NAApr 5, 2016
Removal of Curtaining Effects by a Variational Model with Directional Forward DifferencesJan Henrik Fitschen, Jianwei Ma, Sebastian Schuff
Focused ion beam (FIB) tomography provides high resolution volumetric images on a micro scale. However, due to the physical acquisition process the resulting images are often corrupted by a so-called curtaining or waterfall effect. In this paper, a new convex variational model for removing such effects is proposed. More precisely, an infimal convolution model is applied to split the corrupted 3D image into the clean image and two types of corruptions, namely a striped part and a laminar one. As regularizing terms different direction dependent first and second order differences are used to cope with the specific structure of the corruptions. This generalizes discrete unidirectional total variational (TV) approaches. A minimizer of the model is computed by well-known primal dual techniques. Numerical examples show the very good performance of our new method for artificial and real-world data. Besides FIB tomography, we have also successfully applied our technique for the removal of pure stripes in Moderate Resolution Imaging Spectroradiometer (MODIS) data.
AIDec 16, 2025Code
Seismology modeling agent: A smart assistant for geophysical researchersYukun Ren, Siwei Yu, Kai Chen et al.
To address the steep learning curve and reliance on complex manual file editing and command-line operations in the traditional workflow of the mainstream open-source seismic wave simulation software SPECFEM, this paper proposes an intelligent, interactive workflow powered by Large Language Models (LLMs). We introduce the first Model Context Protocol (MCP) server suite for SPECFEM (supporting 2D, 3D Cartesian, and 3D Globe versions), which decomposes the entire simulation process into discrete, agent-executable tools spanning from parameter generation and mesh partitioning to solver execution and visualization. This approach enables a paradigm shift from file-driven to intent-driven conversational interactions. The framework supports both fully automated execution and human-in-the-loop collaboration, allowing researchers to guide simulation strategies in real time and retain scientific decision-making authority while significantly reducing tedious low-level operations. Validated through multiple case studies, the workflow operates seamlessly in both autonomous and interactive modes, yielding high-fidelity results consistent with standard baselines. As the first application of MCP technology to computational seismology, this study significantly lowers the entry barrier, enhances reproducibility, and offers a promising avenue for advancing computational geophysics toward AI-assisted and automated scientific research. The complete source code is available at https://github.com/RenYukun1563/specfem-mcp.
GEO-PHAug 16, 2022
Wave simulation in non-smooth media by PINN with quadratic neural network and PML conditionYanqi Wu, Hossein S. Aghamiry, Stephane Operto et al.
Frequency-domain simulation of seismic waves plays an important role in seismic inversion, but it remains challenging in large models. The recently proposed physics-informed neural network (PINN), as an effective deep learning method, has achieved successful applications in solving a wide range of partial differential equations (PDEs), and there is still room for improvement on this front. For example, PINN can lead to inaccurate solutions when PDE coefficients are non-smooth and describe structurally-complex media. In this paper, we solve the acoustic and visco-acoustic scattered-field wave equation in the frequency domain with PINN instead of the wave equation to remove source singularity. We first illustrate that non-smooth velocity models lead to inaccurate wavefields when no boundary conditions are implemented in the loss function. Then, we add the perfectly matched layer (PML) conditions in the loss function of PINN and design a quadratic neural network to overcome the detrimental effects of non-smooth models in PINN. We show that PML and quadratic neurons improve the results as well as attenuation and discuss the reason for this improvement. We also illustrate that a network trained during a wavefield simulation can be used to pre-train the neural network of another wavefield simulation after PDE-coefficient alteration and improve the convergence speed accordingly. This pre-training strategy should find application in iterative full waveform inversion (FWI) and time-lag target-oriented imaging when the model perturbation between two consecutive iterations or two consecutive experiments can be small.
NIAug 16, 2022
Traffic Analytics Development Kits (TADK): Enable Real-Time AI Inference in Networking AppsKun Qiu, Harry Chang, Ying Wang et al.
