Tieyong Zeng

Guangwei Gao, Zhengxue Wang, Juncheng Li et al.

Single-image super-resolution (SISR) has achieved significant breakthroughs with the development of deep learning. However, these methods are difficult to be applied in real-world scenarios since they are inevitably accompanied by the problems of computational and memory costs caused by the complex operations. To solve this issue, we propose a Lightweight Bimodal Network (LBNet) for SISR. Specifically, an effective Symmetric CNN is designed for local feature extraction and coarse image reconstruction. Meanwhile, we propose a Recursive Transformer to fully learn the long-term dependence of images thus the global information can be fully used to further refine texture details. Studies show that the hybrid of CNN and Transformer can build a more efficient model. Extensive experiments have proved that our LBNet achieves more prominent performance than other state-of-the-art methods with a relatively low computational cost and memory consumption. The code is available at https://github.com/IVIPLab/LBNet.

Yaofang Liu, Xiaodong Cun, Xuebo Liu et al.

The vision and language generative models have been overgrown in recent years. For video generation, various open-sourced models and public-available services have been developed to generate high-quality videos. However, these methods often use a few metrics, e.g., FVD or IS, to evaluate the performance. We argue that it is hard to judge the large conditional generative models from the simple metrics since these models are often trained on very large datasets with multi-aspect abilities. Thus, we propose a novel framework and pipeline for exhaustively evaluating the performance of the generated videos. Our approach involves generating a diverse and comprehensive list of 700 prompts for text-to-video generation, which is based on an analysis of real-world user data and generated with the assistance of a large language model. Then, we evaluate the state-of-the-art video generative models on our carefully designed benchmark, in terms of visual qualities, content qualities, motion qualities, and text-video alignment with 17 well-selected objective metrics. To obtain the final leaderboard of the models, we further fit a series of coefficients to align the objective metrics to the users' opinions. Based on the proposed human alignment method, our final score shows a higher correlation than simply averaging the metrics, showing the effectiveness of the proposed evaluation method.

Guangwei Gao, Zixiang Xu, Juncheng Li et al.

Recently, deep convolution neural networks (CNNs) steered face super-resolution methods have achieved great progress in restoring degraded facial details by jointly training with facial priors. However, these methods have some obvious limitations. On the one hand, multi-task joint learning requires additional marking on the dataset, and the introduced prior network will significantly increase the computational cost of the model. On the other hand, the limited receptive field of CNN will reduce the fidelity and naturalness of the reconstructed facial images, resulting in suboptimal reconstructed images. In this work, we propose an efficient CNN-Transformer Cooperation Network (CTCNet) for face super-resolution tasks, which uses the multi-scale connected encoder-decoder architecture as the backbone. Specifically, we first devise a novel Local-Global Feature Cooperation Module (LGCM), which is composed of a Facial Structure Attention Unit (FSAU) and a Transformer block, to promote the consistency of local facial detail and global facial structure restoration simultaneously. Then, we design an efficient Feature Refinement Module (FRM) to enhance the encoded features. Finally, to further improve the restoration of fine facial details, we present a Multi-scale Feature Fusion Unit (MFFU) to adaptively fuse the features from different stages in the encoder procedure. Extensive evaluations on various datasets have assessed that the proposed CTCNet can outperform other state-of-the-art methods significantly. Source code will be available at https://github.com/IVIPLab/CTCNet.

Jing-Xiao Liao, Sheng-Lai Wei, Chen-Long Xie et al.

Deep learning has achieved remarkable success in the field of bearing fault diagnosis. However, this success comes with larger models and more complex computations, which cannot be transferred into industrial fields requiring models to be of high speed, strong portability, and low power consumption. In this paper, we propose a lightweight and deployable model for bearing fault diagnosis, referred to as BearingPGA-Net, to address these challenges. Firstly, aided by a well-trained large model, we train BearingPGA-Net via decoupled knowledge distillation. Despite its small size, our model demonstrates excellent fault diagnosis performance compared to other lightweight state-of-the-art methods. Secondly, we design an FPGA acceleration scheme for BearingPGA-Net using Verilog. This scheme involves the customized quantization and designing programmable logic gates for each layer of BearingPGA-Net on the FPGA, with an emphasis on parallel computing and module reuse to enhance the computational speed. To the best of our knowledge, this is the first instance of deploying a CNN-based bearing fault diagnosis model on an FPGA. Experimental results reveal that our deployment scheme achieves over 200 times faster diagnosis speed compared to CPU, while achieving a lower-than-0.4\% performance drop in terms of F1, Recall, and Precision score on our independently-collected bearing dataset. Our code is available at \url{https://github.com/asdvfghg/BearingPGA-Net}.

Hansheng Guo, Juncheng Li, Guangwei Gao et al.

Stereo image super-resolution aims to boost the performance of image super-resolution by exploiting the supplementary information provided by binocular systems. Although previous methods have achieved promising results, they did not fully utilize the information of cross-view and intra-view. To further unleash the potential of binocular images, in this letter, we propose a novel Transformerbased parallax fusion module called Parallax Fusion Transformer (PFT). PFT employs a Cross-view Fusion Transformer (CVFT) to utilize cross-view information and an Intra-view Refinement Transformer (IVRT) for intra-view feature refinement. Meanwhile, we adopted the Swin Transformer as the backbone for feature extraction and SR reconstruction to form a pure Transformer architecture called PFT-SSR. Extensive experiments and ablation studies show that PFT-SSR achieves competitive results and outperforms most SOTA methods. Source code is available at https://github.com/MIVRC/PFT-PyTorch.

Juncheng Li, Bodong Cheng, Ying Chen et al.

Transformer-based image denoising methods have achieved encouraging results in the past year. However, it must uses linear operations to model long-range dependencies, which greatly increases model inference time and consumes GPU storage space. Compared with convolutional neural network-based methods, current Transformer-based image denoising methods cannot achieve a balance between performance improvement and resource consumption. In this paper, we propose an Efficient Wavelet Transformer (EWT) for image denoising. Specifically, we use Discrete Wavelet Transform (DWT) and Inverse Wavelet Transform (IWT) for downsampling and upsampling, respectively. This method can fully preserve the image features while reducing the image resolution, thereby greatly reducing the device resource consumption of the Transformer model. Furthermore, we propose a novel Dual-stream Feature Extraction Block (DFEB) to extract image features at different levels, which can further reduce model inference time and GPU memory usage. Experiments show that our method speeds up the original Transformer by more than 80%, reduces GPU memory usage by more than 60%, and achieves excellent denoising results. All code will be public.

Yingying Fang, Shuang Wu, Sheng Zhang et al.

