Jianping Zhang

Jianping Zhang, Zhuoer Xu, Shiwen Cui et al.

Latent diffusion models achieve state-of-the-art performance on a variety of generative tasks, such as image synthesis and image editing. However, the robustness of latent diffusion models is not well studied. Previous works only focus on the adversarial attacks against the encoder or the output image under white-box settings, regardless of the denoising process. Therefore, in this paper, we aim to analyze the robustness of latent diffusion models more thoroughly. We first study the influence of the components inside latent diffusion models on their white-box robustness. In addition to white-box scenarios, we evaluate the black-box robustness of latent diffusion models via transfer attacks, where we consider both prompt-transfer and model-transfer settings and possible defense mechanisms. However, all these explorations need a comprehensive benchmark dataset, which is missing in the literature. Therefore, to facilitate the research of the robustness of latent diffusion models, we propose two automatic dataset construction pipelines for two kinds of image editing models and release the whole dataset. Our code and dataset are available at \url{https://github.com/jpzhang1810/LDM-Robustness}.

Jianping Zhang, Jen-tse Huang, Wenxuan Wang et al. · pku, tencent-ai

Deep neural networks have achieved unprecedented success on diverse vision tasks. However, they are vulnerable to adversarial noise that is imperceptible to humans. This phenomenon negatively affects their deployment in real-world scenarios, especially security-related ones. To evaluate the robustness of a target model in practice, transfer-based attacks craft adversarial samples with a local model and have attracted increasing attention from researchers due to their high efficiency. The state-of-the-art transfer-based attacks are generally based on data augmentation, which typically augments multiple training images from a linear path when learning adversarial samples. However, such methods selected the image augmentation path heuristically and may augment images that are semantics-inconsistent with the target images, which harms the transferability of the generated adversarial samples. To overcome the pitfall, we propose the Path-Augmented Method (PAM). Specifically, PAM first constructs a candidate augmentation path pool. It then settles the employed augmentation paths during adversarial sample generation with greedy search. Furthermore, to avoid augmenting semantics-inconsistent images, we train a Semantics Predictor (SP) to constrain the length of the augmentation path. Extensive experiments confirm that PAM can achieve an improvement of over 4.8% on average compared with the state-of-the-art baselines in terms of the attack success rates.

Wenxuan Wang, Jen-tse Huang, Weibin Wu et al. · pku, tencent-ai

The exponential growth of social media platforms such as Twitter and Facebook has revolutionized textual communication and textual content publication in human society. However, they have been increasingly exploited to propagate toxic content, such as hate speech, malicious advertisement, and pornography, which can lead to highly negative impacts (e.g., harmful effects on teen mental health). Researchers and practitioners have been enthusiastically developing and extensively deploying textual content moderation software to address this problem. However, we find that malicious users can evade moderation by changing only a few words in the toxic content. Moreover, modern content moderation software performance against malicious inputs remains underexplored. To this end, we propose MTTM, a Metamorphic Testing framework for Textual content Moderation software. Specifically, we conduct a pilot study on 2,000 text messages collected from real users and summarize eleven metamorphic relations across three perturbation levels: character, word, and sentence. MTTM employs these metamorphic relations on toxic textual contents to generate test cases, which are still toxic yet likely to evade moderation. In our evaluation, we employ MTTM to test three commercial textual content moderation software and two state-of-the-art moderation algorithms against three kinds of toxic content. The results show that MTTM achieves up to 83.9%, 51%, and 82.5% error finding rates (EFR) when testing commercial moderation software provided by Google, Baidu, and Huawei, respectively, and it obtains up to 91.2% EFR when testing the state-of-the-art algorithms from the academy. In addition, we leverage the test cases generated by MTTM to retrain the model we explored, which largely improves model robustness (0% to 5.9% EFR) while maintaining the accuracy on the original test set.

