Generating high-quality geometry problems is both an important and challenging task in education. Compared to math word problems, geometry problems further emphasize multi-modal formats and the translation between informal and formal languages. In this paper, we introduce a novel task for geometry problem generation and propose a new pipeline method: the Symbolic Deduction Engine-based Geometry Problem Generation framework (SDE-GPG). The framework leverages a symbolic deduction engine and contains four main steps: (1) searching a predefined mapping table from knowledge points to extended definitions, (2) sampling extended definitions and performing symbolic deduction, (3) filtering out unqualified problems, and (4) generating textual problems and diagrams. Specifically, our method supports to avoid inherent biases in translating natural language into formal language by designing the mapping table, and guarantees to control the generated problems in terms of knowledge points and difficulties by an elaborate checking function. With obtained formal problems, they are translated to natural language and the accompanying diagrams are automatically drew by rule-based methods. We conduct experiments using real-world combinations of knowledge points from two public datasets. The results demonstrate that the SDE-GPG can effectively generate readable, solvable and controllable geometry problems.

In this paper, we study Chinese Spelling Correction (CSC) as a joint decision made by two separate models: a language model and an error model. Through empirical analysis, we find that fine-tuning BERT tends to over-fit the error model while under-fit the language model, resulting in poor generalization to out-of-distribution error patterns. Given that BERT is the backbone of most CSC models, this phenomenon has a significant negative impact. To address this issue, we are releasing a multi-domain benchmark LEMON, with higher quality and diversity than existing benchmarks, to allow a comprehensive assessment of the open domain generalization of CSC models. Then, we demonstrate that a very simple strategy – randomly masking 20% non-error tokens from the input sequence during fine-tuning – is sufficient for learning a much better language model without sacrificing the error model. This technique can be applied to any model architecture and achieves new state-of-the-art results on SIGHAN, ECSpell, and LEMON.

Spelling error correction is an important yet challenging task because a satisfactory solution of it essentially needs human-level language understanding ability. Without loss of generality we consider Chinese spelling error correction (CSC) in this paper. A state-of-the-art method for the task selects a character from a list of candidates for correction (including non-correction) at each position of the sentence on the basis of BERT, the language representation model. The accuracy of the method can be sub-optimal, however, because BERT does not have sufficient capability to detect whether there is an error at each position, apparently due to the way of pre-training it using mask language modeling. In this work, we propose a novel neural architecture to address the aforementioned issue, which consists of a network for error detection and a network for error correction based on BERT, with the former being connected to the latter with what we call soft-masking technique. Our method of using ‘Soft-Masked BERT’ is general, and it may be employed in other language detection-correction problems. Experimental results on two datasets, including one large dataset which we create and plan to release, demonstrate that the performance of our proposed method is significantly better than the baselines including the one solely based on BERT.