arXiv subjects

Chenglong Bao

Publications and source records attributed to Chenglong Bao.

At least 37 records · Page 2Linked to original sources

arXiv2024

Revealing the molecular structures of a-Al2O3(0001)-water interface by machine learning based computational vibrational spectroscopy

Solid-water interfaces are crucial to many physical and chemical processes and are extensively studied using surface-specific sum-frequency generation (SFG) spectroscopy. To establish clear correlations between specific spectral signatures and distinct interfacial water structures, theoretical calculations using molecular dynamics (MD) simulations are required. These MD simulations typically need relatively long trajectories (a few nanoseconds) to achieve reliable SFG response function calculations via the dipole-polarizability time correlation function. However, the requirement for long trajectories limits the use of computationally expensive techniques such as ab initio MD (AIMD) simulations, particularly for complex solid-water interfaces. In this work, we present a pathway for calculating vibrational spectra (IR, Raman, SFG) of solid-water interfaces using machine learning (ML)-accelerated methods. We employ both the dipole moment-polarizability correlation function and the surface-specific velocity-velocity correlation function approaches to calculate SFG spectra. Our results demonstrate the successful acceleration of AIMD simulations and the calculation of SFG spectra using ML methods. This advancement provides an opportunity to calculate SFG spectra for the complicated solid-water systems more rapidly and at a lower computational cost with the aid of ML.

cond-mat.mtrl-sci↗

arXiv2024

Fast and Scalable Semi-Supervised Learning for Multi-View Subspace Clustering

In this paper, we introduce a Fast and Scalable Semi-supervised Multi-view Subspace Clustering (FSSMSC) method, a novel solution to the high computational complexity commonly found in existing approaches. FSSMSC features linear computational and space complexity relative to the size of the data. The method generates a consensus anchor graph across all views, representing each data point as a sparse linear combination of chosen landmarks. Unlike traditional methods that manage the anchor graph construction and the label propagation process separately, this paper proposes a unified optimization model that facilitates simultaneous learning of both. An effective alternating update algorithm with convergence guarantees is proposed to solve the unified optimization model. Additionally, the method employs the obtained anchor graph and landmarks' low-dimensional representations to deduce low-dimensional representations for raw data. Following this, a straightforward clustering approach is conducted on these low-dimensional representations to achieve the final clustering results. The effectiveness and efficiency of FSSMSC are validated through extensive experiments on multiple benchmark datasets of varying scales.

cs.LG↗

arXiv2024

Averaging Orientations with Molecular Symmetry in Cryo-EM

Cryogenic electron microscopy (cryo-EM) is an invaluable technique for determining high-resolution three-dimensional structures of biological macromolecules using transmission particle images. The inherent symmetry in these macromolecules is advantageous, as it allows each image to represent multiple perspectives. However, data processing that incorporates symmetry can inadvertently average out asymmetric features. Therefore, a key preliminary step is to visualize 2D asymmetric features in the particle images, which requires estimating orientation statistics under molecular symmetry constraints. Motivated by this challenge, we introduce a novel method for estimating the mean and variance of orientations with molecular symmetry. Utilizing tools from non-unique games, we show that our proposed non-convex formulation can be simplified as a semi-definite programming problem. Moreover, we propose a novel rounding procedure to determine the representative values. Experimental results demonstrate that the proposed approach can find the global minima and the appropriate representatives with a high degree of probability. We release the code of our method as an open-source Python package named pySymStat. Finally, we apply pySymStat to visualize an asymmetric feature in an icosahedral virus, a feat that proved unachievable using the conventional 2D classification method in RELION.

math.OC↗

arXiv2024

SeNM-VAE: Semi-Supervised Noise Modeling with Hierarchical Variational Autoencoder

The data bottleneck has emerged as a fundamental challenge in learning based image restoration methods. Researchers have attempted to generate synthesized training data using paired or unpaired samples to address this challenge. This study proposes SeNM-VAE, a semi-supervised noise modeling method that leverages both paired and unpaired datasets to generate realistic degraded data. Our approach is based on modeling the conditional distribution of degraded and clean images with a specially designed graphical model. Under the variational inference framework, we develop an objective function for handling both paired and unpaired data. We employ our method to generate paired training samples for real-world image denoising and super-resolution tasks. Our approach excels in the quality of synthetic degraded images compared to other unpaired and paired noise modeling methods. Furthermore, our approach demonstrates remarkable performance in downstream image restoration tasks, even with limited paired data. With more paired data, our method achieves the best performance on the SIDD dataset.