Jen-tse Huang, Jianping Zhang, Wenxuan Wang et al. · pku, tencent-ai

Due to the labor-intensive nature of manual test oracle construction, various automated testing techniques have been proposed to enhance the reliability of Natural Language Processing (NLP) software. In theory, these techniques mutate an existing test case (e.g., a sentence with its label) and assume the generated one preserves an equivalent or similar semantic meaning and thus, the same label. However, in practice, many of the generated test cases fail to preserve similar semantic meaning and are unnatural (e.g., grammar errors), which leads to a high false alarm rate and unnatural test cases. Our evaluation study finds that 44% of the test cases generated by the state-of-the-art (SOTA) approaches are false alarms. These test cases require extensive manual checking effort, and instead of improving NLP software, they can even degrade NLP software when utilized in model training. To address this problem, we propose AEON for Automatic Evaluation Of NLP test cases. For each generated test case, it outputs scores based on semantic similarity and language naturalness. We employ AEON to evaluate test cases generated by four popular testing techniques on five datasets across three typical NLP tasks. The results show that AEON aligns the best with human judgment. In particular, AEON achieves the best average precision in detecting semantic inconsistent test cases, outperforming the best baseline metric by 10%. In addition, AEON also has the highest average precision of finding unnatural test cases, surpassing the baselines by more than 15%. Moreover, model training with test cases prioritized by AEON leads to models that are more accurate and robust, demonstrating AEON's potential in improving NLP software.

Xiaohong Fan, Yin Yang, Ke Chen et al.

Proximal gradient-based optimization is one of the most common strategies to solve inverse problem of images, and it is easy to implement. However, these techniques often generate heavy artifacts in image reconstruction. One of the most popular refinement methods is to fine-tune the regularization parameter to alleviate such artifacts, but it may not always be sufficient or applicable due to increased computational costs. In this work, we propose a deep geometric incremental learning framework based on the second Nesterov proximal gradient optimization. The proposed end-to-end network not only has the powerful learning ability for high-/low-frequency image features, but also can theoretically guarantee that geometric texture details will be reconstructed from preliminary linear reconstruction. Furthermore, it can avoid the risk of intermediate reconstruction results falling outside the geometric decomposition domains and achieve fast convergence. Our reconstruction framework is decomposed into four modules including general linear reconstruction, cascade geometric incremental restoration, Nesterov acceleration, and post-processing. In the image restoration step, a cascade geometric incremental learning module is designed to compensate for missing texture information from different geometric spectral decomposition domains. Inspired by the overlap-tile strategy, we also develop a post-processing module to remove the block effect in patch-wise-based natural image reconstruction. All parameters in the proposed model are learnable, an adaptive initialization technique of physical parameters is also employed to make model flexibility and ensure converging smoothly. We compare the reconstruction performance of the proposed method with existing state-of-the-art methods to demonstrate its superiority. Our source codes are available at https://github.com/fanxiaohong/Nest-DGIL.

Hui Zhu, Shi Shu, Jianping Zhang

Solving variational image segmentation problems with hidden physics is often expensive and requires different algorithms and manually tunes model parameter. The deep learning methods based on the U-Net structure have obtained outstanding performances in many different medical image segmentation tasks, but designing such networks requires a lot of parameters and training data, not always available for practical problems. In this paper, inspired by traditional multi-phase convexity Mumford-Shah variational model and full approximation scheme (FAS) solving the nonlinear systems, we propose a novel variational-model-informed network (denoted as FAS-Unet) that exploits the model and algorithm priors to extract the multi-scale features. The proposed model-informed network integrates image data and mathematical models, and implements them through learning a few convolution kernels. Based on the variational theory and FAS algorithm, we first design a feature extraction sub-network (FAS-Solution module) to solve the model-driven nonlinear systems, where a skip-connection is employed to fuse the multi-scale features. Secondly, we further design a convolution block to fuse the extracted features from the previous stage, resulting in the final segmentation possibility. Experimental results on three different medical image segmentation tasks show that the proposed FAS-Unet is very competitive with other state-of-the-art methods in qualitative, quantitative and model complexity evaluations. Moreover, it may also be possible to train specialized network architectures that automatically satisfy some of the mathematical and physical laws in other image problems for better accuracy, faster training and improved generalization.The code is available at \url{https://github.com/zhuhui100/FASUNet}.

Jianping Zhang, Yizhan Huang, Weibin Wu et al.

