shot classification model architectures using synthetic dataset to classify real images. Current approaches use hand-crafted or model-generated text prompts of text-to-image generative models to generate desired synthetic images, however, they have limited capability of generating diverse images. Especially, their synthetic datasets have relatively limited relevance to the downstream classification tasks. This makes them fairly hard to guarantee training models from synthetic images are efficient in practice. To address this issue, we propose a method capable of adaptively learning proper text prompts for the off-the-shelf diffusion model to generate diverse and classification-aware synthetic images. Our approach shows consistently improvements in various classification datasets, with results comparable to existing prompt designing methods. We find that replacing data generation strategy of existing zero/few-shot methods with proposed method could consistently improve downstream classification performance across different network architectures, demonstrating its model-agnostic potential for few-shot learning. This makes it possible to train an efficient downstream few-shot learning model from synthetic images generated by proposed method for real problems.

ICML Conference 2025 Conference Paper

Improving Memory Efficiency for Training KANs via Meta Learning

• Zhangchi Zhao
• Jun Shu
• Deyu Meng
• Zongben Xu

Inspired by the Kolmogorov-Arnold representation theorem, KANs offer a novel framework for function approximation by replacing traditional neural network weights with learnable univariate functions. This design demonstrates significant potential as an efficient and interpretable alternative to traditional MLPs. However, KANs are characterized by a substantially larger number of trainable parameters, leading to challenges in memory efficiency and higher training costs compared to MLPs. To address this limitation, we propose to generate weights for KANs via a smaller meta-learner, called MetaKANs. By training KANs and MetaKANs in an end-to-end differentiable manner, MetaKANs achieve comparable or even superior performance while significantly reducing the number of trainable parameters and maintaining promising interpretability. Extensive experiments on diverse benchmark tasks, including symbolic regression, partial differential equation solving, and image classification, demonstrate the effectiveness of MetaKANs in improving parameter efficiency and memory usage. The proposed method provides an alternative technique for training KANs, that allows for greater scalability and extensibility, and narrows the training cost gap with MLPs stated in the original paper of KANs. Our code is available at https: //github. com/Murphyzc/MetaKAN.

NeurIPS Conference 2025 Conference Paper

Online Functional Tensor Decomposition via Continual Learning for Streaming Data Completion

• Xi Zhang
• Yanyi Li
• Yisi Luo
• Qi Xie
• Deyu Meng

Online tensor decompositions are powerful and proven techniques that address the challenges in processing high-velocity streaming tensor data, such as traffic flow and weather system. The main aim of this work is to propose a novel online functional tensor decomposition (OFTD) framework, which represents a spatial-temporal continuous function using the CP tensor decomposition parameterized by coordinate-based implicit neural representations (INRs). The INRs allow for natural characterization of continually expanded streaming data by simply adding new coordinates into the network. Particularly, our method transforms the classical online tensor decomposition algorithm into a more dynamic continual learning paradigm of updating the INR weights to fit the new data without forgetting the previous tensor knowledge. To this end, we introduce a long-tail memory replay method that adapts to the local continuity property of INR. Extensive experiments for streaming tensor completion using traffic, weather, user-item, and video data verify the effectiveness of the OFTD approach for streaming data analysis. This endeavor serves as a pivotal inspiration for future research to connect classical online tensor tools with continual learning paradigms to better explore knowledge underlying streaming tensor data.

NeurIPS Conference 2025 Conference Paper

Polyline Path Masked Attention for Vision Transformer

• Zhongchen Zhao
• Chaodong Xiao
• Hui Lin
• Qi Xie
• Lei Zhang
• Deyu Meng

Global dependency modeling and spatial position modeling are two core issues of the foundational architecture design in current deep learning frameworks. Recently, Vision Transformers (ViTs) have achieved remarkable success in computer vision, leveraging the powerful global dependency modeling capability of the self-attention mechanism. Furthermore, Mamba2 has demonstrated its significant potential in natural language processing tasks by explicitly modeling the spatial adjacency prior through the structured mask. In this paper, we propose Polyline Path Masked Attention (PPMA) that integrates the self-attention mechanism of ViTs with an enhanced structured mask of Mamba2, harnessing the complementary strengths of both architectures. Specifically, we first ameliorate the traditional structured mask of Mamba2 by introducing a 2D polyline path scanning strategy and derive its corresponding structured mask, polyline path mask, which better preserves the adjacency relationships among image tokens. Notably, we conduct a thorough theoretical analysis on the structural characteristics of the proposed polyline path mask and design an efficient algorithm for the computation of the polyline path mask. Next, we embed the polyline path mask into the self-attention mechanism of ViTs, enabling explicit modeling of spatial adjacency prior. Extensive experiments on standard benchmarks, including image classification, object detection, and segmentation, demonstrate that our model outperforms previous state-of-the-art approaches based on both state-space models and Transformers. For example, our proposed PPMA-T/S/B models achieve 48. 7%/51. 1%/52. 3% mIoU on the ADE20K semantic segmentation task, surpassing RMT-T/S/B by 0. 7%/1. 3%/0. 3%, respectively. Code is available at https: //github. com/zhongchenzhao/PPMA.

