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Learning meaningful representations of free-hand sketches remains a challenging task given the signal sparsity and the high-level abstraction of sketches. Existing techniques have focused on exploiting either the static nature of sketches with Convolutional Neural Networks (CNNs) or the temporal sequential property with Recurrent Neural Networks (RNNs). In this work, we propose a new representation of sketches as multiple sparsely connected graphs. We design a novel Graph Neural Network (GNN), the Multi-Graph Transformer (MGT), for learning representations of sketches from multiple graphs which simultaneously capture global and local geometric stroke structures, as well as temporal information. We report extensive numerical experiments on a sketch recognition task to demonstrate the performance of the proposed approach. Particularly, MGT applied on 414k sketches from Google QuickDraw: (i) achieves small recognition gap to the CNN-based performance upper bound (72.80% vs. 74.22%), and (ii) outperforms all RNN-based models by a significant margin. To the best of our knowledge, this is the first work proposing to represent sketches as graphs and apply GNNs for sketch recognition. Code and trained models are available at https: //github.com/PengBoXiangShang/ multigraph_transformer.

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End-to-end training of neural network solvers for graph combinatorial optimization problems such as the Travelling Salesperson Problem (TSP) have seen a surge of interest recently, but remain intractable and inefficient beyond graphs with few hundreds of nodes. While state-of-the-art learning-driven approaches for TSP perform closely to classical solvers when trained on trivially small sizes, they are unable to generalize the learnt policy to larger instances at practical scales. This work presents an end-to-end neural combinatorial optimization pipeline that unifies several recent papers in order to identify the inductive biases, model architectures and learning algorithms that promote generalization to instances larger than those seen in training. Our controlled experiments provide the first principled investigation into such zero-shot generalization, revealing that extrapolating beyond training data requires rethinking the neural combinatorial optimization pipeline, from network layers and learning paradigms to evaluation protocols. Additionally, we analyze recent advances in deep learning for routing problems through the lens of our pipeline and provide new directions to stimulate future research.