Vision transformers (ViTs) have been successfully deployed in a variety of computer vision tasks, but they are still vulnerable to adversarial samples. Transfer-based attacks use a local model to generate adversarial samples and directly transfer them to attack a target black-box model. The high efficiency of transfer-based attacks makes it a severe security threat to ViT-based applications. Therefore, it is vital to design effective transfer-based attacks to identify the deficiencies of ViTs beforehand in security-sensitive scenarios. Existing efforts generally focus on regularizing the input gradients to stabilize the updated direction of adversarial samples. However, the variance of the back-propagated gradients in intermediate blocks of ViTs may still be large, which may make the generated adversarial samples focus on some model-specific features and get stuck in poor local optima. To overcome the shortcomings of existing approaches, we propose the Token Gradient Regularization (TGR) method. According to the structural characteristics of ViTs, TGR reduces the variance of the back-propagated gradient in each internal block of ViTs in a token-wise manner and utilizes the regularized gradient to generate adversarial samples. Extensive experiments on attacking both ViTs and CNNs confirm the superiority of our approach. Notably, compared to the state-of-the-art transfer-based attacks, our TGR offers a performance improvement of 8.8% on average.

Yanyan Li, Ke Chen, Chong Chen et al.

Diffeomorphic registration is a widely used technique for finding a smooth and invertible transformation between two coordinate systems, which are measured using template and reference images. The point-wise volume-preserving constraint $\det(\nabla\bm{\varphi}(\bm{x})) =1$ is effective in some cases, but may be too restrictive in others, especially when local deformations are relatively large. This can result in poor matching when enforcing large local deformations. In this paper, we propose a new bi-variant diffeomorphic image registration model that introduces a soft constraint on the Jacobian equation $\det(\nabla\bm{\varphi}(\bm{x})) = f(\bm{x}) > 0$. This allows local deformations to shrink and grow within a flexible range $0<κ_{m}<\det(\nabla\bm{\varphi}(\bm{x}))<κ_{M}$. The Jacobian determinant of transformation is explicitly controlled by optimizing the relaxation function $f(\bm{x})$. To prevent deformation folding and improve the smoothness of the transformation, a positive constraint is imposed on the optimization of the relaxation function $f(\bm{x})$, and a regularizer is used to ensure the smoothness of $f(\bm{x})$. Furthermore, the positivity constraint ensures that $f(\bm{x})$ is as close to one as possible, which helps to achieve a volume-preserving transformation on average. We also analyze the existence of the minimizer for the variational model and propose a penalty-splitting algorithm with a multilevel strategy to solve this model. Numerical experiments demonstrate the convergence of the proposed algorithm and show that the positivity constraint can effectively control the range of relative volume without compromising the accuracy of the registration. Moreover, the proposed model generates diffeomorphic maps for large local deformations and outperforms several existing registration models in terms of performance.

Wenwei Gu, Jinyang Liu, Zhuangbin Chen et al.

Cloud systems are susceptible to performance issues, which may cause service-level agreement violations and financial losses. In current practice, crucial metrics are monitored periodically to provide insight into the operational status of components. Identifying performance issues is often formulated as an anomaly detection problem, which is tackled by analyzing each metric independently. However, this approach overlooks the complex dependencies existing among cloud components. Some graph neural network-based methods take both temporal and relational information into account, however, the correlation violations in the metrics that serve as indicators of underlying performance issues are difficult for them to identify. Furthermore, a large volume of components in a cloud system results in a vast array of noisy metrics. This complexity renders it impractical for engineers to fully comprehend the correlations, making it challenging to identify performance issues accurately. To address these limitations, we propose Identifying Performance Issues based on Relational-Temporal Features (ISOLATE ), a learning-based approach that leverages both the relational and temporal features of metrics to identify performance issues. In particular, it adopts a graph neural network with attention to characterizing the relations among metrics and extracts long-term and multi-scale temporal patterns using a GRU and a convolution network, respectively. The learned graph attention weights can be further used to localize the correlation-violated metrics. Moreover, to relieve the impact of noisy data, ISOLATE utilizes a positive unlabeled learning strategy that tags pseudo-labels based on a small portion of confirmed negative examples. Extensive evaluation on both public and industrial datasets shows that ISOLATE outperforms all baseline models with 0.945 F1-score and 0.920 Hit rate@3.

Zhuoer Xu, Zhangxuan Gu, Jianping Zhang et al.

