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Hongyang Gao

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9 papers

2 author rows

ICLR Conference 2025 Conference Paper

Global Convergence in Neural ODEs: Impact of Activation Functions

Tianxiang Gao
Siyuan Sun
Hailiang Liu
Hongyang Gao

Neural Ordinary Differential Equations (ODEs) have been successful in various applications due to their continuous nature and parameter-sharing efficiency. However, these unique characteristics also introduce challenges in training, particularly with respect to gradient computation accuracy and convergence analysis. In this paper, we address these challenges by investigating the impact of activation functions. We demonstrate that the properties of activation functions—specifically smoothness and nonlinearity—are critical to the training dynamics. Smooth activation functions guarantee globally unique solutions for both forward and backward ODEs, while sufficient nonlinearity is essential for maintaining the spectral properties of the Neural Tangent Kernel (NTK) during training. Together, these properties enable us to establish the global convergence of Neural ODEs under gradient descent in overparameterized regimes. Our theoretical findings are validated by numerical experiments, which not only support our analysis but also provide practical guidelines for scaling Neural ODEs, potentially leading to faster training and improved performance in real-world applications.

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ICLR Conference 2025 Conference Paper

MAGE: Model-Level Graph Neural Networks Explanations via Motif-based Graph Generation

Zhaoning Yu
Hongyang Gao

Graph Neural Networks (GNNs) have shown remarkable success in molecular tasks, yet their interpretability remains challenging. Traditional model-level explanation methods like XGNN and GNNInterpreter often fail to identify valid substructures like rings, leading to questionable interpretability. This limitation stems from XGNN's atom-by-atom approach and GNNInterpreter's reliance on average graph embeddings, which overlook the essential structural elements crucial for molecules. To address these gaps, we introduce an innovative **M**otif-b**A**sed **G**NN **E**xplainer (MAGE) that uses motifs as fundamental units for generating explanations. Our approach begins with extracting potential motifs through a motif decomposition technique. Then, we utilize an attention-based learning method to identify class-specific motifs. Finally, we employ a motif-based graph generator for each class to create molecular graph explanations based on these class-specific motifs. This novel method not only incorporates critical substructures into the explanations but also guarantees their validity, yielding results that are human-understandable. Our proposed method's effectiveness is demonstrated through quantitative and qualitative assessments conducted on six real-world molecular datasets.

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NeurIPS Conference 2023 Conference Paper

Meta-AdaM: An Meta-Learned Adaptive Optimizer with Momentum for Few-Shot Learning

Siyuan Sun
Hongyang Gao

We introduce Meta-AdaM, a meta-learned adaptive optimizer with momentum, designed for few-shot learning tasks that pose significant challenges to deep learning models due to the limited number of labeled examples. Meta-learning has been successfully employed to address these challenges by transferring meta-learned prior knowledge to new tasks. Most existing works focus on meta-learning an optimal model initialization or an adaptive learning rate learner for rapid convergence. However, these approaches either neglect to consider weight-update history for the adaptive learning rate learner or fail to effectively integrate momentum for fast convergence, as seen in many-shot learning settings. To tackle these limitations, we propose a meta-learned learning rate learner that utilizes weight-update history as input to predict more appropriate learning rates for rapid convergence. Furthermore, for the first time, our approach incorporates momentum into the optimization process of few-shot learning via a double look-ahead mechanism, enabling rapid convergence similar to many-shot settings. Extensive experimental results on benchmark datasets demonstrate the effectiveness of the proposed Meta-AdaM.

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NeurIPS Conference 2023 Conference Paper

Wide Neural Networks as Gaussian Processes: Lessons from Deep Equilibrium Models

Tianxiang Gao
Xiaokai Huo
Hailiang Liu
Hongyang Gao

Neural networks with wide layers have attracted significant attention due to their equivalence to Gaussian processes, enabling perfect fitting of training data while maintaining generalization performance, known as benign overfitting. However, existing results mainly focus on shallow or finite-depth networks, necessitating a comprehensive analysis of wide neural networks with infinite-depth layers, such as neural ordinary differential equations (ODEs) and deep equilibrium models (DEQs). In this paper, we specifically investigate the deep equilibrium model (DEQ), an infinite-depth neural network with shared weight matrices across layers. Our analysis reveals that as the width of DEQ layers approaches infinity, it converges to a Gaussian process, establishing what is known as the Neural Network and Gaussian Process (NNGP) correspondence. Remarkably, this convergence holds even when the limits of depth and width are interchanged, which is not observed in typical infinite-depth Multilayer Perceptron (MLP) networks. Furthermore, we demonstrate that the associated Gaussian vector remains non-degenerate for any pairwise distinct input data, ensuring a strictly positive smallest eigenvalue of the corresponding kernel matrix using the NNGP kernel. These findings serve as fundamental elements for studying the training and generalization of DEQs, laying the groundwork for future research in this area.