cs.CV↗

arXiv2024

Convection-Diffusion Equation: A Theoretically Certified Framework for Neural Networks

In this paper, we study the partial differential equation models of neural networks. Neural network can be viewed as a map from a simple base model to a complicate function. Based on solid analysis, we show that this map can be formulated by a convection-diffusion equation. This theoretically certified framework gives mathematical foundation and more understanding of neural networks. Moreover, based on the convection-diffusion equation model, we design a novel network structure, which incorporates diffusion mechanism into network architecture. Extensive experiments on both benchmark datasets and real-world applications validate the performance of the proposed model.

cs.LG↗

arXiv2024

An axiomatized PDE model of deep neural networks

Inspired by the relation between deep neural network (DNN) and partial differential equations (PDEs), we study the general form of the PDE models of deep neural networks. To achieve this goal, we formulate DNN as an evolution operator from a simple base model. Based on several reasonable assumptions, we prove that the evolution operator is actually determined by convection-diffusion equation. This convection-diffusion equation model gives mathematical explanation for several effective networks. Moreover, we show that the convection-diffusion model improves the robustness and reduces the Rademacher complexity. Based on the convection-diffusion equation, we design a new training method for ResNets. Experiments validate the performance of the proposed method.

cs.LG↗

arXiv2024

Globalized distributionally robust optimization with multi core sets

It is essential to capture the true probability distribution of uncertain data in the distributionally robust optimization (DRO). The uncertain data presents multimodality in numerous application scenarios, in the sense that the probability density function of the uncertain data has two or more modes (local maximums). In this paper, we propose a globalized distributionally robust optimization framework with multiple core sets (MGDRO) to handle the multimodal data. This framework captures the multimodal structure via a penalty function composed of the minimum distances from the random vector to all core sets. Under some assumptions, the MGDRO model can be reformulated as tractable semi-definite programs for both moment-based and metric-based ambiguity sets. We applied the MGDRO models to a multi-product newswendor problem with multimodal demands. The numerical results turn out that the MGDRO models outperform traditional DRO models and other multimodal models greatly.

math.OC↗

arXiv2023

Addressing preferred orientation in single-particle cryo-EM through AI-generated auxiliary particles

The single-particle cryo-EM field faces the persistent challenge of preferred orientation, lacking general computational solutions. We introduce cryoPROS, an AI-based approach designed to address the above issue. By generating the auxiliary particles with a conditional deep generative model, cryoPROS addresses the intrinsic bias in orientation estimation for the observed particles. We effectively employed cryoPROS in the cryo-EM single particle analysis of the hemagglutinin trimer, showing the ability to restore the near-atomic resolution structure on non-tilt data. Moreover, the enhanced version named cryoPROS-MP significantly improves the resolution of the membrane protein NaX using the no-tilted data that contains the effects of micelles. Compared to the classical approaches, cryoPROS does not need special experimental or image acquisition techniques, providing a purely computational yet effective solution for the preferred orientation problem. Finally, we conduct extensive experiments that establish the low risk of model bias and the high robustness of cryoPROS.

q-bio.BM↗

arXiv2023

Riemannian Anderson Mixing Methods for Minimizing $C^2$-Functions on Riemannian Manifolds

The Anderson Mixing (AM) method is a popular approach for accelerating fixed-point iterations by leveraging historical information from previous steps. In this paper, we introduce the Riemannian Anderson Mixing (RAM) method, an extension of AM to Riemannian manifolds, and analyze its local linear convergence under reasonable assumptions. Unlike other extrapolation-based algorithms on Riemannian manifolds, RAM does not require computing the inverse retraction or inverse exponential mapping and has a lower per-iteration cost. Furthermore, we propose a variant of RAM called Regularized RAM (RRAM), which establishes global convergence and exhibits similar local convergence properties as RAM. Our proof relies on careful error estimations based on the local geometry of Riemannian manifolds. Finally, we present experimental results on various manifold optimization problems that demonstrate the superior performance of our proposed methods over existing Riemannian gradient descent and LBFGS approaches.

