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Graph kernels are historically the most widely-used technique for graph classification tasks. However, these methods suffer from limited performance because of the hand-crafted combinatorial features of graphs. In recent years, graph neural networks (GNNs) have become the state-of-the-art method in downstream graph-related tasks due to their superior performance. Most GNNs are based on Message Passing Neural Network (MPNN) frameworks. However, recent studies show that MPNNs can not exceed the power of the Weisfeiler-Lehman (WL) algorithm in graph isomorphism test. To address the limitations of existing graph kernel and GNN methods, in this paper, we propose a novel GNN framework, termed Kernel Graph Neural Networks (KerGNNs), which integrates graph kernels into the message passing process of GNNs. Inspired by convolution filters in convolutional neural networks (CNNs), KerGNNs adopt trainable hidden graphs as graph filters which are combined with subgraphs to update node embeddings using graph kernels. In addition, we show that MPNNs can be viewed as special cases of KerGNNs. We apply KerGNNs to multiple graph-related tasks and use cross-validation to make fair comparisons with benchmarks. We show that our method achieves competitive performance compared with existing state-of-the-art methods, demonstrating the potential to increase the representation ability of GNNs. We also show that the trained graph filters in KerGNNs can reveal the local graph structures of the dataset, which significantly improves the model interpretability compared with conventional GNN models.

Deep learning has achieved state-of-the-art accuracies on several computer vision tasks. However, the computational and energy requirements associated with training such deep neural networks can be quite high. In this paper, we propose a cumulative training strategy with Net2Net transformation that achieves training computational efficiency without incurring large accuracy loss, in comparison to a model trained from scratch. We achieve this by first training a small network (with lesser parameters) on a small subset of the original dataset, and then gradually expanding the network using Net2Net transformation to train incrementally on larger subsets of the dataset. This incremental training strategy with Net2Net utilizes function-preserving transformations that transfers knowledge from each previous small network to the next larger network, thereby, reducing the overall training complexity. Our experiments demonstrate that compared with training from scratch, cumulative training yields ~2x reduction in computational complexity for training TinyImageNet using VGG19 at iso-accuracy. Besides training efficiency, a key advantage of our cumulative training strategy is that we can perform pruning during Net2Net expansion to obtain a final network with optimal configuration (~0.4x lower inference compute complexity) compared to conventional training from scratch. We also demonstrate that the final network obtained from cumulative training yields better generalization performance and noise robustness. Further, we show that mutual inference from all the networks created with cumulative Net2Net expansion enables improved adversarial input detection.

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