Graph neural networks extrapolate out-of-distribution for shortest paths

• URL: http://arxiv.org/abs/2503.19173v2
• Date: Mon, 31 Mar 2025 00:46:30 GMT
• Title: Graph neural networks extrapolate out-of-distribution for shortest paths
• Authors: Robert R. Nerem, Samantha Chen, Sanjoy Dasgupta, Yusu Wang,
• Abstract summary: Graph Neural Networks (GNNs) are trained to minimize a sparsity-regularized loss over a small set of shortest path instances.<n>We show that GNNs trained by gradient descent are able to minimize this loss and extrapolate in practice.
• Score: 13.300757448796361
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural networks (NNs), despite their success and wide adoption, still struggle to extrapolate out-of-distribution (OOD), i.e., to inputs that are not well-represented by their training dataset. Addressing the OOD generalization gap is crucial when models are deployed in environments significantly different from the training set, such as applying Graph Neural Networks (GNNs) trained on small graphs to large, real-world graphs. One promising approach for achieving robust OOD generalization is the framework of neural algorithmic alignment, which incorporates ideas from classical algorithms by designing neural architectures that resemble specific algorithmic paradigms (e.g. dynamic programming). The hope is that trained models of this form would have superior OOD capabilities, in much the same way that classical algorithms work for all instances. We rigorously analyze the role of algorithmic alignment in achieving OOD generalization, focusing on graph neural networks (GNNs) applied to the canonical shortest path problem. We prove that GNNs, trained to minimize a sparsity-regularized loss over a small set of shortest path instances, exactly implement the Bellman-Ford (BF) algorithm for shortest paths. In fact, if a GNN minimizes this loss within an error of $\epsilon$, it implements the BF algorithm with an error of $O(\epsilon)$. Consequently, despite limited training data, these GNNs are guaranteed to extrapolate to arbitrary shortest-path problems, including instances of any size. Our empirical results support our theory by showing that NNs trained by gradient descent are able to minimize this loss and extrapolate in practice.

Related papers

• DFA-GNN: Forward Learning of Graph Neural Networks by Direct Feedback Alignment [57.62885438406724]
  Graph neural networks are recognized for their strong performance across various applications. BP has limitations that challenge its biological plausibility and affect the efficiency, scalability and parallelism of training neural networks for graph-based tasks. We propose DFA-GNN, a novel forward learning framework tailored for GNNs with a case study of semi-supervised learning.
  arXiv  Detail & Related papers  (2024-06-04T07:24:51Z)
• Towards Better Out-of-Distribution Generalization of Neural Algorithmic Reasoning Tasks [51.8723187709964]
  We study the OOD generalization of neural algorithmic reasoning tasks. The goal is to learn an algorithm from input-output pairs using deep neural networks.
  arXiv  Detail & Related papers  (2022-11-01T18:33:20Z)
• Graph Neural Networks are Dynamic Programmers [0.0]
  Graph neural networks (GNNs) are claimed to align with dynamic programming (DP) Here we show, using methods from theory and abstract algebra, that there exists an intricate connection between GNNs and DP.
  arXiv  Detail & Related papers  (2022-03-29T13:27:28Z)
• Graph Neural Networks for Wireless Communications: From Theory to Practice [10.61745503150249]
  Graph neural networks (GNNs) can effectively exploit the domain knowledge, i.e., the graph topology in wireless communication problems. For theoretical guarantees, we prove that GNNs achieve near-optimal performance in wireless networks with much fewer training samples than traditional neural architectures. For design guidelines, we propose a unified framework that is applicable to general design problems in wireless networks.
  arXiv  Detail & Related papers  (2022-03-21T08:39:44Z)
• Algorithms for Efficiently Learning Low-Rank Neural Networks [12.916132936159713]
  We study algorithms for learning low-rank neural networks. We present a provably efficient algorithm which learns an optimal low-rank approximation to a single-hidden-layer ReLU network. We propose a novel low-rank framework for training low-rank $textitdeep$ networks.
  arXiv  Detail & Related papers  (2022-02-02T01:08:29Z)
• Why Lottery Ticket Wins? A Theoretical Perspective of Sample Complexity on Pruned Neural Networks [79.74580058178594]
  We analyze the performance of training a pruned neural network by analyzing the geometric structure of the objective function. We show that the convex region near a desirable model with guaranteed generalization enlarges as the neural network model is pruned.
  arXiv  Detail & Related papers  (2021-10-12T01:11:07Z)
• Binary Graph Neural Networks [69.51765073772226]
  Graph Neural Networks (GNNs) have emerged as a powerful and flexible framework for representation learning on irregular data. In this paper, we present and evaluate different strategies for the binarization of graph neural networks. We show that through careful design of the models, and control of the training process, binary graph neural networks can be trained at only a moderate cost in accuracy on challenging benchmarks.
  arXiv  Detail & Related papers  (2020-12-31T18:48:58Z)
• Fast Learning of Graph Neural Networks with Guaranteed Generalizability: One-hidden-layer Case [93.37576644429578]
  Graph neural networks (GNNs) have made great progress recently on learning from graph-structured data in practice. We provide a theoretically-grounded generalizability analysis of GNNs with one hidden layer for both regression and binary classification problems.
  arXiv  Detail & Related papers  (2020-06-25T00:45:52Z)
• Towards an Efficient and General Framework of Robust Training for Graph Neural Networks [96.93500886136532]
  Graph Neural Networks (GNNs) have made significant advances on several fundamental inference tasks. Despite GNNs' impressive performance, it has been observed that carefully crafted perturbations on graph structures lead them to make wrong predictions. We propose a general framework which leverages the greedy search algorithms and zeroth-order methods to obtain robust GNNs.
  arXiv  Detail & Related papers  (2020-02-25T15:17:58Z)

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.