Sophisticated traffic analytics, such as the encrypted traffic analytics and unknown malware detection, emphasizes the need for advanced methods to analyze the network traffic. Traditional methods of using fixed patterns, signature matching, and rules to detect known patterns in network traffic are being replaced with AI (Artificial Intelligence) driven algorithms. However, the absence of a high-performance AI networking-specific framework makes deploying real-time AI-based processing within networking workloads impossible. In this paper, we describe the design of Traffic Analytics Development Kits (TADK), an industry-standard framework specific for AI-based networking workloads processing. TADK can provide real-time AI-based networking workload processing in networking equipment from the data center out to the edge without the need for specialized hardware (e.g., GPUs, Neural Processing Unit, and so on). We have deployed TADK in commodity WAF and 5G UPF, and the evaluation result shows that TADK can achieve a throughput up to 35.3Gbps per core on traffic feature extraction, 6.5Gbps per core on traffic classification, and can decrease SQLi/XSS detection down to 4.5us per request with higher accuracy than fixed pattern solution.
LGMar 3
CGL: Advancing Continual GUI Learning via Reinforcement Fine-TuningZhenquan Yao, Zitong Huang, Yihan Zeng et al.
Graphical User Interface (GUI) Agents, benefiting from recent advances in multimodal large language models (MLLM), have achieved significant development. However, due to the frequent updates of GUI applications, adapting to new tasks without forgetting old tasks in GUI continual learning remains an open problem. In this work, we reveal that while Supervised Fine-Tuning (SFT) facilitates fast adaptation, it often triggers knowledge overwriting, whereas Reinforcement Learning (RL) demonstrates an inherent resilience that shields prior interaction logic from erasure. Based on this insight, we propose a \textbf{C}ontinual \textbf{G}UI \textbf{L}earning (CGL) framework that dynamically balances adaptation efficiency and skill retention by enhancing the synergy between SFT and RL. Specifically, we introduce an SFT proportion adjustment mechanism guided by policy entropy to dynamically control the weight allocation between the SFT and RL training phases. To resolve explicit gradient interference, we further develop a specialized gradient surgery strategy. By projecting exploratory SFT gradients onto GRPO-based anchor gradients, our method explicitly clips the components of SFT gradients that conflict with GRPO. On top of that, we establish an AndroidControl-CL benchmark, which divides GUI applications into distinct task groups to effectively simulate and evaluate the performance of continual GUI learning. Experimental results demonstrate the effectiveness of our proposed CGL framework across continual learning scenarios. The benchmark, code, and model will be made publicly available.
CVDec 16, 2024Code
HGSFusion: Radar-Camera Fusion with Hybrid Generation and Synchronization for 3D Object DetectionZijian Gu, Jianwei Ma, Yan Huang et al.
Millimeter-wave radar plays a vital role in 3D object detection for autonomous driving due to its all-weather and all-lighting-condition capabilities for perception. However, radar point clouds suffer from pronounced sparsity and unavoidable angle estimation errors. To address these limitations, incorporating a camera may partially help mitigate the shortcomings. Nevertheless, the direct fusion of radar and camera data can lead to negative or even opposite effects due to the lack of depth information in images and low-quality image features under adverse lighting conditions. Hence, in this paper, we present the radar-camera fusion network with Hybrid Generation and Synchronization (HGSFusion), designed to better fuse radar potentials and image features for 3D object detection. Specifically, we propose the Radar Hybrid Generation Module (RHGM), which fully considers the Direction-Of-Arrival (DOA) estimation errors in radar signal processing. This module generates denser radar points through different Probability Density Functions (PDFs) with the assistance of semantic information. Meanwhile, we introduce the Dual Sync Module (DSM), comprising spatial sync and modality sync, to enhance image features with radar positional information and facilitate the fusion of distinct characteristics in different modalities. Extensive experiments demonstrate the effectiveness of our approach, outperforming the state-of-the-art methods in the VoD and TJ4DRadSet datasets by $6.53\%$ and $2.03\%$ in RoI AP and BEV AP, respectively. The code is available at https://github.com/garfield-cpp/HGSFusion.
CVJul 24, 2025Code
DATA: Domain-And-Time Alignment for High-Quality Feature Fusion in Collaborative PerceptionChengchang Tian, Jianwei Ma, Yan Huang et al.