Effectively leveraging multimodal data such as various images, laboratory tests and clinical information is gaining traction in a variety of AI-based medical diagnosis and prognosis tasks. Most existing multi-modal techniques only focus on enhancing their performance by leveraging the differences or shared features from various modalities and fusing feature across different modalities. These approaches are generally not optimal for clinical settings, which pose the additional challenges of limited training data, as well as being rife with redundant data or noisy modality channels, leading to subpar performance. To address this gap, we study the robustness of existing methods to data redundancy and noise and propose a generalized dynamic multimodal information bottleneck framework for attaining a robust fused feature representation. Specifically, our information bottleneck module serves to filter out the task-irrelevant information and noises in the fused feature, and we further introduce a sufficiency loss to prevent dropping of task-relevant information, thus explicitly preserving the sufficiency of prediction information in the distilled feature. We validate our model on an in-house and a public COVID19 dataset for mortality prediction as well as two public biomedical datasets for diagnostic tasks. Extensive experiments show that our method surpasses the state-of-the-art and is significantly more robust, being the only method to remain performance when large-scale noisy channels exist. Our code is publicly available at https://github.com/ayanglab/DMIB.

Bodong Cheng, Juncheng Li, Ying Chen et al.

Image restoration under severe weather is a challenging task. Most of the past works focused on removing rain and haze phenomena in images. However, snow is also an extremely common atmospheric phenomenon that will seriously affect the performance of high-level computer vision tasks, such as object detection and semantic segmentation. Recently, some methods have been proposed for snow removing, and most methods deal with snow images directly as the optimization object. However, the distribution of snow location and shape is complex. Therefore, failure to detect snowflakes / snow streak effectively will affect snow removing and limit the model performance. To solve these issues, we propose a Snow Mask Guided Adaptive Residual Network (SMGARN). Specifically, SMGARN consists of three parts, Mask-Net, Guidance-Fusion Network (GF-Net), and Reconstruct-Net. Firstly, we build a Mask-Net with Self-pixel Attention (SA) and Cross-pixel Attention (CA) to capture the features of snowflakes and accurately localized the location of the snow, thus predicting an accurate snow mask. Secondly, the predicted snow mask is sent into the specially designed GF-Net to adaptively guide the model to remove snow. Finally, an efficient Reconstruct-Net is used to remove the veiling effect and correct the image to reconstruct the final snow-free image. Extensive experiments show that our SMGARN numerically outperforms all existing snow removal methods, and the reconstructed images are clearer in visual contrast. All codes will be available.

Zhifan Gao, Yifeng Guo, Jiajing Zhang et al.

The long acquisition time has limited the accessibility of magnetic resonance imaging (MRI) because it leads to patient discomfort and motion artifacts. Although several MRI techniques have been proposed to reduce the acquisition time, compressed sensing in magnetic resonance imaging (CS-MRI) enables fast acquisition without compromising SNR and resolution. However, existing CS-MRI methods suffer from the challenge of aliasing artifacts. This challenge results in the noise-like textures and missing the fine details, thus leading to unsatisfactory reconstruction performance. To tackle this challenge, we propose a hierarchical perception adversarial learning framework (HP-ALF). HP-ALF can perceive the image information in the hierarchical mechanism: image-level perception and patch-level perception. The former can reduce the visual perception difference in the entire image, and thus achieve aliasing artifact removal. The latter can reduce this difference in the regions of the image, and thus recover fine details. Specifically, HP-ALF achieves the hierarchical mechanism by utilizing multilevel perspective discrimination. This discrimination can provide the information from two perspectives (overall and regional) for adversarial learning. It also utilizes a global and local coherent discriminator to provide structure information to the generator during training. In addition, HP-ALF contains a context-aware learning block to effectively exploit the slice information between individual images for better reconstruction performance. The experiments validated on three datasets demonstrate the effectiveness of HP-ALF and its superiority to the comparative methods.

Xiaole Tang, Xile Zhao, Jun Liu et al.

Non-blind deblurring methods achieve decent performance under the accurate blur kernel assumption. Since the kernel uncertainty (i.e. kernel error) is inevitable in practice, semi-blind deblurring is suggested to handle it by introducing the prior of the kernel (or induced) error. However, how to design a suitable prior for the kernel (or induced) error remains challenging. Hand-crafted prior, incorporating domain knowledge, generally performs well but may lead to poor performance when kernel (or induced) error is complex. Data-driven prior, which excessively depends on the diversity and abundance of training data, is vulnerable to out-of-distribution blurs and images. To address this challenge, we suggest a dataset-free deep residual prior for the kernel induced error (termed as residual) expressed by a customized untrained deep neural network, which allows us to flexibly adapt to different blurs and images in real scenarios. By organically integrating the respective strengths of deep priors and hand-crafted priors, we propose an unsupervised semi-blind deblurring model which recovers the latent image from the blurry image and inaccurate blur kernel. To tackle the formulated model, an efficient alternating minimization algorithm is developed. Extensive experiments demonstrate the favorable performance of the proposed method as compared to data-driven and model-driven methods in terms of image quality and the robustness to the kernel error.

Yilin Lyu, Xin Liu, Mingyang Song et al.

Information Bottlenecks (IBs) learn representations that generalize to unseen data by information compression. However, existing IBs are practically unable to guarantee generalization in real-world scenarios due to the vacuous generalization bound. The recent PAC-Bayes IB uses information complexity instead of information compression to establish a connection with the mutual information generalization bound. However, it requires the computation of expensive second-order curvature, which hinders its practical application. In this paper, we establish the connection between the recognizability of representations and the recent functional conditional mutual information (f-CMI) generalization bound, which is significantly easier to estimate. On this basis we propose a Recognizable Information Bottleneck (RIB) which regularizes the recognizability of representations through a recognizability critic optimized by density ratio matching under the Bregman divergence. Extensive experiments on several commonly used datasets demonstrate the effectiveness of the proposed method in regularizing the model and estimating the generalization gap.

Dong Li, Shuisheng Zhou, Tieyong Zeng et al.

K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters k has to be given a priori. To solve these two issues, a multi-prototypes convex merging based K-Means clustering algorithm (MCKM) is presented. First, based on the structure of the spurious local minima of the K-Means problem, a multi-prototypes sampling (MPS) is designed to select the appropriate number of multi-prototypes for data with arbitrary shapes. A theoretical proof is given to guarantee that the multi-prototypes selected by MPS can achieve a constant factor approximation to the optimal cost of the K-Means problem. Then, a merging technique, called convex merging (CM), merges the multi-prototypes to get a better local minima without k being given a priori. Specifically, CM can obtain the optimal merging and estimate the correct k. By integrating these two techniques with K-Means algorithm, the proposed MCKM is an efficient and explainable clustering algorithm for escaping the undesirable local minima of K-Means problem without given k first. Experimental results performed on synthetic and real-world data sets have verified the effectiveness of the proposed algorithm.