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ICLR Conference 2022 Conference Paper

A global convergence theory for deep ReLU implicit networks via over-parameterization

Tianxiang Gao
Hailiang Liu
Jia Liu 0002
Hridesh Rajan
Hongyang Gao

Implicit deep learning has received increasing attention recently due to the fact that it generalizes the recursive prediction rule of many commonly used neural network architectures. Its prediction rule is provided implicitly based on the solution of an equilibrium equation. Although a line of recent empirical studies has demonstrated its superior performances, the theoretical understanding of implicit neural networks is limited. In general, the equilibrium equation may not be well-posed during the training. As a result, there is no guarantee that a vanilla (stochastic) gradient descent (SGD) training nonlinear implicit neural networks can converge. This paper fills the gap by analyzing the gradient flow of Rectified Linear Unit (ReLU) activated implicit neural networks. For an $m$ width implicit neural network with ReLU activation and $n$ training samples, we show that a randomly initialized gradient descent converges to a global minimum at a linear rate for the square loss function if the implicit neural network is over-parameterized. It is worth noting that, unlike existing works on the convergence of (S)GD on finite-layer over-parameterized neural networks, our convergence results hold for implicit neural networks, where the number of layers is infinite.

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ICML Conference 2022 Conference Paper

Molecular Representation Learning via Heterogeneous Motif Graph Neural Networks

Zhaoning Yu
Hongyang Gao

We consider feature representation learning problem of molecular graphs. Graph Neural Networks have been widely used in feature representation learning of molecular graphs. However, most existing methods deal with molecular graphs individually while neglecting their connections, such as motif-level relationships. We propose a novel molecular graph representation learning method by constructing a heterogeneous motif graph to address this issue. In particular, we build a heterogeneous motif graph that contains motif nodes and molecular nodes. Each motif node corresponds to a motif extracted from molecules. Then, we propose a Heterogeneous Motif Graph Neural Network (HM-GNN) to learn feature representations for each node in the heterogeneous motif graph. Our heterogeneous motif graph also enables effective multi-task learning, especially for small molecular datasets. To address the potential efficiency issue, we propose to use an edge sampler, which can significantly reduce computational resources usage. The experimental results show that our model consistently outperforms previous state-of-the-art models. Under multi-task settings, the promising performances of our methods on combined datasets shed light on a new learning paradigm for small molecular datasets. Finally, we show that our model achieves similar performances with significantly less computational resources by using our edge sampler.

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AAAI Conference 2020 Conference Paper

Adaptive Convolutional ReLUs

Hongyang Gao
Lei Cai
Shuiwang Ji

Rectiﬁed linear units (ReLUs) are currently the most popular activation function used in neural networks. Although ReLUs can solve the gradient vanishing problem and accelerate training convergence, it suffers from the dying ReLU problem in which some neurons are never activated if the weights are not updated properly. In this work, we propose a novel activation function, known as the adaptive convolutional ReLU (ConvReLU), that can better mimic brain neuron activation behaviors and overcome the dying ReLU problem. With our novel parameter sharing scheme, ConvReLUs can be applied to convolution layers that allow each input neuron to be activated by different trainable thresholds without involving a large number of extra parameters. We employ the zero initialization scheme in ConvReLU to encourage trainable thresholds to be close to zero. Finally, we develop a partial replacement strategy that only replaces the ReLUs in the early layers of the network. This resolves the dying ReLU problem and retains sparse representations for linear classiﬁers. Experimental results demonstrate that our proposed ConvReLU has consistently better performance compared to ReLU, LeakyReLU, and PReLU. In addition, the partial replacement strategy is shown to be effective not only for our ConvReLU but also for LeakyReLU and PReLU.

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ICML Conference 2019 Conference Paper

Graph U-Nets

Hongyang Gao
Shuiwang Ji

We consider the problem of representation learning for graph data. Convolutional neural networks can naturally operate on images, but have significant challenges in dealing with graph data. Given images are special cases of graphs with nodes lie on 2D lattices, graph embedding tasks have a natural correspondence with image pixel-wise prediction tasks such as segmentation. While encoder-decoder architectures like U-Nets have been successfully applied on many image pixel-wise prediction tasks, similar methods are lacking for graph data. This is due to the fact that pooling and up-sampling operations are not natural on graph data. To address these challenges, we propose novel graph pooling (gPool) and unpooling (gUnpool) operations in this work. The gPool layer adaptively selects some nodes to form a smaller graph based on their scalar projection values on a trainable projection vector. We further propose the gUnpool layer as the inverse operation of the gPool layer. The gUnpool layer restores the graph into its original structure using the position information of nodes selected in the corresponding gPool layer. Based on our proposed gPool and gUnpool layers, we develop an encoder-decoder model on graph, known as the graph U-Nets. Our experimental results on node classification and graph classification tasks demonstrate that our methods achieve consistently better performance than previous models.

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NeurIPS Conference 2018 Conference Paper

ChannelNets: Compact and Efficient Convolutional Neural Networks via Channel-Wise Convolutions

Hongyang Gao
Zhengyang Wang
Shuiwang Ji

Convolutional neural networks (CNNs) have shown great capability of solving various artificial intelligence tasks. However, the increasing model size has raised challenges in employing them in resource-limited applications. In this work, we propose to compress deep models by using channel-wise convolutions, which replace dense connections among feature maps with sparse ones in CNNs. Based on this novel operation, we build light-weight CNNs known as ChannelNets. ChannelNets use three instances of channel-wise convolutions; namely group channel-wise convolutions, depth-wise separable channel-wise convolutions, and the convolutional classification layer. Compared to prior CNNs designed for mobile devices, ChannelNets achieve a significant reduction in terms of the number of parameters and computational cost without loss in accuracy. Notably, our work represents the first attempt to compress the fully-connected classification layer, which usually accounts for about 25% of total parameters in compact CNNs. Experimental results on the ImageNet dataset demonstrate that ChannelNets achieve consistently better performance compared to prior methods.

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