Feature-level fusion shows promise in collaborative perception (CP) through balanced performance and communication bandwidth trade-off. However, its effectiveness critically relies on input feature quality. The acquisition of high-quality features faces domain gaps from hardware diversity and deployment conditions, alongside temporal misalignment from transmission delays. These challenges degrade feature quality with cumulative effects throughout the collaborative network. In this paper, we present the Domain-And-Time Alignment (DATA) network, designed to systematically align features while maximizing their semantic representations for fusion. Specifically, we propose a Consistency-preserving Domain Alignment Module (CDAM) that reduces domain gaps through proximal-region hierarchical downsampling and observability-constrained discriminator. We further propose a Progressive Temporal Alignment Module (PTAM) to handle transmission delays via multi-scale motion modeling and two-stage compensation. Building upon the aligned features, an Instance-focused Feature Aggregation Module (IFAM) is developed to enhance semantic representations. Extensive experiments demonstrate that DATA achieves state-of-the-art performance on three typical datasets, maintaining robustness with severe communication delays and pose errors. The code will be released at https://github.com/ChengchangTian/DATA.
LGMar 12
Personalized Federated Learning via Gaussian Generative ModelingPeng Hu, Jianwei Ma
Federated learning has emerged as a paradigm to train models collaboratively on inherently distributed client data while safeguarding privacy. In this context, personalized federated learning tackles the challenge of data heterogeneity by equipping each client with a dedicated model. A prevalent strategy decouples the model into a shared feature extractor and a personalized classifier head, where the latter actively guides the representation learning. However, previous works have focused on classifier head-guided personalization, neglecting the potential personalized characteristics in the representation distribution. Building on this insight, we propose pFedGM, a method based on Gaussian generative modeling. The approach begins by training a Gaussian generator that models client heterogeneity via weighted re-sampling. A balance between global collaboration and personalization is then struck by employing a dual objective: a shared objective that maximizes inter-class distance across clients, and a local objective that minimizes intra-class distance within them. To achieve this, we decouple the conventional Gaussian classifier into a navigator for global optimization, and a statistic extractor for capturing distributional statistics. Inspired by the Kalman gain, the algorithm then employs a dual-scale fusion framework at global and local levels to equip each client with a personalized classifier head. In this framework, we model the global representation distribution as a prior and the client-specific data as the likelihood, enabling Bayesian inference for class probability estimation. The evaluation covers a comprehensive range of scenarios: heterogeneity in class counts, environmental corruption, and multiple benchmark datasets and configurations. pFedGM achieves superior or competitive performance compared to state-of-the-art methods.
NEMay 3, 2024
No One-Size-Fits-All Neurons: Task-based Neurons for Artificial Neural NetworksFeng-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.
CVApr 5
Hypothesis Graph Refinement: Hypothesis-Driven Exploration with Cascade Error Correction for Embodied NavigationPeixin Chen, Guoxi Zhang, Jianwei Ma et al.
Embodied agents must explore partially observed environments while maintaining reliable long-horizon memory. Existing graph-based navigation systems improve scalability, but they often treat unexplored regions as semantically unknown, leading to inefficient frontier search. Although vision-language models (VLMs) can predict frontier semantics, erroneous predictions may be embedded into memory and propagate through downstream inferences, causing structural error accumulation that confidence attenuation alone cannot resolve. These observations call for a framework that can leverage semantic predictions for directed exploration while systematically retracting errors once new evidence contradicts them. We propose Hypothesis Graph Refinement (HGR), a framework that represents frontier predictions as revisable hypothesis nodes in a dependency-aware graph memory. HGR introduces (1) semantic hypothesis module, which estimates context-conditioned semantic distributions over frontiers and ranks exploration targets by goal relevance, travel cost, and uncertainty, and (2) verification-driven cascade correction, which compares on-site observations against predicted semantics and, upon mismatch, retracts the refuted node together with all its downstream dependents. Unlike additive map-building, this allows the graph to contract by pruning erroneous subgraphs, keeping memory reliable throughout long episodes. We evaluate HGR on multimodal lifelong navigation (GOAT-Bench) and embodied question answering (A-EQA, EM-EQA). HGR achieves 72.41% success rate and 56.22% SPL on GOAT-Bench, and shows consistent improvements on both QA benchmarks. Diagnostic analysis reveals that cascade correction eliminates approximately 20% of structurally redundant hypothesis nodes and reduces revisits to erroneous regions by 4.5x, with specular and transparent surfaces accounting for 67% of corrected prediction errors.