Tingting Wu, Wenna Wu, Ying Yang et al.

The Retinex model is one of the most representative and effective methods for low-light image enhancement. However, the Retinex model does not explicitly tackle the noise problem, and shows unsatisfactory enhancing results. In recent years, due to the excellent performance, deep learning models have been widely used in low-light image enhancement. However, these methods have two limitations: i) The desirable performance can only be achieved by deep learning when a large number of labeled data are available. However, it is not easy to curate massive low/normal-light paired data; ii) Deep learning is notoriously a black-box model [1]. It is difficult to explain their inner-working mechanism and understand their behaviors. In this paper, using a sequential Retinex decomposition strategy, we design a plug-and-play framework based on the Retinex theory for simultaneously image enhancement and noise removal. Meanwhile, we develop a convolutional neural network-based (CNN-based) denoiser into our proposed plug-and-play framework to generate a reflectance component. The final enhanced image is produced by integrating the illumination and reflectance with gamma correction. The proposed plug-and-play framework can facilitate both post hoc and ad hoc interpretability. Extensive experiments on different datasets demonstrate that our framework outcompetes the state-of-the-art methods in both image enhancement and denoising.

Feng-Lei Fan, Yingxin Li, Hanchuan Peng et al.

Throughout history, the development of artificial intelligence, particularly artificial neural networks, has been open to and constantly inspired by the increasingly deepened understanding of the brain, such as the inspiration of neocognitron, which is the pioneering work of convolutional neural networks. Per the motives of the emerging field: NeuroAI, a great amount of neuroscience knowledge can help catalyze the next generation of AI by endowing a network with more powerful capabilities. As we know, the human brain has numerous morphologically and functionally different neurons, while artificial neural networks are almost exclusively built on a single neuron type. In the human brain, neuronal diversity is an enabling factor for all kinds of biological intelligent behaviors. Since an artificial network is a miniature of the human brain, introducing neuronal diversity should be valuable in terms of addressing those essential problems of artificial networks such as efficiency, interpretability, and memory. In this Primer, we first discuss the preliminaries of biological neuronal diversity and the characteristics of information transmission and processing in a biological neuron. Then, we review studies of designing new neurons for artificial networks. Next, we discuss what gains can neuronal diversity bring into artificial networks and exemplary applications in several important fields. Lastly, we discuss the challenges and future directions of neuronal diversity to explore the potential of NeuroAI.

Cheng Chang, Tieyong Zeng

Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset. If appropriate physics constraints (e.g. expressed in partial differential equations) can be incorporated, the amount of data can be greatly reduced and the accuracy further improved. In this work, we propose a hybrid data driven-physics constrained Gaussian process regression framework. We encode the physics knowledge with Boltzmann-Gibbs distribution and derive our model through maximum likelihood (ML) approach. We apply deep kernel learning method. The proposed model learns from both data and physics constraints through the training of a deep neural network, which serves as part of the covariance function in GPR. The proposed model achieves good results in high-dimensional problem, and correctly propagate the uncertainty, with very limited labelled data provided.

Feng-Lei Fan, Hang-Cheng Dong, Zhongming Wu et al.

Inspired by neuronal diversity in the biological neural system, a plethora of studies proposed to design novel types of artificial neurons and introduce neuronal diversity into artificial neural networks. Recently proposed quadratic neuron, which replaces the inner-product operation in conventional neurons with a quadratic one, have achieved great success in many essential tasks. Despite the promising results of quadratic neurons, there is still an unresolved issue: \textit{Is the superior performance of quadratic networks simply due to the increased parameters or due to the intrinsic expressive capability?} Without clarifying this issue, the performance of quadratic networks is always suspicious. Additionally, resolving this issue is reduced to finding killer applications of quadratic networks. In this paper, with theoretical and empirical studies, we show that quadratic networks enjoy parametric efficiency, thereby confirming that the superior performance of quadratic networks is due to the intrinsic expressive capability. This intrinsic expressive ability comes from that quadratic neurons can easily represent nonlinear interaction, while it is hard for conventional neurons. Theoretically, we derive the approximation efficiency of the quadratic network over conventional ones in terms of real space and manifolds. Moreover, from the perspective of the Barron space, we demonstrate that there exists a functional space whose functions can be approximated by quadratic networks in a dimension-free error, but the approximation error of conventional networks is dependent on dimensions. Empirically, experimental results on synthetic data, classic benchmarks, and real-world applications show that quadratic models broadly enjoy parametric efficiency, and the gain of efficiency depends on the task.

Juncheng Li, Hanhui Yang, Qiaosi Yi et al.

Single image denoising (SID) has achieved significant breakthroughs with the development of deep learning. However, the proposed methods are often accompanied by plenty of parameters, which greatly limits their application scenarios. Different from previous works that blindly increase the depth of the network, we explore the degradation mechanism of the noisy image and propose a lightweight Multiple Degradation and Reconstruction Network (MDRN) to progressively remove noise. Meanwhile, we propose two novel Heterogeneous Knowledge Distillation Strategies (HMDS) to enable MDRN to learn richer and more accurate features from heterogeneous models, which make it possible to reconstruct higher-quality denoised images under extreme conditions. Extensive experiments show that our MDRN achieves favorable performance against other SID models with fewer parameters. Meanwhile, plenty of ablation studies demonstrate that the introduced HMDS can improve the performance of tiny models or the model under high noise levels, which is extremely useful for related applications.

Hanhui Yang, Juncheng Li, Lok Ming Lui et al.

Fast and accurate MRI reconstruction is a key concern in modern clinical practice. Recently, numerous Deep-Learning methods have been proposed for MRI reconstruction, however, they usually fail to reconstruct sharp details from the subsampled k-space data. To solve this problem, we propose a lightweight and accurate Edge Attention MRI Reconstruction Network (EAMRI) to reconstruct images with edge guidance. Specifically, we design an efficient Edge Prediction Network to directly predict accurate edges from the blurred image. Meanwhile, we propose a novel Edge Attention Module (EAM) to guide the image reconstruction utilizing the extracted edge priors, as inspired by the popular self-attention mechanism. EAM first projects the input image and edges into Q_image, K_edge, and V_image, respectively. Then EAM pairs the Q_image with K_edge along the channel dimension, such that 1) it can search globally for the high-frequency image features that are activated by the edge priors; 2) the overall computation burdens are largely reduced compared with the traditional spatial-wise attention. With the help of EAM, the predicted edge priors can effectively guide the model to reconstruct high-quality MR images with accurate edges. Extensive experiments show that our proposed EAMRI outperforms other methods with fewer parameters and can recover more accurate edges.

