Self-correction is emerging as a promising approach to mitigate the issue of hallucination in Large Language Models (LLMs). To facilitate effective self-correction, recent research has proposed mistake detection as its initial step. However, current literature suggests that LLMs often struggle with reliably identifying reasoning mistakes when using simplistic prompting strategies. To address this challenge, we introduce a unique prompting strategy, termed the Pedagogical Chain-of-Thought (PedCoT), which is specifically designed to guide the identification of reasoning mistakes, particularly mathematical reasoning mistakes. PedCoT consists of pedagogical principles for prompts (PPP) design, two-stage interaction process (TIP) and grounded PedCoT prompts, all inspired by the educational theory of the Bloom Cognitive Model (BCM). We evaluate our approach on two public datasets featuring math problems of varying difficulty levels. The experiments demonstrate that our zero-shot prompting strategy significantly outperforms strong baselines. The proposed method can achieve the goal of reliable mathematical mistake identification and provide a foundation for automatic math answer grading. The results underscore the significance of educational theory, serving as domain knowledge, in guiding prompting strategy design for addressing challenging tasks with LLMs effectively.

Recurrent neural networks (RNN) combined with attention mechanism has proved to be useful for various NLP tasks including machine translation, sequence labeling and syntactic parsing. The attention mechanism is usually applied by estimating the weights (or importance) of inputs and taking the weighted sum of inputs as derived features. Although such features have demonstrated their effectiveness, they may fail to capture the sequence information due to the simple weighted sum being used to produce them. The order of the words does matter to the meaning or the structure of the sentences, especially for syntactic parsing, which aims to recover the structure from a sequence of words. In this study, we propose an RNN-based attention to capture the relevant and sequence-preserved features from a sentence, and use the derived features to perform the dependency parsing. We evaluated the graph-based and transition-based parsing models enhanced with the RNN-based sequence-preserved attention on the both English PTB and Chinese CTB datasets. The experimental results show that the enhanced systems were improved with significant increase in parsing accuracy.

Existing neural dependency parsers usually encode each word in a sentence with bi-directional LSTMs, and estimate the score of an arc from the LSTM representations of the head and the modifier, possibly missing relevant context information for the arc being considered. In this study, we propose a neural feature extraction method that learns to extract arc-specific features. We apply a neural network-based attention method to collect evidences for and against each possible head-modifier pair, with which our model computes certainty scores of belief and disbelief, and determines the final arc score by subtracting the score of disbelief from the one of belief. By explicitly introducing two kinds of evidences, the arc candidates can compete against each other based on more relevant information, especially for the cases where they share the same head or modifier. It makes possible to better discriminate two or more competing arcs by presenting their rivals (disbelief evidence). Experiments on various datasets show that our arc-specific feature extraction mechanism significantly improves the performance of bi-directional LSTM-based models by explicitly modeling long-distance dependencies. For both English and Chinese, the proposed model achieve a higher accuracy on dependency parsing task than most existing neural attention-based models.

Unsupervised word representations have demonstrated improvements in predictive generalization on various NLP tasks. Most of the existing models are in fact good at capturing the relatedness among words rather than their ''genuine'' similarity because the context representations are often represented by a sum (or an average) of the neighbor's embeddings, which simplifies the computation but ignores an important fact that the meaning of a word is determined by its context, reflecting not only the surrounding words but also the rules used to combine them (i.e. compositionality). On the other hand, much effort has been devoted to learning a single-prototype representation per word, which is problematic because many words are polysemous, and a single-prototype model is incapable of capturing phenomena of homonymy and polysemy. We present a neural network architecture to jointly learn word embeddings and context representations from large data sets. The explicitly produced context representations are further used to learn context-specific and multi-prototype word embeddings. Our embeddings were evaluated on several NLP tasks, and the experimental results demonstrated the proposed model outperformed other competitors and is applicable to intrinsically "character-based" languages.