Deep neural networks based on layer-stacking architectures have historically suffered from poor inherent interpretability. Meanwhile, symbolic probabilistic models function with clear interpretability, but how to combine them with neural networks to enhance their performance remains to be explored. In this paper, we try to marry these two systems for text classification via a structured language model. We propose a Symbolic-Neural model that can learn to explicitly predict class labels of text spans from a constituency tree without requiring any access to span-level gold labels. As the structured language model learns to predict constituency trees in a self-supervised manner, only raw texts and sentence-level labels are required as training data, which makes it essentially a general constituent-level self-interpretable classification model. Our experiments demonstrate that our approach could achieve good prediction accuracy in downstream tasks. Meanwhile, the predicted span labels are consistent with human rationales to a certain degree.

Recently CKY-based models show great potential in unsupervised grammar induction thanks to their human-like encoding paradigm, which runs recursively and hierarchically, but requires $O(n^3)$ time-complexity. Recursive Transformer based on Differentiable Trees (R2D2) makes it possible to scale to large language model pre-training even with complex tree encoder by introducing a heuristic pruning method. However, the rule-based pruning approach suffers from local optimum and slow inference issues. In this paper, we fix those issues in a unified method. We propose to use a top-down parser as a model-based pruning method, which also enables parallel encoding during inference. Typically, our parser casts parsing as a split point scoring task, which first scores all split points for a given sentence, and then recursively splits a span into two by picking a split point with the highest score in the current span. The reverse order of the splits is considered as the order of pruning in R2D2 encoder. Beside the bi-directional language model loss, we also optimize the parser by minimizing the KL distance between tree probabilities from parser and R2D2. Our experiments show that our Fast-R2D2 improves performance significantly in grammar induction and achieves competitive results in downstream classification tasks.