ICLR Conference 2025 Conference Paper

SD-LoRA: Scalable Decoupled Low-Rank Adaptation for Class Incremental Learning

• Yichen Wu
• Hongming Piao
• Long-Kai Huang
• Renzhen Wang
• Wanhua Li 0001
• Hanspeter Pfister
• Deyu Meng
• Kede Ma

Continual Learning (CL) with foundation models has recently emerged as a promising paradigm to exploit abundant knowledge acquired during pre-training for tackling sequential tasks. However, existing prompt-based and Low-Rank Adaptation-based (LoRA-based) methods often require expanding a prompt/LoRA pool or retaining samples of previous tasks, which poses significant scalability challenges as the number of tasks grows. To address these limitations, we propose Scalable Decoupled LoRA (SD-LoRA) for class incremental learning, which continually separates the learning of the magnitude and direction of LoRA components without rehearsal. Our empirical and theoretical analysis reveals that SD-LoRA tends to follow a low-loss trajectory and converges to an overlapping low-loss region for all learned tasks, resulting in an excellent stability-plasticity trade-off. Building upon these insights, we introduce two variants of SD-LoRA with further improved parameter efficiency. All parameters of SD-LoRAs can be end-to-end optimized for CL objectives. Meanwhile, they support efficient inference by allowing direct evaluation with the finally trained model, obviating the need for component selection. Extensive experiments across multiple CL benchmarks and foundation models consistently validate the effectiveness of SD-LoRA. The code is available at https://github.com/WuYichen-97/SD-Lora-CL.

NeurIPS Conference 2025 Conference Paper

Semi-Supervised Regression with Heteroscedastic Pseudo-Labels

• Xueqing Sun
• Renzhen Wang
• Quanziang Wang
• Yichen Wu
• Xixi Jia
• Deyu Meng

Pseudo-labeling is a commonly used paradigm in semi-supervised learning, yet its application to semi-supervised regression (SSR) remains relatively under-explored. Unlike classification, where pseudo-labels are discrete and confidence-based filtering is effective, SSR involves continuous outputs with heteroscedastic noise, making it challenging to assess pseudo-label reliability. As a result, naive pseudo-labeling can lead to error accumulation and overfitting to incorrect labels. To address this, we propose an uncertainty-aware pseudo-labeling framework that dynamically adjusts pseudo-label influence from a bi-level optimization perspective. By jointly minimizing empirical risk over all data and optimizing uncertainty estimates to enhance generalization on labeled data, our method effectively mitigates the impact of unreliable pseudo-labels. We provide theoretical insights and extensive experiments to validate our approach across various benchmark SSR datasets, and the results demonstrate superior robustness and performance compared to existing methods.

ICLR Conference 2025 Conference Paper

Spatial-Mamba: Effective Visual State Space Models via Structure-Aware State Fusion

• Chaodong Xiao
• Minghan Li 0001
• Zhengqiang Zhang
• Deyu Meng
• Lei Zhang 0006

Selective state space models (SSMs), such as Mamba, highly excel at capturing long-range dependencies in 1D sequential data, while their applications to 2D vision tasks still face challenges. Current visual SSMs often convert images into 1D sequences and employ various scanning patterns to incorporate local spatial dependencies. However, these methods are limited in effectively capturing the complex image spatial structures and the increased computational cost caused by the lengthened scanning paths. To address these limitations, we propose Spatial-Mamba, a novel approach that establishes neighborhood connectivity directly in the state space. Instead of relying solely on sequential state transitions, we introduce a structure-aware state fusion equation, which leverages dilated convolutions to capture image spatial structural dependencies, significantly enhancing the flow of visual contextual information. Spatial-Mamba proceeds in three stages: initial state computation in a unidirectional scan, spatial context acquisition through structure-aware state fusion, and final state computation using the observation equation. Our theoretical analysis shows that Spatial-Mamba unifies the original Mamba and linear attention under the same matrix multiplication framework, providing a deeper understanding of our method. Experimental results demonstrate that Spatial-Mamba, even with a single scan, attains or surpasses the state-of-the-art SSM-based models in image classification, detection and segmentation. Source codes and trained models can be found at \url{ https://github.com/EdwardChasel/Spatial-Mamba }.

NeurIPS Conference 2024 Conference Paper

Globally Q-linear Gauss-Newton Method for Overparameterized Non-convex Matrix Sensing

• Xixi Jia
• Fangchen Feng
• Deyu Meng
• Defeng Sun

This paper focuses on the optimization of overparameterized, non-convex low-rank matrix sensing (LRMS)—an essential component in contemporary statistics and machine learning. Recent years have witnessed significant breakthroughs in first-order methods, such as gradient descent, for tackling this non-convex optimization problem. However, the presence of numerous saddle points often prolongs the time required for gradient descent to overcome these obstacles. Moreover, overparameterization can markedly decelerate gradient descent methods, transitioning its convergence rate from linear to sub-linear. In this paper, we introduce an approximated Gauss-Newton (AGN) method for tackling the non-convex LRMS problem. Notably, AGN incurs a computational cost comparable to gradient descent per iteration but converges much faster without being slowed down by saddle points. We prove that, despite the non-convexity of the objective function, AGN achieves Q-linear convergence from random initialization to the global optimal solution. The global Q-linear convergence of AGN represents a substantial enhancement over the convergence of the existing methods for the overparameterized non-convex LRMS. The code for this paper is available at \url{https: //github. com/hsijiaxidian/AGN}.

AAAI Conference 2024 Conference Paper

Gramformer: Learning Crowd Counting via Graph-Modulated Transformer

• Hui Lin
• Zhiheng Ma
• Xiaopeng Hong
• Qinnan Shangguan
• Deyu Meng

Transformer has been popular in recent crowd counting work since it breaks the limited receptive field of traditional CNNs. However, since crowd images always contain a large number of similar patches, the self-attention mechanism in Transformer tends to find a homogenized solution where the attention maps of almost all patches are identical. In this paper, we address this problem by proposing Gramformer: a graph-modulated transformer to enhance the network by adjusting the attention and input node features respectively on the basis of two different types of graphs. Firstly, an attention graph is proposed to diverse attention maps to attend to complementary information. The graph is building upon the dissimilarities between patches, modulating the attention in an anti-similarity fashion. Secondly, a feature-based centrality encoding is proposed to discover the centrality positions or importance of nodes. We encode them with a proposed centrality indices scheme to modulate the node features and similarity relationships. Extensive experiments on four challenging crowd counting datasets have validated the competitiveness of the proposed method. Code is available at https://github.com/LoraLinH/Gramformer.

