Taming Gradient Oversmoothing and Expansion in Graph Neural Networks

• URL: http://arxiv.org/abs/2410.04824v1
• Date: Mon, 7 Oct 2024 08:22:20 GMT
• Title: Taming Gradient Oversmoothing and Expansion in Graph Neural Networks
• Authors: MoonJeong Park, Dongwoo Kim,
• Abstract summary: Oversmoothing has been claimed as a primary bottleneck for graph neural networks (GNNs) We show the presence of $textitgradient oversmoothing$ preventing optimization during training. We provide a simple yet effective normalization method to prevent the gradient expansion.
• Score: 3.0764244780817283
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Oversmoothing has been claimed as a primary bottleneck for multi-layered graph neural networks (GNNs). Multiple analyses have examined how and why oversmoothing occurs. However, none of the prior work addressed how optimization is performed under the oversmoothing regime. In this work, we show the presence of $\textit{gradient oversmoothing}$ preventing optimization during training. We further analyze that GNNs with residual connections, a well-known solution to help gradient flow in deep architecture, introduce $\textit{gradient expansion}$, a phenomenon of the gradient explosion in diverse directions. Therefore, adding residual connections cannot be a solution for making a GNN deep. Our analysis reveals that constraining the Lipschitz bound of each layer can neutralize the gradient expansion. To this end, we provide a simple yet effective normalization method to prevent the gradient expansion. An empirical study shows that the residual GNNs with hundreds of layers can be efficiently trained with the proposed normalization without compromising performance. Additional studies show that the empirical observations corroborate our theoretical analysis.

Related papers

• Towards Training Without Depth Limits: Batch Normalization Without Gradient Explosion [83.90492831583997]
  We show that a batch-normalized network can keep the optimal signal propagation properties, but avoid exploding gradients in depth. We use a Multi-Layer Perceptron (MLP) with linear activations and batch-normalization that provably has bounded depth. We also design an activation shaping scheme that empirically achieves the same properties for certain non-linear activations.
  arXiv  Detail & Related papers  (2023-10-03T12:35:02Z)
• Implicit Stochastic Gradient Descent for Training Physics-informed Neural Networks [51.92362217307946]
  Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems. PINNs are trapped in training failures when the target functions to be approximated exhibit high-frequency or multi-scale features. In this paper, we propose to employ implicit gradient descent (ISGD) method to train PINNs for improving the stability of training process.
  arXiv  Detail & Related papers  (2023-03-03T08:17:47Z)
• Negative Flux Aggregation to Estimate Feature Attributions [15.411534490483495]
  There are increasing demands for understanding deep neural networks' (DNNs) behavior spurred by growing security and/or transparency concerns. To enhance the explainability of DNNs, we estimate the input feature's attributions to the prediction task using divergence and flux. Inspired by the divergence theorem in vector analysis, we develop a novel Negative Flux Aggregation (NeFLAG) formulation and an efficient approximation algorithm to estimate attribution map.
  arXiv  Detail & Related papers  (2023-01-17T16:19:41Z)
• Implicit Bias in Leaky ReLU Networks Trained on High-Dimensional Data [63.34506218832164]
  In this work, we investigate the implicit bias of gradient flow and gradient descent in two-layer fully-connected neural networks with ReLU activations. For gradient flow, we leverage recent work on the implicit bias for homogeneous neural networks to show that leakyally, gradient flow produces a neural network with rank at most two. For gradient descent, provided the random variance is small enough, we show that a single step of gradient descent suffices to drastically reduce the rank of the network, and that the rank remains small throughout training.
  arXiv  Detail & Related papers  (2022-10-13T15:09:54Z)
• SkipNode: On Alleviating Performance Degradation for Deep Graph Convolutional Networks [84.30721808557871]
  We conduct theoretical and experimental analysis to explore the fundamental causes of performance degradation in deep GCNs. We propose a simple yet effective plug-and-play module, Skipnode, to overcome the performance degradation of deep GCNs.
  arXiv  Detail & Related papers  (2021-12-22T02:18:31Z)
• Continuous vs. Discrete Optimization of Deep Neural Networks [15.508460240818575]
  We show that over deep neural networks with homogeneous activations, gradient flow trajectories enjoy favorable curvature. This finding allows us to translate an analysis of gradient flow over deep linear neural networks into a guarantee that gradient descent efficiently converges to global minimum. We hypothesize that the theory of gradient flows will be central to unraveling mysteries behind deep learning.
  arXiv  Detail & Related papers  (2021-07-14T10:59:57Z)
• Overparameterization of deep ResNet: zero loss and mean-field analysis [19.45069138853531]
  Finding parameters in a deep neural network (NN) that fit data is a non optimization problem. We show that a basic first-order optimization method (gradient descent) finds a global solution with perfect fit in many practical situations. We give estimates of the depth and width needed to reduce the loss below a given threshold, with high probability.
  arXiv  Detail & Related papers  (2021-05-30T02:46:09Z)
• Improved Analysis of Clipping Algorithms for Non-convex Optimization [19.507750439784605]
  Recently, citetzhang 2019gradient show that clipped (stochastic) Gradient Descent (GD) converges faster than vanilla GD/SGD. Experiments confirm the superiority of clipping-based methods in deep learning tasks.
  arXiv  Detail & Related papers  (2020-10-05T14:36:59Z)
• Layer-wise Conditioning Analysis in Exploring the Learning Dynamics of DNNs [115.35745188028169]
  We extend conditioning analysis to deep neural networks (DNNs) in order to investigate their learning dynamics. We show that batch normalization (BN) can stabilize the training, but sometimes result in the false impression of a local minimum. We experimentally observe that BN can improve the layer-wise conditioning of the optimization problem.
  arXiv  Detail & Related papers  (2020-02-25T11:40:27Z)
• Towards Better Understanding of Adaptive Gradient Algorithms in Generative Adversarial Nets [71.05306664267832]
  Adaptive algorithms perform gradient updates using the history of gradients and are ubiquitous in training deep neural networks. In this paper we analyze a variant of OptimisticOA algorithm for nonconcave minmax problems. Our experiments show that adaptive GAN non-adaptive gradient algorithms can be observed empirically.
  arXiv  Detail & Related papers  (2019-12-26T22:10:10Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.