Ziwen Wang, Yancheng Yuan, Jiaming Ma et al.

In this paper, we propose a randomly projected convex clustering model for clustering a collection of $n$ high dimensional data points in $\mathbb{R}^d$ with $K$ hidden clusters. Compared to the convex clustering model for clustering original data with dimension $d$, we prove that, under some mild conditions, the perfect recovery of the cluster membership assignments of the convex clustering model, if exists, can be preserved by the randomly projected convex clustering model with embedding dimension $m = O(ε^{-2}\log(n))$, where $0 < ε< 1$ is some given parameter. We further prove that the embedding dimension can be improved to be $O(ε^{-2}\log(K))$, which is independent of the number of data points. Extensive numerical experiment results will be presented in this paper to demonstrate the robustness and superior performance of the randomly projected convex clustering model. The numerical results presented in this paper also demonstrate that the randomly projected convex clustering model can outperform the randomly projected K-means model in practice.

Jianfei Li, Chaoyan Huang, Raymond Chan et al.

Spherical image processing has been widely applied in many important fields, such as omnidirectional vision for autonomous cars, global climate modelling, and medical imaging. It is non-trivial to extend an algorithm developed for flat images to the spherical ones. In this work, we focus on the challenging task of spherical image inpainting with deep learning-based regularizer. Instead of a naive application of existing models for planar images, we employ a fast directional spherical Haar framelet transform and develop a novel optimization framework based on a sparsity assumption of the framelet transform. Furthermore, by employing progressive encoder-decoder architecture, a new and better-performed deep CNN denoiser is carefully designed and works as an implicit regularizer. Finally, we use a plug-and-play method to handle the proposed optimization model, which can be implemented efficiently by training the CNN denoiser prior. Numerical experiments are conducted and show that the proposed algorithms can greatly recover damaged spherical images and achieve the best performance over purely using deep learning denoiser and plug-and-play model.

Ao Chen, Jinghua Zhang, Md Mamunur Rahaman et al.

The accurate detection of sperms and impurities is a very challenging task, facing problems such as the small size of targets, indefinite target morphologies, low contrast and resolution of the video, and similarity of sperms and impurities. So far, the detection of sperms and impurities still largely relies on the traditional image processing and detection techniques which only yield limited performance and often require manual intervention in the detection process, therefore unfavorably escalating the time cost and injecting the subjective bias into the analysis. Encouraged by the successes of deep learning methods in numerous object detection tasks, here we report a deep learning model based on Double Branch Feature Extraction Network (DBFEN) and Cross-conjugate Feature Pyramid Networks (CCFPN).DBFEN is designed to extract visual features from tiny objects with a double branch structure, and CCFPN is further introduced to fuse the features extracted by DBFEN to enhance the description of position and high-level semantic information. Our work is the pioneer of introducing deep learning approaches to the detection of sperms and impurities. Experiments show that the highest AP50 of the sperm and impurity detection is 91.13% and 59.64%, which lead its competitors by a substantial margin and establish new state-of-the-art results in this problem.

Jianwei Niu, Hok Shing Wong, Tieyong Zeng

Phase retrieval is an important problem with significant physical and industrial applications. In this paper, we consider the case where the magnitude of the measurement of an underlying signal is corrupted by Gaussian noise. We introduce a convex augmentation approach for phase retrieval based on total variation regularization. In contrast to popular convex relaxation models like PhaseLift, our model can be efficiently solved by a modified semi-proximal alternating direction method of multipliers (sPADMM). The modified sPADMM is more general and flexible than the standard one, and its convergence is also established in this paper. Extensive numerical experiments are conducted to showcase the effectiveness of the proposed method.

Fenglei Fan, Juntong Fan, Dayang Wang et al.

The rapid growth of large models' size has far outpaced that of computing resources. To bridge this gap, encouraged by the parsimonious relationship between genotype and phenotype in the brain's growth and development, we propose the so-called Hyper-Compression that turns the model compression into the issue of parameter representation via a hyperfunction. Specifically, it is known that the trajectory of some low-dimensional dynamic systems can fill the high-dimensional space eventually. Thus, Hyper-Compression, using these dynamic systems as the hyperfunctions, represents the parameters of the target network by their corresponding composition number or trajectory length. This suggests a novel mechanism for model compression, substantially different from the existing pruning, quantization, distillation, and decomposition. Along this direction, we methodologically identify a suitable dynamic system with the irrational winding as the hyperfunction and theoretically derive its associated error bound. Next, guided by our theoretical insights, we propose several engineering twists to make the Hyper-Compression pragmatic and effective. Lastly, systematic and comprehensive experiments on \textcolor{black}{NLP models such as LLaMA and Qwen series and vision models} confirm that Hyper-Compression enjoys the following \textbf{PNAS} merits: 1) \textbf{P}referable compression ratio; 2) \textbf{N}o post-hoc retraining; 3) \textbf{A}ffordable inference time; and 4) \textbf{S}hort compression time. It compresses LLaMA2-7B in an hour and achieves close-to-int4-quantization performance, without retraining and with a performance drop of less than 1\%. We have open-sourced our code in https://github.com/Juntongkuki/Hyper-Compression.git for free download and evaluation.

Yu Guo, Guoqing Chen, Tieyong Zeng et al.

Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates the underlying low-rank structure of quaternion-encoded color images. Theoretical proofs are provided to ensure the method's mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.

Qianchao Wang, Shijun Zhang, Dong Zeng et al.

In this paper, we propose a new super-expressive activation function called the Parametric Elementary Universal Activation Function (PEUAF). We demonstrate the effectiveness of PEUAF through systematic and comprehensive experiments on various industrial and image datasets, including CIFAR10, Tiny-ImageNet, and ImageNet. Moreover, we significantly generalize the family of super-expressive activation functions, whose existence has been demonstrated in several recent works by showing that any continuous function can be approximated to any desired accuracy by a fixed-size network with a specific super-expressive activation function. Specifically, our work addresses two major bottlenecks in impeding the development of super-expressive activation functions: the limited identification of super-expressive functions, which raises doubts about their broad applicability, and their often peculiar forms, which lead to skepticism regarding their scalability and practicality in real-world applications.

Tingting Wu, Zhiyan Du, Zhi Li et al.