ICLR Conference 2024 Conference Paper

Meta Continual Learning Revisited: Implicitly Enhancing Online Hessian Approximation via Variance Reduction

• Yichen Wu
• Long-Kai Huang
• Renzhen Wang
• Deyu Meng
• Ying Wei 0001

Regularization-based methods have so far been among the *de facto* choices for continual learning. Recent theoretical studies have revealed that these methods all boil down to relying on the Hessian matrix approximation of model weights. However, these methods suffer from suboptimal trade-offs between knowledge transfer and forgetting due to fixed and unchanging Hessian estimations during training. Another seemingly parallel strand of Meta-Continual Learning (Meta-CL) algorithms enforces alignment between gradients of previous tasks and that of the current task. In this work we revisit Meta-CL and for the first time bridge it with regularization-based methods. Concretely, Meta-CL implicitly approximates Hessian in an online manner, which enjoys the benefits of timely adaptation but meantime suffers from high variance induced by random memory buffer sampling. We are thus highly motivated to combine the best of both worlds, through the proposal of Variance Reduced Meta-CL (VR-MCL) to achieve both timely and accurate Hessian approximation. Through comprehensive experiments across three datasets and various settings, we consistently observe that VR-MCL outperforms other SOTA methods, which further validates the effectiveness of VR-MCL.

AAAI Conference 2024 Conference Paper

Which Is More Effective in Label Noise Cleaning, Correction or Filtering?

• Gaoxia Jiang
• Jia Zhang
• Xuefei Bai
• Wenjian Wang
• Deyu Meng

Most noise cleaning methods adopt one of the correction and filtering modes to build robust models. However, their effectiveness, applicability, and hyper-parameter insensitivity have not been carefully studied. We compare the two cleaning modes via a rebuilt error bound in noisy environments. At the dataset level, Theorem 5 implies that correction is more effective than filtering when the cleaned datasets have close noise rates. At the sample level, Theorem 6 indicates that confident label noises (large noise probabilities) are more suitable to be corrected, and unconfident noises (medium noise probabilities) should be filtered. Besides, an imperfect hyper-parameter may have fewer negative impacts on filtering than correction. Unlike existing methods with a single cleaning mode, the proposed Fusion cleaning framework of Correction and Filtering (FCF) combines the advantages of different modes to deal with diverse suspicious labels. Experimental results demonstrate that our FCF method can achieve state-of-the-art performance on benchmark datasets.

ICLR Conference 2023 Conference Paper

Imbalanced Semi-supervised Learning with Bias Adaptive Classifier

• Renzhen Wang
• Xixi Jia
• Quanziang Wang
• Yichen Wu
• Deyu Meng

Pseudo-labeling has proven to be a promising semi-supervised learning (SSL) paradigm. Existing pseudo-labeling methods commonly assume that the class distributions of training data are balanced. However, such an assumption is far from realistic scenarios and thus severely limits the performance of current pseudo-labeling methods under the context of class-imbalance. To alleviate this problem, we design a bias adaptive classifier that targets the imbalanced SSL setups. The core idea is to automatically assimilate the training bias caused by class imbalance via the bias adaptive classifier, which is composed of a novel bias attractor and the original linear classifier. The bias attractor is designed as a light-weight residual network and learned through a bi-level learning framework, which enables the bias adaptive classifier to fit imbalanced training data, while the linear classifier can provide unbiased label prediction for each class. We conduct extensive experiments under various imbalanced semi-supervised setups, and the results demonstrate that our method can be applied to different pseudo-labeling models and is superior to current state-of-the-art methods.

JMLR Journal 2023 Journal Article

Learning an Explicit Hyper-parameter Prediction Function Conditioned on Tasks

• Jun Shu
• Deyu Meng
• Zongben Xu

Meta learning has attracted much attention recently in machine learning community. Contrary to conventional machine learning aiming to learn inherent prediction rules to predict labels for new query data, meta learning aims to learn the learning methodology for machine learning from observed tasks, so as to generalize to new query tasks by leveraging the meta-learned learning methodology. In this study, we achieve such learning methodology by learning an explicit hyper-parameter prediction function shared by all training tasks, and we call this learning process as Simulating Learning Methodology (SLeM). Specifically, this function is represented as a parameterized function called meta-learner, mapping from a training/test task to its suitable hyper-parameter setting, extracted from a pre-specified function set called meta learning machine. Such setting guarantees that the meta-learned learning methodology is able to flexibly fit diverse query tasks, instead of only obtaining fixed hyper-parameters by many current meta learning methods, with less adaptability to query task's variations. Such understanding of meta learning also makes it easily succeed from traditional learning theory for analyzing its generalization bounds with general losses/tasks/models. The theory naturally leads to some feasible controlling strategies for ameliorating the quality of the extracted meta-learner, verified to be able to finely ameliorate its generalization capability in some typical meta learning applications, including few-shot regression, few-shot classification and domain generalization. The source code of our method is released at https://github.com/xjtushujun/SLeM-Theory. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

NeurIPS Conference 2023 Conference Paper

Preconditioning Matters: Fast Global Convergence of Non-convex Matrix Factorization via Scaled Gradient Descent