Deep neural networks are vulnerable to adversarial examples, dictating the imperativeness to test the model's robustness before deployment. Transfer-based attackers craft adversarial examples against surrogate models and transfer them to victim models deployed in the black-box situation. To enhance the adversarial transferability, structure-based attackers adjust the backpropagation path to avoid the attack from overfitting the surrogate model. However, existing structure-based attackers fail to explore the convolution module in CNNs and modify the backpropagation graph heuristically, leading to limited effectiveness. In this paper, we propose backPropagation pAth Search (PAS), solving the aforementioned two problems. We first propose SkipConv to adjust the backpropagation path of convolution by structural reparameterization. To overcome the drawback of heuristically designed backpropagation paths, we further construct a DAG-based search space, utilize one-step approximation for path evaluation and employ Bayesian Optimization to search for the optimal path. We conduct comprehensive experiments in a wide range of transfer settings, showing that PAS improves the attack success rate by a huge margin for both normally trained and defense models.

Teng Wang, Wing-Yin Yu, Ruifeng She et al.

Mixed Integer Programming (MIP) has been extensively applied in areas requiring mathematical solvers to address complex instances within tight time constraints. However, as the problem scale increases, the complexity of model formulation and finding feasible solutions escalates significantly. In contrast, the model-building cost for end-to-end models, such as large language models (LLMs), remains largely unaffected by problem scale due to their pattern recognition capabilities. While LLMs, like GPT-4, without fine-tuning, can handle some traditional medium-scale MIP problems, they struggle with uncommon or highly specialized MIP scenarios. Fine-tuning LLMs can yield some feasible solutions for medium-scale MIP instances, but these models typically fail to explore diverse solutions when constrained by a low and constant temperature, limiting their performance. In this paper, we propose and evaluate a recursively dynamic temperature method integrated with a chain-of-thought approach. Our findings show that starting with a high temperature and gradually lowering it leads to better feasible solutions compared to other dynamic temperature strategies. Additionally, by comparing results generated by the LLM with those from Gurobi, we demonstrate that the LLM can produce solutions that complement traditional solvers by accelerating the pruning process and improving overall efficiency.

Yujie Feng, Yin Yang, Xiaohong Fan et al.

Recently, deep learning methods have gained remarkable achievements in the field of image restoration for remote sensing (RS). However, most existing RS image restoration methods focus mainly on conventional first-order degradation models, which may not effectively capture the imaging mechanisms of remote sensing images. Furthermore, many RS image restoration approaches that use deep learning are often criticized for their lacks of architecture transparency and model interpretability. To address these problems, we propose a novel progressive restoration network for high-order degradation imaging (HDI-PRNet), to progressively restore different image degradation. HDI-PRNet is developed based on the theoretical framework of degradation imaging, also Markov properties of the high-order degradation process and Maximum a posteriori (MAP) estimation, offering the benefit of mathematical interpretability within the unfolding network. The framework is composed of three main components: a module for image denoising that relies on proximal mapping prior learning, a module for image deblurring that integrates Neumann series expansion with dual-domain degradation learning, and a module for super-resolution. Extensive experiments demonstrate that our method achieves superior performance on both synthetic and real remote sensing images.

Jinqiu Deng, Ke Chen, Mingke Li et al.

Diffeomorphic image registration is crucial for various medical imaging applications because it can preserve the topology of the transformation. This study introduces DCCNN-LSTM-Reg, a learning framework that evolves dynamically and learns a symmetrical registration path by satisfying a specified control increment system. This framework aims to obtain symmetric diffeomorphic deformations between moving and fixed images. To achieve this, we combine deep learning networks with diffeomorphic mathematical mechanisms to create a continuous and dynamic registration architecture, which consists of multiple Symmetric Registration (SR) modules cascaded on five different scales. Specifically, our method first uses two U-nets with shared parameters to extract multiscale feature pyramids from the images. We then develop an SR-module comprising a sequential CNN-LSTM architecture to progressively correct the forward and reverse multiscale deformation fields using control increment learning and the homotopy continuation technique. Through extensive experiments on three 3D registration tasks, we demonstrate that our method outperforms existing approaches in both quantitative and qualitative evaluations.

Wenxuan Wang, Jingyuan Huang, Chang Chen et al.