Recovering clear images from blurry ones with an unknown blur kernel is a challenging problem. Deep image prior (DIP) proposes to use the deep network as a regularizer for a single image rather than as a supervised model, which achieves encouraging results in the nonblind deblurring problem. However, since the relationship between images and the network architectures is unclear, it is hard to find a suitable architecture to provide sufficient constraints on the estimated blur kernels and clean images. Also, DIP uses the sparse maximum a posteriori (MAP), which is insufficient to enforce the selection of the recovery image. Recently, variational deep image prior (VDIP) was proposed to impose constraints on both blur kernels and recovery images and take the standard deviation of the image into account during the optimization process by the variational principle. However, we empirically find that VDIP struggles with processing image details and tends to generate suboptimal results when the blur kernel is large. Therefore, we combine total generalized variational (TGV) regularization with VDIP in this paper to overcome these shortcomings of VDIP. TGV is a flexible regularization that utilizes the characteristics of partial derivatives of varying orders to regularize images at different scales, reducing oil painting artifacts while maintaining sharp edges. The proposed VDIP-TGV effectively recovers image edges and details by supplementing extra gradient information through TGV. Additionally, this model is solved by the alternating direction method of multipliers (ADMM), which effectively combines traditional algorithms and deep learning methods. Experiments show that our proposed VDIP-TGV surpasses various state-of-the-art models quantitatively and qualitatively.

Yang Liu, Yaofang Liu, Jinshan Pan et al.

Most existing super-resolution methods and datasets have been developed to improve the image quality in well-lighted conditions. However, these methods do not work well in real-world low-light conditions as the images captured in such conditions lose most important information and contain significant unknown noises. To solve this problem, we propose a SRRIIE dataset with an efficient conditional diffusion probabilistic models-based method. The proposed dataset contains 4800 paired low-high quality images. To ensure that the dataset are able to model the real-world image degradation in low-illumination environments, we capture images using an ILDC camera and an optical zoom lens with exposure levels ranging from -6 EV to 0 EV and ISO levels ranging from 50 to 12800. We comprehensively evaluate with various reconstruction and perceptual metrics and demonstrate the practicabilities of the SRRIIE dataset for deep learning-based methods. We show that most existing methods are less effective in preserving the structures and sharpness of restored images from complicated noises. To overcome this problem, we revise the condition for Raw sensor data and propose a novel time-melding condition for diffusion probabilistic model. Comprehensive quantitative and qualitative experimental results on the real-world benchmark datasets demonstrate the feasibility and effectivenesses of the proposed conditional diffusion probabilistic model on Raw sensor data. Code and dataset will be available at https://github.com/Yaofang-Liu/Super-Resolving

Yu Guo, Caiying Wu, Yaxin Li et al.

Sparse view computed tomography (CT) reconstruction poses a challenging ill-posed inverse problem, necessitating effective regularization techniques. In this letter, we employ $L_p$-norm ($0<p<1$) regularization to induce sparsity and introduce inertial steps, leading to the development of the inertial $L_p$-norm half-quadratic splitting algorithm. We rigorously prove the convergence of this algorithm. Furthermore, we leverage deep learning to initialize the conjugate gradient method, resulting in a deep unrolling network with theoretical guarantees. Our extensive numerical experiments demonstrate that our proposed algorithm surpasses existing methods, particularly excelling in fewer scanned views and complex noise conditions.

Yiming Cui, Lecheng Ruan, Hang-Cheng Dong et al.

The networks for point cloud tasks are expected to be invariant when the point clouds are affinely transformed such as rotation and reflection. So far, relative to the rotational invariance that has been attracting major research attention in the past years, the reflection invariance is little addressed. Notwithstanding, reflection symmetry can find itself in very common and important scenarios, e.g., static reflection symmetry of structured streets, dynamic reflection symmetry from bidirectional motion of moving objects (such as pedestrians), and left- and right-hand traffic practices in different countries. To the best of our knowledge, unfortunately, no reflection-invariant network has been reported in point cloud analysis till now. To fill this gap, we propose a framework by using quadratic neurons and PCA canonical representation, referred to as Cloud-RAIN, to endow point \underline{Cloud} models with \underline{R}eflection\underline{A}l \underline{IN}variance. We prove a theorem to explain why Cloud-RAIN can enjoy reflection symmetry. Furthermore, extensive experiments also corroborate the reflection property of the proposed Cloud-RAIN and show that Cloud-RAIN is superior to data augmentation. Our code is available at https://github.com/YimingCuiCuiCui/Cloud-RAIN.

Zhisheng Lu, Juncheng Li, Hong Liu et al.

Single image super-resolution (SISR) has witnessed great strides with the development of deep learning. However, most existing studies focus on building more complex networks with a massive number of layers. Recently, more and more researchers start to explore the application of Transformer in computer vision tasks. However, the heavy computational cost and high GPU memory occupation of the vision Transformer cannot be ignored. In this paper, we propose a novel Efficient Super-Resolution Transformer (ESRT) for SISR. ESRT is a hybrid model, which consists of a Lightweight CNN Backbone (LCB) and a Lightweight Transformer Backbone (LTB). Among them, LCB can dynamically adjust the size of the feature map to extract deep features with a low computational cost. LTB is composed of a series of Efficient Transformers (ET), which occupies a small GPU memory occupation, thanks to the specially designed Efficient Multi-Head Attention (EMHA). Extensive experiments show that ESRT achieves competitive results with low computational costs. Compared with the original Transformer which occupies 16,057M GPU memory, ESRT only occupies 4,191M GPU memory. All codes are available at https://github.com/luissen/ESRT.

Qiaosi Yi, Juncheng Li, Qinyan Dai et al.

Single image deraining is important for many high-level computer vision tasks since the rain streaks can severely degrade the visibility of images, thereby affecting the recognition and analysis of the image. Recently, many CNN-based methods have been proposed for rain removal. Although these methods can remove part of the rain streaks, it is difficult for them to adapt to real-world scenarios and restore high-quality rain-free images with clear and accurate structures. To solve this problem, we propose a Structure-Preserving Deraining Network (SPDNet) with RCP guidance. SPDNet directly generates high-quality rain-free images with clear and accurate structures under the guidance of RCP but does not rely on any rain-generating assumptions. Specifically, we found that the RCP of images contains more accurate structural information than rainy images. Therefore, we introduced it to our deraining network to protect structure information of the rain-free image. Meanwhile, a Wavelet-based Multi-Level Module (WMLM) is proposed as the backbone for learning the background information of rainy images and an Interactive Fusion Module (IFM) is designed to make full use of RCP information. In addition, an iterative guidance strategy is proposed to gradually improve the accuracy of RCP, refining the result in a progressive path. Extensive experimental results on both synthetic and real-world datasets demonstrate that the proposed model achieves new state-of-the-art results. Code: https://github.com/Joyies/SPDNet

Le Jiang, Li Yan Ma, Tie Yong Zeng et al.