• Xixi Jia
• Hailin Wang
• Jiangjun Peng
• Xiangchu Feng
• Deyu Meng

Low-rank matrix factorization (LRMF) is a canonical problem in non-convex optimization, the objective function to be minimized is non-convex and even non-smooth, which makes the global convergence guarantee of gradient-based algorithm quite challenging. Recent work made a breakthrough on proving that standard gradient descent converges to the $\varepsilon$-global minima after $O( \frac{d \kappa^2}{\tau^2} {\rm ln} \frac{d \sigma_d}{\tau} + \frac{d \kappa^2}{\tau^2} {\rm ln} \frac{\sigma_d}{\varepsilon})$ iterations from small initialization with a very small learning rate (both are related to the small constant $\tau$). While the dependence of the convergence on the \textit{condition number} $\kappa$ and \textit{small learning rate} makes it not practical especially for ill-conditioned LRMF problem. In this paper, we show that precondition helps in accelerating the convergence and prove that the scaled gradient descent (ScaledGD) and its variant, alternating scaled gradient descent (AltScaledGD) converge to an $\varepsilon$-global minima after $O( {\rm ln} \frac{d}{\delta} + {\rm ln} \frac{d}{\varepsilon})$ iterations from general random initialization. Meanwhile, for small initialization as in gradient descent, both ScaledGD and AltScaledGD converge to $\varepsilon$-global minima after only $O({\rm ln} \frac{d}{\varepsilon})$ iterations. Furthermore, we prove that as a proximity to the alternating minimization, AltScaledGD converges faster than ScaledGD, its global convergence does not rely on small learning rate and small initialization, which certificates the advantages of AltScaledGD in LRMF.

EAAI Journal 2023 Journal Article

Progressive convolutional transformer for image restoration

• Yecong Wan
• Mingwen Shao
• Yuanshuo Cheng
• Deyu Meng
• Wangmeng Zuo

In the past few years, convolutional neural networks (CNNs) have become the primary workhorse for image restoration tasks. However, the deficiency of modeling long-range dependencies due to the local computational property of convolution greatly limits the restoration performance. To overcome this limitation, we propose a novel multi-stage progressive convolutional Transformer to recursively restore the degraded images, termed PCformer, which enjoys a high capability for capturing local context and global dependencies with friendly computational cost. Specifically, each stage of PCformer is an asymmetric encoder–decoder network whose bottleneck is built upon a tailored Transformer block with convolution operation deployed to avoid any loss of local context. Both encoder and decoder are convolution-based modules, thus allowing to explore rich contextualized information for image recovery. Taking the low-resolution features encoded by the encoder as tokens input into the Transformer bottleneck guarantees that long-range pixel interactions are captured while reducing the computational burden. Meanwhile, we apply a gated module for filtering redundant information propagation between every two phases. In addition, long-range enhanced inpainting is further introduced to mining the ability of PCformer to exploit distant complementary features. Extensive experiments yield superior results and in particular establishing new state-of-the-art results on several image restoration tasks, including deraining ( + 0. 37 dB on Rain13K), denoising ( + 0. 11 dB on DND), dehazing ( + 0. 56 dB on I-HAZE), enhancement ( + 0. 72 dB on SICE), and shadow removal ( + 0. 65 RMSE on ISTD). The implementation code is available at https: //github. com/Jeasco/PCformer.

AAAI Conference 2023 Conference Paper

Tensor Compressive Sensing Fused Low-Rankness and Local-Smoothness

• Xinling Liu
• Jingyao Hou
• Jiangjun Peng
• Hailin Wang
• Deyu Meng
• Jianjun Wang

A plethora of previous studies indicates that making full use of multifarious intrinsic properties of primordial data is a valid pathway to recover original images from their degraded observations. Typically, both low-rankness and local-smoothness broadly exist in real-world tensor data such as hyperspectral images and videos. Modeling based on both properties has received a great deal of attention, whereas most studies concentrate on experimental performance, and theoretical investigations are still lacking. In this paper, we study the tensor compressive sensing problem based on the tensor correlated total variation, which is a new regularizer used to simultaneously capture both properties existing in the same dataset. The new regularizer has the outstanding advantage of not using a trade-off parameter to balance the two properties. The obtained theories provide a robust recovery guarantee, where the error bound shows that our model certainly benefits from both properties in ground-truth data adaptively. Moreover, based on the ADMM update procedure, we design an algorithm with a global convergence guarantee to solve this model. At last, we carry out experiments to apply our model to hyperspectral image and video restoration problems. The experimental results show that our method is prominently better than many other competing ones. Our code and Supplementary Material are available at https://github.com/fsliuxl/cs-tctv.

JMLR Journal 2023 Journal Article

Variational Inverting Network for Statistical Inverse Problems of Partial Differential Equations

• Junxiong Jia
• Yanni Wu
• Peijun Li
• Deyu Meng

To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have been developed to construct dimension-independent algorithms. However, there are three challenges for these infinite-dimensional Bayesian methods: prior measures usually act as regularizers and are not able to incorporate prior information efficiently; complex noises, such as more practical non-i.i.d. distributed noises, are rarely considered; and time-consuming forward PDE solvers are needed to estimate posterior statistical quantities. To address these issues, an infinite-dimensional inference framework has been proposed based on the infinite-dimensional variational inference method and deep generative models. Specifically, by introducing some measure equivalence assumptions, we derive the evidence lower bound in the infinite-dimensional setting and provide possible parametric strategies that yield a general inference framework called the Variational Inverting Network (VINet). This inference framework can encode prior and noise information from learning examples. In addition, relying on the power of deep neural networks, the posterior mean and variance can be efficiently and explicitly generated in the inference stage. In numerical experiments, we design specific network structures that yield a computable VINet from the general inference framework. Numerical examples of linear inverse problems of an elliptic equation and the Helmholtz equation are presented to illustrate the effectiveness of the proposed inference framework. [abs] [ pdf ][ bib ] &copy JMLR 2023. ( edit, beta )

