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Bao Wang

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9 papers

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NeurIPS Conference 2025 Conference Paper

Towards Multiscale Graph-based Protein Learning with Geometric Secondary Structural Motifs

Shih-Hsin Wang
Yuhao Huang
Taos Transue
Justin Baker
Jonathan Forstater
Thomas Strohmer
Bao Wang

Graph neural networks (GNNs) have emerged as powerful tools for learning protein structures by capturing spatial relationships at the residue level. However, existing GNN-based methods often face challenges in learning multiscale representations and modeling long-range dependencies efficiently. In this work, we propose an efficient multiscale graph-based learning framework tailored to proteins. Our proposed framework contains two crucial components: (1) It constructs a hierarchical graph representation comprising a collection of fine-grained subgraphs, each corresponding to a secondary structure motif (e. g. , $\alpha$-helices, $\beta$-strands, loops), and a single coarse-grained graph that connects these motifs based on their spatial arrangement and relative orientation. (2) It employs two GNNs for feature learning: the first operates within individual secondary motifs to capture local interactions, and the second models higher-level structural relationships across motifs. Our modular framework allows a flexible choice of GNN in each stage. Theoretically, we show that our hierarchical framework preserves the desired maximal expressiveness, ensuring no loss of critical structural information. Empirically, we demonstrate that integrating baseline GNNs into our multiscale framework remarkably improves prediction accuracy and reduces computational cost across various benchmarks.

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TMLR Journal 2023 Journal Article

Pairwise Learning with Adaptive Online Gradient Descent

Tao Sun
Qingsong Wang
Yunwen Lei
Dongsheng Li
Bao Wang

In this paper, we propose an adaptive online gradient descent method with momentum for pairwise learning, in which the stepsize is determined by historical information. Due to the structure of pairwise learning, the sample pairs are dependent on the parameters, causing difficulties in the convergence analysis. To this end, we develop novel techniques for the convergence analysis of the proposed algorithm. We show that the proposed algorithm can output the desired solution in strongly convex, convex, and nonconvex cases. Furthermore, we present theoretical explanations for why our proposed algorithm can accelerate previous workhorses for online pairwise learning. All assumptions used in the theoretical analysis are mild and common, making our results applicable to various pairwise learning problems. To demonstrate the efficiency of our algorithm, we compare the proposed adaptive method with the non-adaptive counterpart on the benchmark online AUC maximization problem.

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NeurIPS Conference 2022 Conference Paper

Finite-Time Analysis of Adaptive Temporal Difference Learning with Deep Neural Networks

Tao Sun
Dongsheng Li
Bao Wang

Temporal difference (TD) learning with function approximations (linear functions or neural networks) has achieved remarkable empirical success, giving impetus to the development of finite-time analysis. As an accelerated version of TD, the adaptive TD has been proposed and proved to enjoy finite-time convergence under the linear function approximation. Existing numerical results have demonstrated the superiority of adaptive algorithms to vanilla ones. Nevertheless, the performance guarantee of adaptive TD with neural network approximation remains widely unknown. This paper establishes the finite-time analysis for the adaptive TD with multi-layer ReLU network approximation whose samples are generated from a Markov decision process. Our established theory shows that if the width of the deep neural network is large enough, the adaptive TD using neural network approximation can find the (optimal) value function with high probabilities under the same iteration complexity as TD in general cases. Furthermore, we show that the adaptive TD using neural network approximation, with the same width and searching area, can achieve theoretical acceleration when the stochastic semi-gradients decay fast.

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NeurIPS Conference 2021 Conference Paper

FMMformer: Efficient and Flexible Transformer via Decomposed Near-field and Far-field Attention

Tan Nguyen
Vai Suliafu
Stanley Osher
Long Chen
Bao Wang

We propose FMMformers, a class of efficient and flexible transformers inspired by the celebrated fast multipole method (FMM) for accelerating interacting particle simulation. FMM decomposes particle-particle interaction into near-field and far-field components and then performs direct and coarse-grained computation, respectively. Similarly, FMMformers decompose the attention into near-field and far-field attention, modeling the near-field attention by a banded matrix and the far-field attention by a low-rank matrix. Computing the attention matrix for FMMformers requires linear complexity in computational time and memory footprint with respect to the sequence length. In contrast, standard transformers suffer from quadratic complexity. We analyze and validate the advantage of FMMformers over the standard transformer on the Long Range Arena and language modeling benchmarks. FMMformers can even outperform the standard transformer in terms of accuracy by a significant margin. For instance, FMMformers achieve an average classification accuracy of $60. 74\%$ over the five Long Range Arena tasks, which is significantly better than the standard transformer's average accuracy of $58. 70\%$.

