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   Graph embeddings have been tremendously successful at producing node representations that are discriminative for downstream tasks. In this paper, we study the problem of graph transfer learning: given two graphs and labels in the nodes of the first graph, we wish to predict the labels on the second graph. We propose a tractable, noncombinatorial method for solving the graph transfer learning problem by combining classification and embedding losses with a continuous, convex penalty motivated by tractable graph distances. We demonstrate that our method successfully predicts labels across graphs with almost perfect accuracy; in the same scenarios, training embeddings through standard methods leads to predictions that are no better than random. 

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   Transfer learning leverages feature representations of deep neural networks (DNNs) pretrained on source tasks with rich data to empower effective finetuning on downstream tasks. However, the pre-trained models are often prohibitively large for delivering generalizable representations, which limits their deployment on edge devices with constrained resources. To close this gap, we propose a new transfer learning pipeline, which leverages our finding that robust tickets can transfer better, i.e., subnetworks drawn with properly induced adversarial robustness can win better transferability over vanilla lottery ticket subnetworks. Extensive experiments and ablation studies validate that our proposed transfer learning pipeline can achieve enhanced accuracy-sparsity trade-offs across both diverse downstream tasks and sparsity patterns, further enriching the lottery ticket hypothesis. 

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