Partially supervised segmentation is a label-saving method based on datasets with fractional classes labeled and intersectant. However, it is still far from landing on real-world medical applications due to privacy concerns and data heterogeneity. As a remedy without privacy leakage, federated partially supervised segmentation (FPSS) is formulated in this work. The main challenges for FPSS are class heterogeneity and client drift. We propose a Unified Federated Partially-labeled Segmentation (UFPS) framework to segment pixels within all classes for partially-annotated datasets by training a totipotential global model without class collision. Our framework includes Unified Label Learning and sparsed Unified Sharpness Aware Minimization for unification of class and feature space, respectively. We find that vanilla combinations for traditional methods in partially supervised segmentation and federated learning are mainly hampered by class collision through empirical study. Our comprehensive experiments on real medical datasets demonstrate better deconflicting and generalization ability of UFPS compared with modified methods.

Xiaohao Cai, Raymond Chan, Mila Nikolova et al. · mila

In this paper, we propose a SLaT (Smoothing, Lifting and Thresholding) method with three stages for multiphase segmentation of color images corrupted by different degradations: noise, information loss, and blur. At the first stage, a convex variant of the Mumford-Shah model is applied to each channel to obtain a smooth image. We show that the model has unique solution under the different degradations. In order to properly handle the color information, the second stage is dimension lifting where we consider a new vector-valued image composed of the restored image and its transform in the secondary color space with additional information. This ensures that even if the first color space has highly correlated channels, we can still have enough information to give good segmentation results. In the last stage, we apply multichannel thresholding to the combined vector-valued image to find the segmentation. The number of phases is only required in the last stage, so users can choose or change it all without the need of solving the previous stages again. Experiments demonstrate that our SLaT method gives excellent results in terms of segmentation quality and CPU time in comparison with other state-of-the-art segmentation methods.

Hongjun Wang, Jiyuan Chen, Yinqiang Zheng et al.

Deep learning has led to a dramatic leap on Single Image Super-Resolution (SISR) performances in recent years. %Despite the substantial advancement% While most existing work assumes a simple and fixed degradation model (e.g., bicubic downsampling), the research of Blind SR seeks to improve model generalization ability with unknown degradation. Recently, Kong et al pioneer the investigation of a more suitable training strategy for Blind SR using Dropout. Although such method indeed brings substantial generalization improvements via mitigating overfitting, we argue that Dropout simultaneously introduces undesirable side-effect that compromises model's capacity to faithfully reconstruct fine details. We show both the theoretical and experimental analyses in our paper, and furthermore, we present another easy yet effective training strategy that enhances the generalization ability of the model by simply modulating its first and second-order features statistics. Experimental results have shown that our method could serve as a model-agnostic regularization and outperforms Dropout on seven benchmark datasets including both synthetic and real-world scenarios.

Rina Su, Yu Guo, Caiying Wu et al.

The main objective of the Multiple Kernel k-Means (MKKM) algorithm is to extract non-linear information and achieve optimal clustering by optimizing base kernel matrices. Current methods enhance information diversity and reduce redundancy by exploiting interdependencies among multiple kernels based on correlations or dissimilarities. Nevertheless, relying solely on a single metric, such as correlation or dissimilarity, to define kernel relationships introduces bias and incomplete characterization. Consequently, this limitation hinders efficient information extraction, ultimately compromising clustering performance. To tackle this challenge, we introduce a novel method that systematically integrates both kernel correlation and dissimilarity. Our approach comprehensively captures kernel relationships, facilitating more efficient classification information extraction and improving clustering performance. By emphasizing the coherence between kernel correlation and dissimilarity, our method offers a more objective and transparent strategy for extracting non-linear information and significantly improving clustering precision, supported by theoretical rationale. We assess the performance of our algorithm on 13 challenging benchmark datasets, demonstrating its superiority over contemporary state-of-the-art MKKM techniques.

Feng-Lei Fan, Meng Wang, Hang-Cheng Dong et al.

Biologically, the brain does not rely on a single type of neuron that universally functions in all aspects. Instead, it acts as a sophisticated designer of task-based neurons. In this study, we address the following question: since the human brain is a task-based neuron user, can the artificial network design go from the task-based architecture design to the task-based neuron design? Since methodologically there are no one-size-fits-all neurons, given the same structure, task-based neurons can enhance the feature representation ability relative to the existing universal neurons due to the intrinsic inductive bias for the task. Specifically, we propose a two-step framework for prototyping task-based neurons. First, symbolic regression is used to identify optimal formulas that fit input data by utilizing base functions such as logarithmic, trigonometric, and exponential functions. We introduce vectorized symbolic regression that stacks all variables in a vector and regularizes each input variable to perform the same computation, which can expedite the regression speed, facilitate parallel computation, and avoid overfitting. Second, we parameterize the acquired elementary formula to make parameters learnable, which serves as the aggregation function of the neuron. The activation functions such as ReLU and the sigmoidal functions remain the same because they have proven to be good. Empirically, experimental results on synthetic data, classic benchmarks, and real-world applications show that the proposed task-based neuron design is not only feasible but also delivers competitive performance over other state-of-the-art models.

Chi Kit Ng, Long Bai, Guankun Wang et al.

In endoscopic procedures, autonomous tracking of abnormal regions and following circumferential cutting markers can significantly reduce the cognitive burden on endoscopists. However, conventional model-based pipelines are fragile for each component (e.g., detection, motion planning) requires manual tuning and struggles to incorporate high-level endoscopic intent, leading to poor generalization across diverse scenes. Vision-Language-Action (VLA) models, which integrate visual perception, language grounding, and motion planning within an end-to-end framework, offer a promising alternative by semantically adapting to surgeon prompts without manual recalibration. Despite their potential, applying VLA models to robotic endoscopy presents unique challenges due to the complex and dynamic anatomical environments of the gastrointestinal (GI) tract. To address this, we introduce EndoVLA, designed specifically for continuum robots in GI interventions. Given endoscopic images and surgeon-issued tracking prompts, EndoVLA performs three core tasks: (1) polyp tracking, (2) delineation and following of abnormal mucosal regions, and (3) adherence to circular markers during circumferential cutting. To tackle data scarcity and domain shifts, we propose a dual-phase strategy comprising supervised fine-tuning on our EndoVLA-Motion dataset and reinforcement fine-tuning with task-aware rewards. Our approach significantly improves tracking performance in endoscopy and enables zero-shot generalization in diverse scenes and complex sequential tasks.