math.OC↗

arXiv2023

Convergence Analysis for Restarted Anderson Mixing and Beyond

Anderson mixing (AM) is a classical method that can accelerate fixed-point iterations by exploring historical information. Despite the successful application of AM in scientific computing, the theoretical properties of AM are still under exploration. In this paper, we study the restarted version of the Type-I and Type-II AM methods, i.e., restarted AM. With a multi-step analysis, we give a unified convergence analysis for the two types of restarted AM and justify that the restarted Type-II AM can locally improve the convergence rate of the fixed-point iteration. Furthermore, we propose an adaptive mixing strategy by estimating the spectrum of the Jacobian matrix. If the Jacobian matrix is symmetric, we develop the short-term recurrence forms of restarted AM to reduce the memory cost. Finally, experimental results on various problems validate our theoretical findings.

math.NA↗

arXiv2023

Diffusion Mechanism in Residual Neural Network: Theory and Applications

Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data points and is a critical component for achieving high classification accuracy. Many existing deep learning approaches directly impose the fusion loss when training neural networks. In this work, inspired by the convection-diffusion ordinary differential equations (ODEs), we propose a novel diffusion residual network (Diff-ResNet), internally introduces diffusion into the architectures of neural networks. Under the structured data assumption, it is proved that the proposed diffusion block can increase the distance-diameter ratio that improves the separability of inter-class points and reduces the distance among local intra-class points. Moreover, this property can be easily adopted by the residual networks for constructing the separable hyperplanes. Extensive experiments of synthetic binary classification, semi-supervised graph node classification and few-shot image classification in various datasets validate the effectiveness of the proposed method.

cs.LG↗

arXiv2023

Convergence Rates of Training Deep Neural Networks via Alternating Minimization Methods

Training deep neural networks (DNNs) is an important and challenging optimization problem in machine learning due to its non-convexity and non-separable structure. The alternating minimization (AM) approaches split the composition structure of DNNs and have drawn great interest in the deep learning and optimization communities. In this paper, we propose a unified framework for analyzing the convergence rate of AM-type network training methods. Our analysis is based on the non-monotone $j$-step sufficient decrease conditions and the Kurdyka-Lojasiewicz (KL) property, which relaxes the requirement of designing descent algorithms. We show the detailed local convergence rate if the KL exponent $θ$ varies in $[0,1)$. Moreover, the local R-linear convergence is discussed under a stronger $j$-step sufficient decrease condition.

cs.LG↗

arXiv2022

Learn from Unpaired Data for Image Restoration: A Variational Bayes Approach

Collecting paired training data is difficult in practice, but the unpaired samples broadly exist. Current approaches aim at generating synthesized training data from unpaired samples by exploring the relationship between the corrupted and clean data. This work proposes LUD-VAE, a deep generative method to learn the joint probability density function from data sampled from marginal distributions. Our approach is based on a carefully designed probabilistic graphical model in which the clean and corrupted data domains are conditionally independent. Using variational inference, we maximize the evidence lower bound (ELBO) to estimate the joint probability density function. Furthermore, we show that the ELBO is computable without paired samples under the inference invariant assumption. This property provides the mathematical rationale of our approach in the unpaired setting. Finally, we apply our method to real-world image denoising, super-resolution, and low-light image enhancement tasks and train the models using the synthetic data generated by the LUD-VAE. Experimental results validate the advantages of our method over other approaches.

eess.IV↗

arXiv2022

Semi-Supervised Clustering via Dynamic Graph Structure Learning

Most existing semi-supervised graph-based clustering methods exploit the supervisory information by either refining the affinity matrix or directly constraining the low-dimensional representations of data points. The affinity matrix represents the graph structure and is vital to the performance of semi-supervised graph-based clustering. However, existing methods adopt a static affinity matrix to learn the low-dimensional representations of data points and do not optimize the affinity matrix during the learning process. In this paper, we propose a novel dynamic graph structure learning method for semi-supervised clustering. In this method, we simultaneously optimize the affinity matrix and the low-dimensional representations of data points by leveraging the given pairwise constraints. Moreover, we propose an alternating minimization approach with proven convergence to solve the proposed nonconvex model. During the iteration process, our method cyclically updates the low-dimensional representations of data points and refines the affinity matrix, leading to a dynamic affinity matrix (graph structure). Specifically, for the update of the affinity matrix, we enforce the data points with remarkably different low-dimensional representations to have an affinity value of 0. Furthermore, we construct the initial affinity matrix by integrating the local distance and global self-representation among data points. Experimental results on eight benchmark datasets under different settings show the advantages of the proposed approach.