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NeurIPS Conference 2021 Conference Paper

Heavy Ball Neural Ordinary Differential Equations

Hedi Xia
Vai Suliafu
Hangjie Ji
Tan Nguyen
Andrea Bertozzi
Stanley Osher
Bao Wang

We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the continuous limit of the classical momentum accelerated gradient descent, to improve neural ODEs (NODEs) training and inference. HBNODEs have two properties that imply practical advantages over NODEs: (i) The adjoint state of an HBNODE also satisfies an HBNODE, accelerating both forward and backward ODE solvers, thus significantly reducing the number of function evaluations (NFEs) and improving the utility of the trained models. (ii) The spectrum of HBNODEs is well structured, enabling effective learning of long-term dependencies from complex sequential data. We verify the advantages of HBNODEs over NODEs on benchmark tasks, including image classification, learning complex dynamics, and sequential modeling. Our method requires remarkably fewer forward and backward NFEs, is more accurate, and learns long-term dependencies more effectively than the other ODE-based neural network models. Code is available at \url{https: //github. com/hedixia/HeavyBallNODE}.

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AAAI Conference 2021 Conference Paper

Stability and Generalization of Decentralized Stochastic Gradient Descent

Tao Sun
Dongsheng Li
Bao Wang

The stability and generalization of stochastic gradient-based methods provide valuable insights into understanding the algorithmic performance of machine learning models. As the main workhorse for deep learning, stochastic gradient descent has received a considerable amount of studies. Nevertheless, the community paid little attention to its decentralized variants. In this paper, we provide a novel formulation of the decentralized stochastic gradient descent. Leveraging this formulation together with (non)convex optimization theory, we establish the first stability and generalization guarantees for the decentralized stochastic gradient descent. Our theoretical results are built on top of a few common and mild assumptions and reveal that the decentralization deteriorates the stability of SGD for the first time. We verify our theoretical findings by using a variety of decentralized settings and benchmark machine learning models.

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NeurIPS Conference 2020 Conference Paper

MomentumRNN: Integrating Momentum into Recurrent Neural Networks

Tan Nguyen
Richard Baraniuk
Andrea Bertozzi
Stanley Osher
Bao Wang

Designing deep neural networks is an art that often involves an expensive search over candidate architectures. To overcome this for recurrent neural nets (RNNs), we establish a connection between the hidden state dynamics in an RNN and gradient descent (GD). We then integrate momentum into this framework and propose a new family of RNNs, called {\em MomentumRNNs}. We theoretically prove and numerically demonstrate that MomentumRNNs alleviate the vanishing gradient issue in training RNNs. We study the momentum long-short term memory (MomentumLSTM) and verify its advantages in convergence speed and accuracy over its LSTM counterpart across a variety of benchmarks. We also demonstrate that MomentumRNN is applicable to many types of recurrent cells, including those in the state-of-the-art orthogonal RNNs. Finally, we show that other advanced momentum-based optimization methods, such as Adam and Nesterov accelerated gradients with a restart, can be easily incorporated into the MomentumRNN framework for designing new recurrent cells with even better performance.

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NeurIPS Conference 2019 Conference Paper

ResNets Ensemble via the Feynman-Kac Formalism to Improve Natural and Robust Accuracies

Bao Wang
Zuoqiang Shi
Stanley Osher

We unify the theory of optimal control of transport equations with the practice of training and testing of ResNets. Based on this unified viewpoint, we propose a simple yet effective ResNets ensemble algorithm to boost the accuracy of the robustly trained model on both clean and adversarial images. The proposed algorithm consists of two components: First, we modify the base ResNets by injecting a variance specified Gaussian noise to the output of each residual mapping. Second, we average over the production of multiple jointly trained modified ResNets to get the final prediction. These two steps give an approximation to the Feynman-Kac formula for representing the solution of a convection-diffusion equation. For the CIFAR10 benchmark, this simple algorithm leads to a robust model with a natural accuracy of {\bf 85. 62}\% on clean images and a robust accuracy of ${\bf 57. 94 \%}$ under the 20 iterations of the IFGSM attack, which outperforms the current state-of-the-art in defending against IFGSM attack on the CIFAR10.

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NeurIPS Conference 2018 Conference Paper

Deep Neural Nets with Interpolating Function as Output Activation

Bao Wang
xiyang luo
Zhen Li
Wei Zhu
Zuoqiang Shi
Stanley Osher

We replace the output layer of deep neural nets, typically the softmax function, by a novel interpolating function. And we propose end-to-end training and testing algorithms for this new architecture. Compared to classical neural nets with softmax function as output activation, the surrogate with interpolating function as output activation combines advantages of both deep and manifold learning. The new framework demonstrates the following major advantages: First, it is better applicable to the case with insufficient training data. Second, it significantly improves the generalization accuracy on a wide variety of networks. The algorithm is implemented in PyTorch, and the code is available at https: //github. com/ BaoWangMath/DNN-DataDependentActivation.

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