Deliang Wei, Peng Chen, Haobo Xu et al.

Plug-and-play (PnP) methods with deep denoisers have shown impressive results in imaging problems. They typically require strong convexity or smoothness of the fidelity term and a (residual) non-expansive denoiser for convergence. These assumptions, however, are violated in Poisson inverse problems, and non-expansiveness can hinder denoising performance. To address these challenges, we propose a cocoercive conservative (CoCo) denoiser, which may be (residual) expansive, leading to improved denoising. By leveraging the generalized Helmholtz decomposition, we introduce a novel training strategy that combines Hamiltonian regularization to promote conservativeness and spectral regularization to ensure cocoerciveness. We prove that CoCo denoiser is a proximal operator of a weakly convex function, enabling a restoration model with an implicit weakly convex prior. The global convergence of PnP methods to a stationary point of this restoration model is established. Extensive experimental results demonstrate that our approach outperforms closely related methods in both visual quality and quantitative metrics.

Guanyu Chen, Shengze Xu, Dong Ni et al.

We propose a general framework for the Discontinuous Galerkin-induced Neural Network (DGNN), inspired by the Interior Penalty Discontinuous Galerkin Method (IPDGM). In this approach, the trial space consists of piecewise neural network space defined over the computational domain, while the test function space is composed of piecewise polynomials. We demonstrate the advantages of DGNN in terms of accuracy and training efficiency across several numerical examples, including stationary and time-dependent problems. Specifically, DGNN easily handles high perturbations, discontinuous solutions, and complex geometric domains.

Chaoyan Huang, Zhongming Wu, Tieyong Zeng

Prior-based methods for low-light image enhancement often face challenges in extracting available prior information from dim images. To overcome this limitation, we introduce a simple yet effective Retinex model with the proposed edge extraction prior. More specifically, we design an edge extraction network to capture the fine edge features from the low-light image directly. Building upon the Retinex theory, we decompose the low-light image into its illumination and reflectance components and introduce an edge-guided Retinex model for enhancing low-light images. To solve the proposed model, we propose a novel inertial Bregman alternating linearized minimization algorithm. This algorithm addresses the optimization problem associated with the edge-guided Retinex model, enabling effective enhancement of low-light images. Through rigorous theoretical analysis, we establish the convergence properties of the algorithm. Besides, we prove that the proposed algorithm converges to a stationary point of the problem through nonconvex optimization theory. Furthermore, extensive experiments are conducted on multiple real-world low-light image datasets to demonstrate the efficiency and superiority of the proposed scheme.

Juntong Fan, Shuyi Fan, Debesh Jha et al.

Accurate endoscopic image segmentation on the polyps is critical for early colorectal cancer detection. However, this task remains challenging due to low contrast with surrounding mucosa, specular highlights, and indistinct boundaries. To address these challenges, we propose FOCUS-Med, which stands for Fusion of spatial and structural graph with attentional context-aware polyp segmentation in endoscopic medical imaging. FOCUS-Med integrates a Dual Graph Convolutional Network (Dual-GCN) module to capture contextual spatial and topological structural dependencies. This graph-based representation enables the model to better distinguish polyps from background tissues by leveraging topological cues and spatial connectivity, which are often obscured in raw image intensities. It enhances the model's ability to preserve boundaries and delineate complex shapes typical of polyps. In addition, a location-fused stand-alone self-attention is employed to strengthen global context integration. To bridge the semantic gap between encoder-decoder layers, we incorporate a trainable weighted fast normalized fusion strategy for efficient multi-scale aggregation. Notably, we are the first to introduce the use of a Large Language Model (LLM) to provide detailed qualitative evaluations of segmentation quality. Extensive experiments on public benchmarks demonstrate that FOCUS-Med achieves state-of-the-art performance across five key metrics, underscoring its effectiveness and clinical potential for AI-assisted colonoscopy.

Yu Guo, Guoqing Chen, Tieyong Zeng et al.

Recovering hidden structures from incomplete or noisy data remains a pervasive challenge across many fields, particularly where multi-dimensional data representation is essential. Quaternion matrices, with their ability to naturally model multi-dimensional data, offer a promising framework for this problem. This paper introduces the quaternion nuclear norm over the Frobenius norm (QNOF) as a novel nonconvex approximation for the rank of quaternion matrices. QNOF is parameter-free and scale-invariant. Utilizing quaternion singular value decomposition, we prove that solving the QNOF can be simplified to solving the singular value $L_1/L_2$ problem. Additionally, we extend the QNOF to robust quaternion matrix completion, employing the alternating direction multiplier method to derive solutions that guarantee weak convergence under mild conditions. Extensive numerical experiments validate the proposed model's superiority, consistently outperforming state-of-the-art quaternion methods.

Qingsong Wang, Shengze Xu, Xiaojiao Tong et al.

Image deblurring remains a central research area within image processing, critical for its role in enhancing image quality and facilitating clearer visual representations across diverse applications. This paper tackles the optimization problem of image deblurring, assuming a known blurring kernel. We introduce an improved optimal proximal gradient algorithm (IOptISTA), which builds upon the optimal gradient method and a weighting matrix, to efficiently address the non-blind image deblurring problem. Based on two regularization cases, namely the $l_1$ norm and total variation norm, we perform numerical experiments to assess the performance of our proposed algorithm. The results indicate that our algorithm yields enhanced PSNR and SSIM values, as well as a reduced tolerance, compared to existing methods.

Shuren Qi, Fei Wang, Tieyong Zeng et al.

Integrating invariance into data representations is a principled design in intelligent systems and web applications. Representations play a fundamental role, where systems and applications are both built on meaningful representations of digital inputs (rather than the raw data). In fact, the proper design/learning of such representations relies on priors w.r.t. the task of interest. Here, the concept of symmetry from the Erlangen Program may be the most fruitful prior -- informally, a symmetry of a system is a transformation that leaves a certain property of the system invariant. Symmetry priors are ubiquitous, e.g., translation as a symmetry of the object classification, where object category is invariant under translation. The quest for invariance is as old as pattern recognition and data mining itself. Invariant design has been the cornerstone of various representations in the era before deep learning, such as the SIFT. As we enter the early era of deep learning, the invariance principle is largely ignored and replaced by a data-driven paradigm, such as the CNN. However, this neglect did not last long before they encountered bottlenecks regarding robustness, interpretability, efficiency, and so on. The invariance principle has returned in the era of rethinking deep learning, forming a new field known as Geometric Deep Learning (GDL). In this tutorial, we will give a historical perspective of the invariance in data representations. More importantly, we will identify those research dilemmas, promising works, future directions, and web applications.