IJCAI Conference 2022 Conference Paper

Adaptive Convolutional Dictionary Network for CT Metal Artifact Reduction

• Hong Wang
• Yuexiang Li
• Deyu Meng
• Yefeng Zheng

Inspired by the great success of deep neural networks, learning-based methods have gained promising performances for metal artifact reduction (MAR) in computed tomography (CT) images. However, most of the existing approaches put less emphasis on modelling and embedding the intrinsic prior knowledge underlying this specific MAR task into their network designs. Against this issue, we propose an adaptive convolutional dictionary network (ACDNet), which leverages both model-based and learning-based methods. Specifically, we explore the prior structures of metal artifacts, e. g. , non-local repetitive streaking patterns, and encode them as an explicit weighted convolutional dictionary model. Then, a simple-yet-effective algorithm is carefully designed to solve the model. By unfolding every iterative substep of the proposed algorithm into a network module, we explicitly embed the prior structure into a deep network, i. e. , a clear interpretability for the MAR task. Furthermore, our ACDNet can automatically learn the prior for artifact-free CT images via training data and adaptively adjust the representation kernels for each input CT image based on its content. Hence, our method inherits the clear interpretability of model-based methods and maintains the powerful representation ability of learning-based methods. Comprehensive experiments executed on synthetic and clinical datasets show the superiority of our ACDNet in terms of effectiveness and model generalization. Code and supplementary material are available at https: //github. com/hongwang01/ACDNet.

NeurIPS Conference 2022 Conference Paper

Deep Fourier Up-Sampling

• Man Zhou
• Hu Yu
• Jie Huang
• Feng Zhao
• Jinwei Gu
• Chen Change Loy
• Deyu Meng
• Chongyi Li

Existing convolutional neural networks widely adopt spatial down-/up-sampling for multi-scale modeling. However, spatial up-sampling operators (e. g. , interpolation, transposed convolution, and un-pooling) heavily depend on local pixel attention, incapably exploring the global dependency. In contrast, the Fourier domain is in accordance with the nature of global modeling according to the spectral convolution theorem. Unlike the spatial domain that easily performs up-sampling with the property of local similarity, up-sampling in the Fourier domain is more challenging as it does not follow such a local property. In this study, we propose a theoretically feasible Deep Fourier Up-Sampling (FourierUp) to solve these issues. We revisit the relationships between spatial and Fourier domains and reveal the transform rules on the features of different resolutions in the Fourier domain, which provide key insights for FourierUp's designs. FourierUp as a generic operator consists of three key components: 2D discrete Fourier transform, Fourier dimension increase rules, and 2D inverse Fourier transform, which can be directly integrated with existing networks. Extensive experiments across multiple computer vision tasks, including object detection, image segmentation, image de-raining, image dehazing, and guided image super-resolution, demonstrate the consistent performance gains obtained by introducing our FourierUp. Code will be publicly available.

ICML Conference 2022 Conference Paper

Fast and Provable Nonconvex Tensor RPCA

• Haiquan Qiu
• Yao Wang 0003
• Shaojie Tang 0001
• Deyu Meng
• Quanming Yao

In this paper, we study nonconvex tensor robust principal component analysis (RPCA) based on the $t$-SVD. We first propose an alternating projection method, i. e. , APT, which converges linearly to the ground-truth under the incoherence conditions of tensors. However, as the projection to the low-rank tensor space in APT can be slow, we further propose to speedup such a process by utilizing the property of the tangent space of low-rank. The resulting algorithm, i. e. , EAPT, is not only more efficient than APT but also keeps the linear convergence. Compared with existing tensor RPCA works, the proposed method, especially EAPT, is not only more effective due to the recovery guarantee and adaption in the transformed (frequency) domain but also more efficient due to faster convergence rate and lower iteration complexity. These benefits are also empirically verified both on synthetic data, and real applications, e. g. , hyperspectral image denoising and video background subtraction.

NeurIPS Conference 2022 Conference Paper

Tensor Wheel Decomposition and Its Tensor Completion Application

• Zhong-Cheng Wu
• Ting-Zhu Huang
• Liang-Jian Deng
• Hong-Xia Dou
• Deyu Meng

Recently, tensor network (TN) decompositions have gained prominence in computer vision and contributed promising results to high-order data recovery tasks. However, current TN models are rather being developed towards more intricate structures to pursue incremental improvements, which instead leads to a dramatic increase in rank numbers, thus encountering laborious hyper-parameter selection, especially for higher-order cases. In this paper, we propose a novel TN decomposition, dubbed tensor wheel (TW) decomposition, in which a high-order tensor is represented by a set of latent factors mapped into a specific wheel topology. Such decomposition is constructed starting from analyzing the graph structure, aiming to more accurately characterize the complex interactions inside objectives while maintaining a lower hyper-parameter scale, theoretically alleviating the above deficiencies. Furthermore, to investigate the potentiality of TW decomposition, we provide its one numerical application, i. e. , tensor completion (TC), yet develop an efficient proximal alternating minimization-based solving algorithm with guaranteed convergence. Experimental results elaborate that the proposed method is significantly superior to other tensor decomposition-based state-of-the-art methods on synthetic and real-world data, implying the merits of TW decomposition. The code is available at: https: //github. com/zhongchengwu/code_TWDec.

AAAI Conference 2021 Conference Paper

Alternative Baselines for Low-Shot 3D Medical Image Segmentation—An Atlas Perspective

• Shuxin Wang
• Shilei Cao
• Dong Wei
• Cong Xie
• Kai Ma
• Liansheng Wang
• Deyu Meng
• Yefeng Zheng

Low-shot (one/few-shot) segmentation has attracted increasing attention as it works well with limited annotation. Stateof-the-art low-shot segmentation methods on natural images usually focus on implicit representation learning for each novel class, such as learning prototypes, deriving guidance features via masked average pooling, and segmenting using cosine similarity in feature space. We argue that low-shot segmentation on medical images should step further to explicitly learn dense correspondences between images to utilize the anatomical similarity. The core ideas are inspired by the classical practice of multi-atlas segmentation, where the indispensable parts of atlas-based segmentation, i. e. , registration, label propagation, and label fusion are unified into a single framework in our work. Specifically, we propose two alternative baselines, i. e. , the Siamese-Baseline and Individual- Difference-Aware Baseline, where the former is targeted at anatomically stable structures (such as brain tissues), and the latter possesses a strong generalization ability to organs suffering large morphological variations (such as abdominal organs). In summary, this work sets up a benchmark for lowshot 3D medical image segmentation and sheds light on further understanding of atlas-based few-shot segmentation.