MLAug 27, 2025
Fractal Flow: Hierarchical and Interpretable Normalizing Flow via Topic Modeling and Recursive StrategyBinhui Zhang, Jianwei Ma
Normalizing Flows provide a principled framework for high-dimensional density estimation and generative modeling by constructing invertible transformations with tractable Jacobian determinants. We propose Fractal Flow, a novel normalizing flow architecture that enhances both expressiveness and interpretability through two key innovations. First, we integrate Kolmogorov-Arnold Networks and incorporate Latent Dirichlet Allocation into normalizing flows to construct a structured, interpretable latent space and model hierarchical semantic clusters. Second, inspired by Fractal Generative Models, we introduce a recursive modular design into normalizing flows to improve transformation interpretability and estimation accuracy. Experiments on MNIST, FashionMNIST, CIFAR-10, and geophysical data demonstrate that the Fractal Flow achieves latent clustering, controllable generation, and superior estimation accuracy.
CVAug 26, 2025
Feature-Space Planes Searcher: A Universal Domain Adaptation Framework for Interpretability and Computational EfficiencyZhitong Cheng, Yiran Jiang, Yulong Ge et al.
Domain shift, characterized by degraded model performance during transition from labeled source domains to unlabeled target domains, poses a persistent challenge for deploying deep learning systems. Current unsupervised domain adaptation (UDA) methods predominantly rely on fine-tuning feature extractors - an approach limited by inefficiency, reduced interpretability, and poor scalability to modern architectures. Our analysis reveals that models pretrained on large-scale data exhibit domain-invariant geometric patterns in their feature space, characterized by intra-class clustering and inter-class separation, thereby preserving transferable discriminative structures. These findings indicate that domain shifts primarily manifest as boundary misalignment rather than feature degradation. Unlike fine-tuning entire pre-trained models - which risks introducing unpredictable feature distortions - we propose the Feature-space Planes Searcher (FPS): a novel domain adaptation framework that optimizes decision boundaries by leveraging these geometric patterns while keeping the feature encoder frozen. This streamlined approach enables interpretative analysis of adaptation while substantially reducing memory and computational costs through offline feature extraction, permitting full-dataset optimization in a single computation cycle. Evaluations on public benchmarks demonstrate that FPS achieves competitive or superior performance to state-of-the-art methods. FPS scales efficiently with multimodal large models and shows versatility across diverse domains including protein structure prediction, remote sensing classification, and earthquake detection. We anticipate FPS will provide a simple, effective, and generalizable paradigm for transfer learning, particularly in domain adaptation tasks. .
NAFeb 4, 2024
A fast and gridless ORKA algorithm for tracking moving and deforming objectsFlorian Bossmann, Jianwei Ma, Wenze wu
Identifying objects in given data is a task frequently encountered in many applications. Finding vehicles or persons in video data, tracking seismic waves in geophysical exploration data, or predicting a storm front movement from meteorological measurements are only some of the possible applications. In many cases, the object of interest changes its form or position from one measurement to another. For example, vehicles in a video may change its position or angle to the camera in each frame. Seismic waves can change its arrival time, frequency, or intensity depending on the sensor position. Storm fronts can change its form and position over time. This complicates the identification and tracking as the algorithm needs to deal with the changing object over the given measurements. In a previous work, the authors presented a new algorithm to solve this problem - Object reconstruction using K-approximation (ORKA). The algorithm can solve the problem at hand but suffers from two disadvantages. On the one hand, the reconstructed object movement is bound to a grid that depends on the data resolution. On the other hand, the complexity of the algorithm increases exponentially with the resolution. We overcome both disadvantages by introducing an iterative strategy that uses a resampling method to create multiple resolutions of the data. In each iteration the resolution is increased to reconstruct more details of the object of interest. This way, we can even go beyond the original resolution by artificially upsampling the data. We give error bounds and a complexity analysis of the new method. Furthermore, we analyze its performance in several numerical experiments as well as on real data. We also give a brief introduction on the original ORKA algorithm. Knowledge of the previous work is thus not required.
