In order to efficiently learn with small amount of data on new tasks, meta-learning transfers knowledge learned from previous tasks to the new ones. However, a critical challenge in meta-learning is the task heterogeneity which cannot be well handled by traditional globally shared meta-learning methods. In addition, current task-specific meta-learning methods may either suffer from hand-crafted structure design or lack the capability to capture complex relations between tasks. In this paper, motivated by the way of knowledge organization in knowledge bases, we propose an automated relational meta-learning (ARML) framework that automatically extracts the cross-task relations and constructs the meta-knowledge graph. When a new task arrives, it can quickly find the most relevant structure and tailor the learned structure knowledge to the meta-learner. As a result, the proposed framework not only addresses the challenge of task heterogeneity by a learned meta-knowledge graph, but also increases the model interpretability. We conduct extensive experiments on 2D toy regression and few-shot image classification and the results demonstrate the superiority of ARML over state-of-the-art baselines. Learning quickly is the key characteristic of human intelligence, which remains a daunting problem in machine intelligence. The mechanism of meta-learning is widely used to generalize and transfer prior knowledge learned from previous tasks to improve the effectiveness of learning on new tasks, which has benefited various applications, such as computer vision (Kang et al., 2019; , natural language processing (Gu et al., 2018; Lin et al., 2019) and social good (Zhang et al., 2019; Yao et al., 2019a) . Most of existing meta-learning algorithms learn a globally shared meta-learner (e.g., parameter initialization (Finn et al., 2017; , meta-optimizer (Ravi & Larochelle, 2016) , metric space (Snell et al., 2017; Garcia & Bruna, 2017; Oreshkin et al., 2018) ). However, globally shared meta-learners fail to handle tasks lying in different distributions, which is known as task heterogeneity (Vuorio et al., 2018; Yao et al., 2019b) . Task heterogeneity has been regarded as one of the most challenging issues in meta-learning, and thus it is desirable to design meta-learning models that effectively optimize each of the heterogeneous tasks. The key challenge to deal with task heterogeneity is how to customize globally shared meta-learner by using task-specific information? Recently, a handful of works try to solve the problem by learning a task-specific representation for tailoring the transferred knowledge to each task (Oreshkin et al., 2018; Vuorio et al., 2018; Lee & Choi, 2018) . However, the expressiveness of these methods is limited due to the impaired knowledge generalization between highly related tasks. Recently, learning the underlying structure across tasks provides a more effective way for balancing the customization and generalization. Representatively, Yao et al. propose a hierarchically structured meta-learning method to customize the globally shared knowledge to each cluster (Yao et al., 2019b) . Nonetheless, the hierarchical clustering structure completely relies on the handcrafted design which needs to be tuned carefully and may lack the capability to capture complex relationships. Hence, we are motivated to propose a framework to automatically extract underlying relational structures from historical tasks and leverage those relational structures to facilitate knowledge customization on a new task. This inspiration comes from the way of structuring knowledge in knowledge bases (i.e., knowledge graphs). In knowledge bases, the underlying relational structures across text entities are automatically constructed and applied to a new query to improve the searching efficiency. In the meta-learning problem, similarly, we aim at automatically establishing the metaknowledge graph between prior knowledge learned from previous tasks. When a new task arrives, it queries the meta-knowledge graph and quickly attends to the most relevant entities (vertices), and then takes advantage of the relational knowledge structures between them to boost the learning effectiveness with the limited training data. The proposed meta-learning framework is named as Automated Relational Meta-Learning (ARML). Specifically, the ARML automatically builds the meta-knowledge graph from meta-training tasks to memorize and organize learned knowledge from historical tasks, where each vertex represents one type of meta-knowledge (e.g., the common contour between birds and aircrafts). To learn the meta-knowledge graph at meta-training time, for each task, we construct a prototype-based relational graph for each class, where each vertex represents one prototype. The prototype-based relational graph not only captures the underlying relationship behind samples, but alleviates the potential effects of abnormal samples. The meta-knowledge graph is then learned by summarizing the information from the corresponding prototype-based relational graphs of meta-training tasks. After constructing the meta-knowledge graph, when a new task comes in, the prototype-based relational graph of the new task taps into the meta-knowledge graph for acquiring the most relevant knowledge, which further enhances the task representation and facilitates its training process. Our major contributions of the proposed ARML are three-fold: (1) it automatically constructs the meta-knowledge graph to facilitate learning a new task; (2) it empirically outperforms the state-ofthe-art meta-learning algorithms; (3) the meta-knowledge graph well captures the relationship among tasks and improves the interpretability of meta-learning algorithms. In this paper, to improve the effectiveness of meta-learning for handling heterogeneous task, we propose a new framework called ARML, which automatically extract relation across tasks and construct a meta-knowledge graph. When a new task comes in, it can quickly find the most relevant relations through the meta-knowledge graph and use this knowledge to facilitate its training process. The experiments demonstrate the effectiveness of our proposed algorithm. In the future, we plan to investigate the problem in the following directions: (1) we are interested to investigate the more explainable semantic meaning in the meta-knowledge graph on this problem; (2) Figure 3 : Interpretation of meta-knowledge graph on Art-Multi dataset. For each subdataset, we randomly select one task from them. In the left, we show the similarity heatmap between prototypes (P0-P5) and meta-knowledge vertices (V0-V7). In the right part, we show the meta-knowledge graph. we plan to extend the ARML to the continual learning scenario where the structure of meta-knowledge graph will change over time; (3) our proposed model focuses on tasks where the feature space, the label space are shared. We plan to explore the relational structure on tasks with different feature and label spaces. In this dataset, we use pencil and blur filers to change the task distribution. To investigate the effect of pencil and blur filters, we provide one example in Figure 4 . We can observe that different filters result in different data distributions. All used filter are provided by OpenCV 1 .
Addressing task heterogeneity problem in meta-learning by introducing meta-knowledge graph
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