The exponential growth of social media platforms, such as Facebook and TikTok, has revolutionized communication and content publication in human society. Users on these platforms can publish multimedia content that delivers information via the combination of text, audio, images, and video. Meanwhile, the multimedia content release facility has been increasingly exploited to propagate toxic content, such as hate speech, malicious advertisements, and pornography. To this end, content moderation software has been widely deployed on these platforms to detect and blocks toxic content. However, due to the complexity of content moderation models and the difficulty of understanding information across multiple modalities, existing content moderation software can fail to detect toxic content, which often leads to extremely negative impacts. We introduce Semantic Fusion, a general, effective methodology for validating multimedia content moderation software. Our key idea is to fuse two or more existing single-modal inputs (e.g., a textual sentence and an image) into a new input that combines the semantics of its ancestors in a novel manner and has toxic nature by construction. This fused input is then used for validating multimedia content moderation software. We realized Semantic Fusion as DUO, a practical content moderation software testing tool. In our evaluation, we employ DUO to test five commercial content moderation software and two state-of-the-art models against three kinds of toxic content. The results show that DUO achieves up to 100% error finding rate (EFR) when testing moderation software. In addition, we leverage the test cases generated by DUO to retrain the two models we explored, which largely improves model robustness while maintaining the accuracy on the original test set.

Jianping Zhang, Weibin Wu, Jen-tse Huang et al.

Deep neural networks (DNNs) are known to be vulnerable to adversarial examples. It is thus imperative to devise effective attack algorithms to identify the deficiencies of DNNs beforehand in security-sensitive applications. To efficiently tackle the black-box setting where the target model's particulars are unknown, feature-level transfer-based attacks propose to contaminate the intermediate feature outputs of local models, and then directly employ the crafted adversarial samples to attack the target model. Due to the transferability of features, feature-level attacks have shown promise in synthesizing more transferable adversarial samples. However, existing feature-level attacks generally employ inaccurate neuron importance estimations, which deteriorates their transferability. To overcome such pitfalls, in this paper, we propose the Neuron Attribution-based Attack (NAA), which conducts feature-level attacks with more accurate neuron importance estimations. Specifically, we first completely attribute a model's output to each neuron in a middle layer. We then derive an approximation scheme of neuron attribution to tremendously reduce the computation overhead. Finally, we weight neurons based on their attribution results and launch feature-level attacks. Extensive experiments confirm the superiority of our approach to the state-of-the-art benchmarks.

Daoping Zhang, Gary P. T. Choi, Jianping Zhang et al.

With the advancement of computer technology, there is a surge of interest in effective mapping methods for objects in higher-dimensional spaces. To establish a one-to-one correspondence between objects, higher-dimensional quasi-conformal theory can be utilized for ensuring the bijectivity of the mappings. In addition, it is often desirable for the mappings to satisfy certain prescribed geometric constraints and possess low distortion in conformality or volume. In this work, we develop a unifying framework for computing $n$-dimensional quasi-conformal mappings. More specifically, we propose a variational model that integrates quasi-conformal distortion, volumetric distortion, landmark correspondence, intensity mismatch and volume prior information to handle a large variety of deformation problems. We further prove the existence of a minimizer for the proposed model and devise efficient numerical methods to solve the optimization problem. We demonstrate the effectiveness of the proposed framework using various experiments in two- and three-dimensions, with applications to medical image registration, adaptive remeshing and shape modeling.

Rishi Chhatwal, Robert Keeling, Peter Gronvall et al.

Protecting privileged communications and data from disclosure is paramount for legal teams. Legal advice, such as attorney-client communications or litigation strategy are typically exempt from disclosure in litigations or regulatory events and are vital to the attorney-client relationship. To protect this information from disclosure, companies and outside counsel often review vast amounts of documents to determine those that contain privileged material. This process is extremely costly and time consuming. As data volumes increase, legal counsel normally employs methods to reduce the number of documents requiring review while balancing the need to ensure the protection of privileged information. Keyword searching is relied upon as a method to target privileged information and reduce document review populations. Keyword searches are effective at casting a wide net but often return overly inclusive results - most of which do not contain privileged information. To overcome the weaknesses of keyword searching, legal teams increasingly are using machine learning techniques to target privileged information. In these studies, classic text classification techniques are applied to build classification models to identify privileged documents. In this paper, the authors propose a different method by applying machine learning / convolutional neural network techniques (CNN) to identify privileged documents. Our proposed method combines keyword searching with CNN. For each keyword term, a CNN model is created using the context of the occurrences of the keyword. In addition, a method was proposed to select reliable privileged (positive) training keyword occurrences from labeled positive training documents. Extensive experiments were conducted, and the results show that the proposed methods can significantly reduce false positives while still capturing most of the true positives.

Robert Keeling, Rishi Chhatwal, Nathaniel Huber-Fliflet et al.