IVSep 23, 2021
Revisit Geophysical Imaging in A New View of Physics-informed Generative Adversarial LearningFangshu Yang, Jianwei Ma
Seismic full waveform inversion (FWI) is a powerful geophysical imaging technique that produces high-resolution subsurface models by iteratively minimizing the misfit between the simulated and observed seismograms. Unfortunately, conventional FWI with least-squares function suffers from many drawbacks such as the local-minima problem and computation of explicit gradient. It is particularly challenging with the contaminated measurements or poor starting models. Recent works relying on partial differential equations and neural networks show promising performance for two-dimensional FWI. Inspired by the competitive learning of generative adversarial networks, we proposed an unsupervised learning paradigm that integrates wave equation with a discriminate network to accurately estimate the physically consistent models in a distribution sense. Our framework needs no labelled training data nor pretraining of the network, is flexible to achieve multi-parameters inversion with minimal user interaction. The proposed method faithfully recovers the well-known synthetic models that outperforms the classical algorithms. Furthermore, our work paves the way to sidestep the local-minima issue via reducing the sensitivity to initial models and noise.
IVSep 24, 2020
Robust Phase Unwrapping via Deep Image Prior for Quantitative Phase ImagingFangshu Yang, Thanh-an Pham, Nathalie Brandenberg et al.
Quantitative phase imaging (QPI) is an emerging label-free technique that produces images containing morphological and dynamical information without contrast agents. Unfortunately, the phase is wrapped in most imaging system. Phase unwrapping is the computational process that recovers a more informative image. It is particularly challenging with thick and complex samples such as organoids. Recent works that rely on supervised training show that deep learning is a powerful method to unwrap the phase; however, supervised approaches require large and representative datasets which are difficult to obtain for complex biological samples. Inspired by the concept of deep image priors, we propose a deep-learning-based method that does not need any training set. Our framework relies on an untrained convolutional neural network to accurately unwrap the phase while ensuring the consistency of the measurements. We experimentally demonstrate that the proposed method faithfully recovers the phase of complex samples on both real and simulated data. Our work paves the way to reliable phase imaging of thick and complex samples with QPI.
GEO-PHJul 13, 2020
Data-driven geophysics: from dictionary learning to deep learningSiwei Yu, Jianwei Ma
Understanding the principles of geophysical phenomena is an essential and challenging task. "Model-driven" approaches have supported the development of geophysics for a long time; however, such methods suffer from the curse of dimensionality and may inaccurately model the subsurface. "Data-driven" techniques may overcome these issues with increasingly available geophysical data. In this article, we review the basic concepts of and recent advances in data-driven approaches from dictionary learning to deep learning in a variety of geophysical scenarios. Explorational geophysics including data processing, inversion and interpretation will be mainly focused. Artificial intelligence applications on geoscience involving deep Earth, earthquake, water resource, atmospheric science, satellite remoe sensing and space sciences are also reviewed. We present a coding tutorial and a summary of tips for beginners and interested geophysical readers to rapidly explore deep learning. Some promising directions are provided for future research involving deep learning in geophysics, such as unsupervised learning, transfer learning, multimodal deep learning, federated learning, uncertainty estimation, and activate learning.
