Metric-based meta-learning is one of the de facto standards in few-shot learning. It composes of representation learning and metrics calculation designs. Previous works construct class representations in different ways, varying from mean output embedding to covariance and distributions. However, using embeddings in space lacks expressivity and cannot capture class information robustly, while statistical complex modeling poses difficulty to metric designs. In this work, we use tensor fields (``areas'') to model classes from the geometrical perspective for few-shot learning. We present a simple and effective method, dubbed hypersphere prototypes (HyperProto), where class information is represented by hyperspheres with dynamic sizes with two sets of learnable parameters: the hypersphere's center and the radius. Extending from points to areas, hyperspheres are much more expressive than embeddings. Moreover, it is more convenient to perform metric-based classification with hypersphere prototypes than statistical modeling, as we only need to calculate the distance from a data point to the surface of the hypersphere. Following this idea, we also develop two variants of prototypes under other measurements. Extensive experiments and analysis on few-shot learning tasks across NLP and CV and comparison with 20+ competitive baselines demonstrate the effectiveness of our approach.

The recent emergence of contrastive learning approaches facilitates the research on graph representation learning (GRL), introducing graph contrastive learning (GCL) into the literature. These methods contrast semantically similar and dissimilar sample pairs to encode the semantics into node or graph embeddings. However, most existing works only performed model-level evaluation, and did not explore the combination space of modules for more comprehensive and systematic studies. For effective module-level evaluation, we propose a framework that decomposes GCL models into four modules: (1) a sampler to generate anchor, positive and negative data samples (nodes or graphs); (2) an encoder and a readout function to get sample embeddings; (3) a discriminator to score each sample pair (anchor-positive and anchor-negative); and (4) an estimator to define the loss function. Based on this framework, we conduct controlled experiments over a wide range of architectural designs and hyperparameter settings on node and graph classification tasks. Specifically, we manage to quantify the impact of a single module, investigate the interaction between modules, and compare the overall performance with current model architectures. Our key findings include a set of module-level guidelines for GCL, e.g., simple samplers from LINE and DeepWalk are strong and robust; an MLP encoder associated with Sum readout could achieve competitive performance on graph classification. Finally, we release our implementations and results as OpenGCL, a modularized toolkit that allows convenient reproduction, standard model and module evaluation, and easy extension.

Attributed graph embedding, which learns vector representations from graph topology and node features, is a challenging task for graph analysis. Recently, methods based on graph convolutional networks (GCNs) have made great progress on this task. However,existing GCN-based methods have three major drawbacks. Firstly,our experiments indicate that the entanglement of graph convolutional filters and weight matrices will harm both the performance and robustness. Secondly, we show that graph convolutional filters in these methods reveal to be special cases of generalized Laplacian smoothing filters, but they do not preserve optimal low-pass characteristics. Finally, the training objectives of existing algorithms are usually recovering the adjacency matrix or feature matrix, which are not always consistent with real-world applications. To address these issues, we propose Adaptive Graph Encoder (AGE), a novel attributed graph embedding framework. AGE consists of two modules: (1) To better alleviate the high-frequency noises in the node features, AGE first applies a carefully-designed Laplacian smoothing filter. (2) AGE employs an adaptive encoder that iteratively strengthens the filtered features for better node embeddings. We conduct experiments using four public benchmark datasets to validate AGE on node clustering and link prediction tasks. Experimental results show that AGE consistently outperforms state-of-the-art graph embedding methods considerably on these tasks.

Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics system, learning molecular fingerprints, predicting protein interface, and classifying diseases require that a model learns from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures, like the dependency tree of sentences and the scene graph of images, is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are connectionist models that capture the dependence of graphs via message passing between the nodes of graphs. Unlike standard neural networks, graph neural networks retain a state that can represent information from its neighborhood with arbitrary depth. Although the primitive GNNs have been found difficult to train for a fixed point, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful learning with them. In recent years, systems based on graph convolutional network (GCN) and gated graph neural network (GGNN) have demonstrated ground-breaking performance on many tasks mentioned above. In this survey, we provide a detailed review over existing graph neural network models, systematically categorize the applications, and propose four open problems for future research.