cs.LG↗

arXiv2022

A Semismooth Newton based Augmented Lagrangian Method for Nonsmooth Optimization on Matrix Manifolds

This paper is devoted to studying an augmented Lagrangian method for solving a class of manifold optimization problems, which have nonsmooth objective functions and nonlinear constraints. Under the constant positive linear dependence condition on manifolds, we show that the proposed method converges to a stationary point of the nonsmooth manifold optimization problem. Moreover, we propose a globalized semismooth Newton method to solve the augmented Lagrangian subproblem on manifolds efficiently. The local superlinear convergence of the manifold semismooth Newton method is also established under some suitable conditions. We also prove that the semismoothness on submanifolds can be inherited from that in the ambient manifold. Finally, numerical experiments on compressed modes and (constrained) sparse principal component analysis illustrate the advantages of the proposed method.

math.OC↗

arXiv2022

A scalable deep learning approach for solving high-dimensional dynamic optimal transport

The dynamic formulation of optimal transport has attracted growing interests in scientific computing and machine learning, and its computation requires to solve a PDE-constrained optimization problem. The classical Eulerian discretization based approaches suffer from the curse of dimensionality, which arises from the approximation of high-dimensional velocity field. In this work, we propose a deep learning based method to solve the dynamic optimal transport in high dimensional space. Our method contains three main ingredients: a carefully designed representation of the velocity field, the discretization of the PDE constraint along the characteristics, and the computation of high dimensional integral by Monte Carlo method in each time step. Specifically, in the representation of the velocity field, we apply the classical nodal basis function in time and the deep neural networks in space domain with the H1-norm regularization. This technique promotes the regularity of the velocity field in both time and space such that the discretization along the characteristic remains to be stable during the training process. Extensive numerical examples have been conducted to test the proposed method. Compared to other solvers of optimal transport, our method could give more accurate results in high dimensional cases and has very good scalability with respect to dimension. Finally, we extend our method to more complicated cases such as crowd motion problem.

cs.LG↗

arXiv2022

Unsupervised Deep Learning Meets Chan-Vese Model

The Chan-Vese (CV) model is a classic region-based method in image segmentation. However, its piecewise constant assumption does not always hold for practical applications. Many improvements have been proposed but the issue is still far from well solved. In this work, we propose an unsupervised image segmentation approach that integrates the CV model with deep neural networks, which significantly improves the original CV model's segmentation accuracy. Our basic idea is to apply a deep neural network that maps the image into a latent space to alleviate the violation of the piecewise constant assumption in image space. We formulate this idea under the classic Bayesian framework by approximating the likelihood with an evidence lower bound (ELBO) term while keeping the prior term in the CV model. Thus, our model only needs the input image itself and does not require pre-training from external datasets. Moreover, we extend the idea to multi-phase case and dataset based unsupervised image segmentation. Extensive experiments validate the effectiveness of our model and show that the proposed method is noticeably better than other unsupervised segmentation approaches.

cs.CV↗

arXiv2021

AFEC: Active Forgetting of Negative Transfer in Continual Learning

Continual learning aims to learn a sequence of tasks from dynamic data distributions. Without accessing to the old training samples, knowledge transfer from the old tasks to each new task is difficult to determine, which might be either positive or negative. If the old knowledge interferes with the learning of a new task, i.e., the forward knowledge transfer is negative, then precisely remembering the old tasks will further aggravate the interference, thus decreasing the performance of continual learning. By contrast, biological neural networks can actively forget the old knowledge that conflicts with the learning of a new experience, through regulating the learning-triggered synaptic expansion and synaptic convergence. Inspired by the biological active forgetting, we propose to actively forget the old knowledge that limits the learning of new tasks to benefit continual learning. Under the framework of Bayesian continual learning, we develop a novel approach named Active Forgetting with synaptic Expansion-Convergence (AFEC). Our method dynamically expands parameters to learn each new task and then selectively combines them, which is formally consistent with the underlying mechanism of biological active forgetting. We extensively evaluate AFEC on a variety of continual learning benchmarks, including CIFAR-10 regression tasks, visual classification tasks and Atari reinforcement tasks, where AFEC effectively improves the learning of new tasks and achieves the state-of-the-art performance in a plug-and-play way.

cs.LG↗