AAAI Conference 2021 Conference Paper

Learning to Purify Noisy Labels via Meta Soft Label Corrector

• Yichen Wu
• Jun Shu
• Qi Xie
• Qian Zhao
• Deyu Meng

Recent deep neural networks (DNNs) can easily overfit to biased training data with noisy labels. Label correction strategy is commonly used to alleviate this issue by identifying suspected noisy labels and then correcting them. Current approaches to correcting corrupted labels usually need manually pre-defined label correction rules, which makes it hard to apply in practice due to the large variations of such manual strategies with respect to different problems. To address this issue, we propose a meta-learning model, aiming at attaining an automatic scheme which can estimate soft labels through meta-gradient descent step under the guidance of a small amount of noise-free meta data. By viewing the label correction procedure as a meta-process and using a metalearner to automatically correct labels, our method can adaptively obtain rectified soft labels gradually in iteration according to current training problems. Besides, our method is model-agnostic and can be combined with any other existing classification models with ease to make it available to noisy label cases. Comprehensive experiments substantiate the superiority of our method in both synthetic and real-world problems with noisy labels compared with current state-of-the-art label correction strategies.

JMLR Journal 2020 Journal Article

Self-paced Multi-view Co-training

• Fan Ma
• Deyu Meng
• Xuanyi Dong
• Yi Yang

Co-training is a well-known semi-supervised learning approach which trains classifiers on two or more different views and exchanges pseudo labels of unlabeled instances in an iterative way. During the co-training process, pseudo labels of unlabeled instances are very likely to be false especially in the initial training, while the standard co-training algorithm adopts a 'draw without replacement' strategy and does not remove these wrongly labeled instances from training stages. Besides, most of the traditional co-training approaches are implemented for two-view cases, and their extensions in multi-view scenarios are not intuitive. These issues not only degenerate their performance as well as available application range but also hamper their fundamental theory. Moreover, there is no optimization model to explain the objective a co-training process manages to optimize. To address these issues, in this study we design a unified self-paced multi-view co-training (SPamCo) framework which draws unlabeled instances with replacement. Two specified co-regularization terms are formulated to develop different strategies for selecting pseudo-labeled instances during training. Both forms share the same optimization strategy which is consistent with the iteration process in co-training and can be naturally extended to multi-view scenarios. A distributed optimization strategy is also introduced to train the classifier of each view in parallel to further improve the efficiency of the algorithm. Furthermore, the SPamCo algorithm is proved to be PAC learnable, supporting its theoretical soundness. Experiments conducted on synthetic, text categorization, person re-identification, image recognition and object detection data sets substantiate the superiority of the proposed method. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2020. ( edit, beta )

NeurIPS Conference 2019 Conference Paper

Meta-Weight-Net: Learning an Explicit Mapping For Sample Weighting

• Jun Shu
• Qi Xie
• Lixuan Yi
• Qian Zhao
• Sanping Zhou
• Zongben Xu
• Deyu Meng

Current deep neural networks(DNNs) can easily overfit to biased training data with corrupted labels or class imbalance. Sample re-weighting strategy is commonly used to alleviate this issue by designing a weighting function mapping from training loss to sample weight, and then iterating between weight recalculating and classifier updating. Current approaches, however, need manually pre-specify the weighting function as well as its additional hyper-parameters. It makes them fairly hard to be generally applied in practice due to the significant variation of proper weighting schemes relying on the investigated problem and training data. To address this issue, we propose a method capable of adaptively learning an explicit weighting function directly from data. The weighting function is an MLP with one hidden layer, constituting a universal approximator to almost any continuous functions, making the method able to fit a wide range of weighting function forms including those assumed in conventional research. Guided by a small amount of unbiased meta-data, the parameters of the weighting function can be finely updated simultaneously with the learning process of the classifiers. Synthetic and real experiments substantiate the capability of our method for achieving proper weighting functions in class imbalance and noisy label cases, fully complying with the common settings in traditional methods, and more complicated scenarios beyond conventional cases. This naturally leads to its better accuracy than other state-of-the-art methods.

NeurIPS Conference 2019 Conference Paper

Variational Denoising Network: Toward Blind Noise Modeling and Removal

• Zongsheng Yue
• Hongwei Yong
• Qian Zhao
• Deyu Meng
• Lei Zhang

Blind image denoising is an important yet very challenging problem in computer vision due to the complicated acquisition process of real images. In this work we propose a new variational inference method, which integrates both noise estimation and image denoising into a unique Bayesian framework, for blind image denoising. Specifically, an approximate posterior, parameterized by deep neural networks, is presented by taking the intrinsic clean image and noise variances as latent variables conditioned on the input noisy image. This posterior provides explicit parametric forms for all its involved hyper-parameters, and thus can be easily implemented for blind image denoising with automatic noise estimation for the test noisy image. On one hand, as other data-driven deep learning methods, our method, namely variational denoising network (VDN), can perform denoising efficiently due to its explicit form of posterior expression. On the other hand, VDN inherits the advantages of traditional model-driven approaches, especially the good generalization capability of generative models. VDN has good interpretability and can be flexibly utilized to estimate and remove complicated non-i. i. d. noise collected in real scenarios. Comprehensive experiments are performed to substantiate the superiority of our method in blind image denoising.

