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Pretraining language models on formal language can improve their acquisition of natural language. Which features of the formal language impart an inductive bias that leads to effective transfer? Drawing on insights from linguistics and complexity theory, we hypothesize that effective transfer occurs when two conditions are met: the formal language should capture the dependency structures present in natural language, and it should remain within the computational limitations of the model architecture. We experiment with pre-pretraining (training on formal language before natural languages) on transformers and find that formal languages capturing hierarchical dependencies indeed enable language models to achieve lower loss on natural language and better linguistic generalization compared to other formal languages. We also find modest support for the hypothesis that the formal language should fall within the computational limitations of the architecture. Strikingly, pre-pretraining reduces loss more efficiently than training on a matched amount of natural language. For a 1B-parameter language model trained on roughly 1.6B tokens of natural language, pre-pretraining achieves the same loss and better linguistic generalization with a 33% smaller token budget. Finally, we also give mechanistic evidence of transfer from formal to natural language: attention heads acquired during pre-pretraining remain crucial for the model's performance on syntactic evaluations. 

Heterogeneous Graph Neural Networks (HGNNs) have drawn increasing attention in recent years and achieved outstanding performance in many tasks. The success of the existing HGNNs relies on one fundamental assumption, i.e., the original heterogeneous graph structure is reliable. However, this assumption is usually unrealistic, since the heterogeneous graph in reality is inevitably noisy or incomplete. Therefore, it is vital to learn the heterogeneous graph structure for HGNNs rather than rely only on the raw graph structure. In light of this, we make the first attempt towards learning an optimal heterogeneous graph structure for HGNNs and propose a novel framework HGSL, which jointly performs Heterogeneous Graph Structure Learning and GNN parameters learning for classification task. Different from traditional GSL on homogeneous graph, considering the heterogeneity of different relations in heterogeneous graph, HGSL generates each relation subgraph independently. Specifically, in each generated relation subgraph, HGSL not only considers the feature similarity by generating feature similarity graph, but also considers the complex heterogeneous interactions in features and semantics by generating feature propagation graph and semantic graph. Then, these graphs are fused to a learned heterogeneous graph and optimized together with a GNN towards classification objective. Extensive experiments on real-world graphs demonstrate that the proposed framework significantly outperforms the state-of-the-art methods.