Research has shown that Convolutional Neural Networks (CNN) can be effectively applied to text classification as part of a predictive coding protocol. That said, most research to date has been conducted on data sets with short documents that do not reflect the variety of documents in real world document reviews. Using data from four actual reviews with documents of varying lengths, we compared CNN with other popular machine learning algorithms for text classification, including Logistic Regression, Support Vector Machine, and Random Forest. For each data set, classification models were trained with different training sample sizes using different learning algorithms. These models were then evaluated using a large randomly sampled test set of documents, and the results were compared using precision and recall curves. Our study demonstrates that CNN performed well, but that there was no single algorithm that performed the best across the combination of data sets and training sample sizes. These results will help advance research into the legal profession's use of machine learning algorithms that maximize performance.

Christian J. Mahoney, Nathaniel Huber-Fliflet, Haozhen Zhao et al.

Active learning is a popular methodology in text classification - known in the legal domain as "predictive coding" or "Technology Assisted Review" or "TAR" - due to its potential to minimize the required review effort to build effective classifiers. In this study, we use extensive experimentation to examine the impact of popular seed set selection strategies in active learning, within a predictive coding exercise, and evaluate different active learning strategies against well-researched continuous active learning strategies for the purpose of determining efficient training methods for classifying large populations quickly and precisely. We study how random sampling, keyword models and clustering based seed set selection strategies combined together with top-ranked, uncertain, random, recall inspired, and hybrid active learning document selection strategies affect the performance of active learning for predictive coding. We use the percentage of documents requiring review to reach 75% recall as the "benchmark" metric to evaluate and compare our approaches. In most cases we find that seed set selection methods have a minor impact, though they do show significant impact in lower richness data sets or when choosing a top-ranked active learning selection strategy. Our results also show that active learning selection strategies implementing uncertainty, random, or 75% recall selection strategies has the potential to reach the optimum active learning round much earlier than the popular continuous active learning approach (top-ranked selection). The results of our research shed light on the impact of active learning seed set selection strategies and also the effectiveness of the selection strategies for the following learning rounds. Legal practitioners can use the results of this study to enhance the efficiency, precision, and simplicity of their predictive coding process.

Peter Gronvall, Nathaniel Huber-Fliflet, Jianping Zhang et al.

Protecting privileged communications and data from disclosure is paramount for legal teams. Unrestricted legal advice, such as attorney-client communications or litigation strategy. are vital to the legal process and are exempt from disclosure in litigations or regulatory events. To protect this information from being disclosed, companies and outside counsel must review vast amounts of documents to determine those that contain privileged material. This process is extremely costly and time consuming. As data volumes increase, legal counsel employ methods to reduce the number of documents requiring review while balancing the need to ensure the protection of privileged information. Keyword searching is relied upon as a method to target privileged information and reduce document review populations. Keyword searches are effective at casting a wide net but return over inclusive results -- most of which do not contain privileged information -- and without detailed knowledge of the data, keyword lists cannot be crafted to find all privilege material. Overly-inclusive keyword searching can also be problematic, because even while it drives up costs, it also can cast `too far of a net' and thus produce unreliable results.To overcome these weaknesses of keyword searching, legal teams are using a new method to target privileged information called predictive modeling. Predictive modeling can successfully identify privileged material but little research has been published to confirm its effectiveness when compared to keyword searching. This paper summarizes a study of the effectiveness of keyword searching and predictive modeling when applied to real-world data. With this study, this group of collaborators wanted to examine and understand the benefits and weaknesses of both approaches to legal teams with identifying privilege material in document populations.

Jianping Zhang, Ke Chen

To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order derivative based total $α$-order variation model, which can outperform the currently popular high order regularization models. There exist several previous works using total $α$-order variations for image restoration; however first no analysis is done yet and second all tested formulations, differing from each other, utilize the zero Dirichlet boundary conditions which are not realistic (while non-zero boundary conditions violate definitions of fractional-order derivatives). This paper first reviews some results of fractional-order derivatives and then analyzes the theoretical properties of the proposed total $α$-order variational model rigorously. It then develops four algorithms for solving the variational problem, one based on the variational Split-Bregman idea and three based on direct solution of the discretise-optimization problem. Numerical experiments show that, in terms of restoration quality and solution efficiency, the proposed model can produce highly competitive results, for smooth images, to two established high order models: the mean curvature and the total generalized variation.