ICML Conference 2017 Conference Paper

Self-Paced Co-training

• Fan Ma
• Deyu Meng
• Qi Xie 0002
• Zina Li
• Xuanyi Dong

Co-training is a well-known semi-supervised learning approach which trains classifiers on two different views and exchanges labels of unlabeled instances in an iterative way. During co-training process, labels of unlabeled instances in the training pool are very likely to be false especially in the initial training rounds, while the standard co-training algorithm utilizes a “draw without replacement” manner and does not remove these false labeled instances from training. This issue not only tends to degenerate its performance but also hampers its fundamental theory. Besides, there is no optimization model to explain what objective a cotraining process optimizes. To these issues, in this study we design a new co-training algorithm named self-paced cotraining (SPaCo) with a “draw with replacement” learning mode. The rationality of SPaCo can be proved under theoretical assumptions utilized in traditional co-training research, and furthermore, the algorithm exactly complies with the alternative optimization process for an optimization model of self-paced curriculum learning, which can be finely explained in robust learning manner. Experimental results substantiate the superiority of the proposed method as compared with current state-of-the-art co-training methods.

IJCAI Conference 2016 Conference Paper

Bridging Saliency Detection to Weakly Supervised Object Detection Based on Self-Paced Curriculum Learning

• Dingwen Zhang
• Deyu Meng
• Long Zhao
• Junwei Han

Weakly-supervised object detection (WOD) is a challenging problems in computer vision. The key problem is to simultaneously infer the exact object locations in the training images and train the object detectors, given only the training images with weak image-level labels. Intuitively, by simulating the selective attention mechanism of human visual system, saliency detection technique can select attractive objects in scenes and thus is a potential way to provide useful priors for WOD. However, the way to adopt saliency detection in WOD is not trivial since the detected saliency region might be possibly highly ambiguous in complex cases. To this end, this paper first comprehensively analyzes the challenges in applying saliency detection to WOD. Then, we make one of the earliest efforts to bridge saliency detection to WOD via the self-paced curriculum learning, which can guide the learning procedure to gradually achieve faithful knowledge of multi-class objects from easy to hard. The experimental results demonstrate that the proposed approach can successfully bridge saliency detection and WOD tasks and achieve the state-of-the-art object detection results under the weak supervision.

IJCAI Conference 2016 Conference Paper

Learning to Detect Concepts from Webly-Labeled Video Data

• Junwei Liang
• Lu Jiang
• Deyu Meng
• Alexander Hauptmann

Learning detectors that can recognize concepts, such as people actions, objects, etc. , in video content is an interesting but challenging problem. In this paper, we study the problem of automatically learning detectors from the big video data on the web without any additional manual annotations. The contextual information available on the web provides noisy labels to the video content. To leverage the noisy web labels, we propose a novel method called WEbly-Labeled Learning (WELL). It is established on two theories called curriculum learning and self-paced learning and exhibits useful properties that can be theoretically verified. We provide compelling insights on the latent non-convex robust loss that is being minimized on the noisy data. In addition, we propose two novel techniques that not only enable WELL to be applied to big data but also lead to more accurate results. The efficacy and the scalability of WELL have been extensively demonstrated on two public benchmarks, including the largest multimedia dataset and the largest manually-labeled video set. Experimental results show that WELL significantly outperforms the state-of-the-art methods. To the best of our knowledge, WELL achieves by far the best reported performance on these two webly-labeled big video datasets.

AAAI Conference 2016 Conference Paper

Multi-Objective Self-Paced Learning

• Hao Li
• Maoguo Gong
• Deyu Meng
• Qiguang Miao

Current self-paced learning (SPL) regimes adopt the greedy strategy to obtain the solution with a gradually increasing pace parameter while where to optimally terminate this increasing process is difficult to determine. Besides, most SPL implementations are very sensitive to initialization and short of a theoretical result to clarify where SPL converges to with pace parameter increasing. In this paper, we propose a novel multi-objective self-paced learning (MOSPL) method to address these issues. Specifically, we decompose the objective functions as two terms, including the loss and the self-paced regularizer, respectively, and treat the problem as the compromise between these two objectives. This naturally reformulates the SPL problem as a standard multi-objective issue. A multi-objective evolutionary algorithm is used to optimize the two objectives simultaneously to facilitate the rational selection of a proper pace parameter. The proposed technique is capable of ameliorating a set of solutions with respect to a range of pace parameters through finely compromising these solutions inbetween, and making them perform robustly even under bad initialization. A good solution can then be naturally achieved from these solutions by making use of some offthe-shelf tools in multi-objective optimization. Experimental results on matrix factorization and action recognition demonstrate the superiority of the proposed method against the existing issues in current SPL research.

IJCAI Conference 2016 Conference Paper

Self-Paced Boost Learning for Classification

• Te Pi
• Xi Li
• Zhongfei Zhang
• Deyu Meng
• Fei Wu
• Jun Xiao
• Yueting Zhuang

Effectiveness and robustness are two essential aspects of supervised learning studies. For effective learning, ensemble methods are developed to build a strong effective model from ensemble of weak models. For robust learning, self-paced learning (SPL) is proposed to learn in a self-controlled pace from easy samples to complex ones. Motivated by simultaneously enhancing the learning effectiveness and robustness, we propose a unified framework, Self-Paced Boost Learning (SPBL). With an adaptive from-easy-to-hard pace in boosting process, SPBL asymptotically guides the model to focus more on the insufficiently learned samples with higher reliability. Via a max-margin boosting optimization with self-paced sample selection, SPBL is capable of capturing the intrinsic inter-class discriminative patterns while ensuring the reliability of the samples involved in learning. We formulate SPBL as a fully-corrective optimization for classification. The experiments on several real-world datasets show the superiority of SPBL in terms of both effectiveness and robustness.