GEO-PHFeb 27, 2019
Can learning from natural image denoising be used for seismic data interpolation?Hao Zhang, Xiuyan Yang, Jianwei Ma
We propose a convolutional neural network (CNN) denoising based method for seismic data interpolation. It provides a simple and efficient way to break though the lack problem of geophysical training labels that are often required by deep learning methods. The new method consists of two steps: (1) Train a set of CNN denoisers from natural image clean-noisy pairs to learn denoising; (2) Integrate the trained CNN denoisers into project onto convex set (POCS) framework to perform seismic data interpolation. The method alleviates the demanding of seismic big data with similar features as applications of end-to-end deep learning on seismic data interpolation. Additionally, the proposed method is flexible for many cases of traces missing because missing cases are not involved in the training step, and thus it is of plug-and-play nature. These indicate the high generalizability of our approach and the reduction of the need of the problem-specific training. Primary results on synthetic and field data show promising interpolation performances of the presented CNN-POCS method in terms of signal-to-noise ratio, de-aliasing and weak-feature reconstruction, in comparison with traditional $f$-$x$ prediction filtering and curvelet transform based POCS methods.
GEO-PHFeb 17, 2019
Deep-learning inversion: a next generation seismic velocity-model building methodFangshu Yang, Jianwei Ma
Seismic velocity is one of the most important parameters used in seismic exploration. Accurate velocity models are key prerequisites for reverse-time migration and other high-resolution seismic imaging techniques. Such velocity information has traditionally been derived by tomography or full-waveform inversion (FWI), which are time consuming and computationally expensive, and they rely heavily on human interaction and quality control. We investigate a novel method based on the supervised deep fully convolutional neural network (FCN) for velocity-model building (VMB) directly from raw seismograms. Unlike the conventional inversion method based on physical models, the supervised deep-learning methods are based on big-data training rather than prior-knowledge assumptions. During the training stage, the network establishes a nonlinear projection from the multi-shot seismic data to the corresponding velocity models. During the prediction stage, the trained network can be used to estimate the velocity models from the new input seismic data. One key characteristic of the deep-learning method is that it can automatically extract multi-layer useful features without the need for human-curated activities and initial velocity setup. The data-driven method usually requires more time during the training stage, and actual predictions take less time, with only seconds needed. Therefore, the computational time of geophysical inversions, including real-time inversions, can be dramatically reduced once a good generalized network is built. By using numerical experiments on synthetic models, the promising performances of our proposed method are shown in comparison with conventional FWI even when the input data are in more realistic scenarios. Discussions on the deep-learning methods, training dataset, lack of low frequencies, and advantages and disadvantages of the new method are also provided.
GEO-PHOct 27, 2018
Deep learning for denoisingSiwei Yu, Jianwei Ma, Wenlong Wang
Compared with traditional seismic noise attenuation algorithms that depend on signal models and their corresponding prior assumptions, removing noise with a deep neural network is trained based on a large training set, where the inputs are the raw datasets and the corresponding outputs are the desired clean data. After the completion of training, the deep learning method achieves adaptive denoising with no requirements of (i) accurate modelings of the signal and noise, or (ii) optimal parameters tuning. We call this intelligent denoising. We use a convolutional neural network as the basic tool for deep learning. In random and linear noise attenuation, the training set is generated with artificially added noise. In the multiple attenuation step, the training set is generated with acoustic wave equation. Stochastic gradient descent is used to solve the optimal parameters for the convolutional neural network. The runtime of deep learning on a graphics processing unit for denoising has the same order as the $f-x$ deconvolution method. Synthetic and field results show the potential applications of deep learning in automatic attenuation of random noise (with unknown variance), linear noise, and multiples.
CVOct 7, 2018
Hartley Spectral Pooling for Deep LearningHao Zhang, Jianwei Ma
In most convolution neural networks (CNNs), downsampling hidden layers is adopted for increasing computation efficiency and the receptive field size. Such operation is commonly so-called pooling. Maximation and averaging over sliding windows (max/average pooling), and plain downsampling in the form of strided convolution are popular pooling methods. Since the pooling is a lossy procedure, a motivation of our work is to design a new pooling approach for less lossy in the dimensionality reduction. Inspired by the Fourier spectral pooling(FSP) proposed by Rippel et. al. [1], we present the Hartley transform based spectral pooling method in CNNs. Compared with FSP, the proposed spectral pooling avoids the use of complex arithmetic for frequency representation and reduces the computation. Spectral pooling preserves more structure features for network's discriminability than max and average pooling. We empirically show that Hartley spectral pooling gives rise to the convergence of training CNNs on MNIST and CIFAR-10 datasets.