Tingting Wu, Ruyi Min, Peixuan Song et al.

The accurate segmentation of retinal blood vessels plays a crucial role in the early diagnosis and treatment of various ophthalmic diseases. Designing a network model for this task requires meticulous tuning and extensive experimentation to handle the tiny and intertwined morphology of retinal blood vessels. To tackle this challenge, Neural Architecture Search (NAS) methods are developed to fully explore the space of potential network architectures and go after the most powerful one. Inspired by neuronal diversity which is the biological foundation of all kinds of intelligent behaviors in our brain, this paper introduces a novel and foundational approach to neural network design, termed ``neuron programming'', to automatically search neuronal types into a network to enhance a network's representation ability at the neuronal level, which is complementary to architecture-level enhancement done by NAS. Additionally, to mitigate the time and computational intensity of neuron programming, we develop a hypernetwork that leverages the search-derived architectural information to predict optimal neuronal configurations. Comprehensive experiments validate that neuron programming can achieve competitive performance in retinal blood segmentation, demonstrating the strong potential of neuronal diversity in medical image analysis.

Yuxiang Hui, Yang Liu, Yaofang Liu et al.

Video restoration task aims to recover high-quality videos from low-quality observations. This contains various important sub-tasks, such as video denoising, deblurring and low-light enhancement, since video often faces different types of degradation, such as blur, low light, and noise. Even worse, these kinds of degradation could happen simultaneously when taking videos in extreme environments. This poses significant challenges if one wants to remove these artifacts at the same time. In this paper, to the best of our knowledge, we are the first to propose an efficient end-to-end video transformer approach for the joint task of video deblurring, low-light enhancement, and denoising. This work builds a novel multi-tier transformer where each tier uses a different level of degraded video as a target to learn the features of video effectively. Moreover, we carefully design a new tier-to-tier feature fusion scheme to learn video features incrementally and accelerate the training process with a suitable adaptive weighting scheme. We also provide a new Multiscene-Lowlight-Blur-Noise (MLBN) dataset, which is generated according to the characteristics of the joint task based on the RealBlur dataset and YouTube videos to simulate realistic scenes as far as possible. We have conducted extensive experiments, compared with many previous state-of-the-art methods, to show the effectiveness of our approach clearly.

Cheng Chang, Zhouping Xin, Tieyong Zeng

Maxwell-Ampère-Nernst-Planck (MANP) equations were recently proposed to model the dynamics of charged particles. In this study, we enhance a numerical algorithm of this system with deep learning tools. The proposed hybrid algorithm provides an automated means to determine a proper approximation for the dummy variables, which can otherwise only be obtained through massive numerical tests. In addition, the original method is validated for 2-dimensional problems. However, when the spatial dimension is one, the original curl-free relaxation component is inapplicable, and the approximation formula for dummy variables, which works well in a 2-dimensional scenario, fails to provide a reasonable output in the 1-dimensional case. The proposed method can be readily generalised to cases with one spatial dimension. Experiments show numerical stability and good convergence to the steady-state solution obtained from Poisson-Boltzmann type equations in the 1-dimensional case. The experiments conducted in the 2-dimensional case indicate that the proposed method preserves the conservation properties.

Feng-Lei Fan, Wei Huang, Xiangru Zhong et al.

A ReLU network is a piecewise linear function over polytopes. Figuring out the properties of such polytopes is of fundamental importance for the research and development of neural networks. So far, either theoretical or empirical studies on polytopes only stay at the level of counting their number, which is far from a complete characterization. Here, we propose to study the shapes of polytopes via the number of faces of the polytope. Then, by computing and analyzing the histogram of faces across polytopes, we find that a ReLU network has relatively simple polytopes under both initialization and gradient descent, although these polytopes can be rather diverse and complicated by a specific design. This finding can be appreciated as a kind of generalized implicit bias, subjected to the intrinsic geometric constraint in space partition of a ReLU network. Next, we perform a combinatorial analysis to explain why adding depth does not generate a more complicated polytope by bounding the average number of faces of polytopes with the dimensionality. Our results concretely reveal what kind of simple functions a network learns and what will happen when a network goes deep. Also, by characterizing the shape of polytopes, the number of faces can be a novel leverage for other problems, \textit{e.g.}, serving as a generic tool to explain the power of popular shortcut networks such as ResNet and analyzing the impact of different regularization strategies on a network's space partition.

Feng-Lei Fan, Ze-Yu Li, Huan Xiong et al.

In this work, beyond width and depth, we augment a neural network with a new dimension called height by intra-linking neurons in the same layer to create an intra-layer hierarchy, which gives rise to the notion of height. We call a neural network characterized by width, depth, and height a 3D network. To put a 3D network in perspective, we theoretically and empirically investigate the expressivity of height. We show via bound estimation and explicit construction that given the same number of neurons and parameters, a 3D ReLU network of width $W$, depth $K$, and height $H$ has greater expressive power than a 2D network of width $H\times W$ and depth $K$, \textit{i.e.}, $\mathcal{O}((2^H-1)W)^K)$ vs $\mathcal{O}((HW)^K)$, in terms of generating more pieces in a piecewise linear function. Next, through approximation rate analysis, we show that by introducing intra-layer links into networks, a ReLU network of width $\mathcal{O}(W)$ and depth $\mathcal{O}(K)$ can approximate polynomials in $[0,1]^d$ with error $\mathcal{O}\left(2^{-2WK}\right)$, which improves $\mathcal{O}\left(W^{-K}\right)$ and $\mathcal{O}\left(2^{-K}\right)$ for fixed width networks. Lastly, numerical experiments on 5 synthetic datasets, 15 tabular datasets, and 3 image benchmarks verify that 3D networks can deliver competitive regression and classification performance.

Xinlei Zhou, Han Liu, Farhad Pourpanah et al.

Quantifying the uncertainty of supervised learning models plays an important role in making more reliable predictions. Epistemic uncertainty, which usually is due to insufficient knowledge about the model, can be reduced by collecting more data or refining the learning models. Over the last few years, scholars have proposed many epistemic uncertainty handling techniques which can be roughly grouped into two categories, i.e., Bayesian and ensemble. This paper provides a comprehensive review of epistemic uncertainty learning techniques in supervised learning over the last five years. As such, we, first, decompose the epistemic uncertainty into bias and variance terms. Then, a hierarchical categorization of epistemic uncertainty learning techniques along with their representative models is introduced. In addition, several applications such as computer vision (CV) and natural language processing (NLP) are presented, followed by a discussion on research gaps and possible future research directions.