AAAI Conference 2016 Conference Paper

Two-Stream Contextualized CNN for Fine-Grained Image Classification

• Jiang Liu
• Chenqiang Gao
• Deyu Meng
• Wangmeng Zuo

Human’s cognition system prompts that context information provides potentially powerful clue while recognizing objects. However, for fine-grained image classification, the contribution of context may vary over different images, and sometimes the context even confuses the classification result. To alleviate this problem, in our work, we develop a novel approach, two-stream contextualized Convolutional Neural Network, which provides a simple but efficient contextcontent joint classification model under deep learning framework. The network merely requires the raw image and a coarse segmentation as input to extract both content and context features without need of human interaction. Moreover, our network adopts a weighted fusion scheme to combine the content and the context classifiers, while a subnetwork is introduced to adaptively determine the weight for each image. According to our experiments on public datasets, our approach achieves considerable high recognition accuracy without any tedious human’s involvements, as compared with the state-of-the-art approaches.

AAAI Conference 2015 Conference Paper

Complex Event Detection via Event Oriented Dictionary Learning

• Yan Yan
• Yi Yang
• Haoquan Shen
• Deyu Meng
• Gaowen Liu
• Alex Hauptmann
• Nicu Sebe

Complex event detection is a retrieval task with the goal of finding videos of a particular event in a largescale unconstrained internet video archive, given example videos and text descriptions. Nowadays, different multimodal fusion schemes of low-level and high-level features are extensively investigated and evaluated for the complex event detection task. However, how to effectively select the high-level semantic meaningful concepts from a large pool to assist complex event detection is rarely studied in the literature. In this paper, we propose two novel strategies to automatically select semantic meaningful concepts for the event detection task based on both the events-kit text descriptions and the concepts high-level feature descriptions. Moreover, we introduce a novel event oriented dictionary representation based on the selected semantic concepts. Towards this goal, we leverage training samples of selected concepts from the Semantic Indexing (SIN) dataset with a pool of 346 concepts, into a novel supervised multitask dictionary learning framework. Extensive experimental results on TRECVID Multimedia Event Detection (MED) dataset demonstrate the efficacy of our proposed method.

AAAI Conference 2015 Conference Paper

Self-Paced Curriculum Learning

• Lu Jiang
• Deyu Meng
• Qian Zhao
• Shiguang Shan
• Alexander Hauptmann

AAAI Conference 2015 Conference Paper

Self-Paced Learning for Matrix Factorization

• Qian Zhao
• Deyu Meng
• Lu Jiang
• Qi Xie
• Zongben Xu
• Alexander Hauptmann

Matrix factorization (MF) has been attracting much attention due to its wide applications. However, since MF models are generally non-convex, most of the existing methods are easily stuck into bad local minima, especially in the presence of outliers and missing data. To alleviate this deficiency, in this study we present a new MF learning methodology by gradually including matrix elements into MF training from easy to complex. This corresponds to a recently proposed learning fashion called self-paced learning (SPL), which has been demonstrated to be beneficial in avoiding bad local minima. We also generalize the conventional binary (hard) weighting scheme for SPL to a more effective realvalued (soft) weighting manner. The effectiveness of the proposed self-paced MF method is substantiated by a series of experiments on synthetic, structure from motion and background subtraction data.

ICML Conference 2014 Conference Paper

Robust Principal Component Analysis with Complex Noise

• Qian Zhao 0002
• Deyu Meng
• Zongben Xu
• Wangmeng Zuo
• Lei Zhang 0006

The research on robust principal component analysis (RPCA) has been attracting much attention recently. The original RPCA model assumes sparse noise, and use the L_1-norm to characterize the error term. In practice, however, the noise is much more complex and it is not appropriate to simply use a certain L_p-norm for noise modeling. We propose a generative RPCA model under the Bayesian framework by modeling data noise as a mixture of Gaussians (MoG). The MoG is a universal approximator to continuous distributions and thus our model is able to fit a wide range of noises such as Laplacian, Gaussian, sparse noises and any combinations of them. A variational Bayes algorithm is presented to infer the posterior of the proposed model. All involved parameters can be recursively updated in closed form. The advantage of our method is demonstrated by extensive experiments on synthetic data, face modeling and background subtraction.

NeurIPS Conference 2014 Conference Paper

Self-Paced Learning with Diversity

• Lu Jiang
• Deyu Meng
• Shoou-I Yu
• Zhenzhong Lan
• Shiguang Shan
• Alexander Hauptmann

Self-paced learning (SPL) is a recently proposed learning regime inspired by the learning process of humans and animals that gradually incorporates easy to more complex samples into training. Existing methods are limited in that they ignore an important aspect in learning: diversity. To incorporate this information, we propose an approach called self-paced learning with diversity (SPLD) which formalizes the preference for both easy and diverse samples into a general regularizer. This regularization term is independent of the learning objective, and thus can be easily generalized into various learning tasks. Albeit non-convex, the optimization of the variables included in this SPLD regularization term for sample selection can be globally solved in linearithmic time. We demonstrate that our method significantly outperforms the conventional SPL on three real-world datasets. Specifically, SPLD achieves the best MAP so far reported in literature on the Hollywood2 and Olympic Sports datasets.

AAAI Conference 2013 Conference Paper

A Cyclic Weighted Median Method for L1 Low-Rank Matrix Factorization with Missing Entries

• Deyu Meng
• Zongben Xu
• Lei Zhang
• Ji Zhao

A challenging problem in machine learning, information retrieval and computer vision research is how to recover a low-rank representation of the given data in the presence of outliers and missing entries. The L1-norm low-rank matrix factorization (LRMF) has been a popular approach to solving this problem. However, L1-norm LRMF is difficult to achieve due to its non-convexity and non-smoothness, and existing methods are often inefficient and fail to converge to a desired solution. In this paper we propose a novel cyclic weighted median (CWM) method, which is intrinsically a coordinate decent algorithm, for L1-norm LRMF. The CWM method minimizes the objective by solving a sequence of scalar minimization sub-problems, each of which is convex and can be easily solved by the weighted median filter. The extensive experimental results validate that the CWM method outperforms state-of-the-arts in terms of both accuracy and computational efficiency.