Existing methods on visual knowledge extraction often rely on the predefined format (e.g., sub-verb-obj tuples) or vocabulary (e.g., relation types), restricting the expressiveness of the extracted knowledge. In this work, we take a first exploration to a new paradigm of open visual knowledge extraction.

Recent studies have demonstrated that Large Language Models (LLMs) have strong mathematical reasoning abilities but rely on hundreds of billions of parameters. To tackle the challenge of poor reasoning in Small Language Models (SLMs), existing methods typically leverage LLMs to generate massive amounts of data for cramming training. In psychology, they are akin to System 1 thinking, which resolves reasoning problems rapidly based on experience and intuition. However, human learning also requires System 2 thinking, where knowledge is first acquired and then reinforced through practice. Inspired by such two distinct modes of thinking, we propose a novel method based on the multi-LoRA Interaction for mathematical reasoning Distillation (LoRID). First, we input the question and reasoning of each sample into an LLM to create knowledge-enhanced datasets. Subsequently, we train a LoRA block on the student model as an Intuitive Reasoner (IR), which directly generates Chain-of-Thoughts for problem-solving. Then, to imitate System 2 thinking, we train the Knowledge Generator (KG) and Deep Reasoner (DR), respectively. The former outputs only knowledge after receiving problems, while the latter uses that knowledge to perform reasoning. Finally, to address the randomness in the generation of IR and DR, we evaluate whether their outputs are consistent, and the inference process needs to be iterated if not. This step can enhance the mathematical reasoning ability of SLMs through mutual feedback. Experimental results show that LoRID achieves state-of-the-art performance, especially on the GSM8K dataset, where it outperforms the second-best method by 2.3%, 16.1%, 2.4%, 12.3%, and 1.8% accuracy across the five base models, respectively.

Large language models (LLMs) outperform information retrieval techniques for downstream knowledge-intensive tasks when being prompted to generate world knowledge. However, community concerns abound regarding the factuality and potential implications of using this uncensored knowledge. In light of this, we introduce CONNER, a COmpreheNsive kNowledge Evaluation fRamework, designed to systematically and automatically evaluate generated knowledge from six important perspectives -- Factuality, Relevance, Coherence, Informativeness, Helpfulness and Validity. We conduct an extensive empirical analysis of the generated knowledge from three different types of LLMs on two widely studied knowledge-intensive tasks, i.e., open-domain question answering and knowledge-grounded dialogue. Surprisingly, our study reveals that the factuality of generated knowledge, even if lower, does not significantly hinder downstream tasks. Instead, the relevance and coherence of the outputs are more important than small factual mistakes. Further, we show how to use CONNER to improve knowledge-intensive tasks by designing two strategies: Prompt Engineering and Knowledge Selection. Our evaluation code and LLM-generated knowledge with human annotations will be released to facilitate future research.