Hallucinations in large language models (LLMs) pose significant challenges in tasks requiring complex multi-step reasoning, such as mathematical problem-solving. Existing approaches primarily detect the presence of hallucinations but lack a nuanced understanding of their types and manifestations. In this paper, we first introduce a comprehensive taxonomy that categorizes the common hallucinations in mathematical reasoning tasks into six types: fabrication, factual inconsistency, context inconsistency, instruction inconsistency, logical inconsistency, and logical error. We then propose FG-PRM (Fine-Grained Process Reward Model), an augmented model designed to detect and mitigate hallucinations in a finegrained, step-level manner. To address the limitations of manually labeling training data, we propose an automated method for generating fine-grained hallucination data using LLMs. By injecting hallucinations into reasoning steps of correct solutions, we create a diverse and balanced synthetic dataset for training FG-PRM, which consists of six specialized Process Reward Models (PRMs), each tailored to detect a specific hallucination type. Our FG-PRM demonstrates superior performance across two key tasks: 1) Fine-grained hallucination detection: classifying hallucination types for each reasoning step; and 2) Verification: ranking multiple LLM-generated outputs to select the most accurate solution, mitigating reasoning hallucinations. Our experiments show that FG-PRM outperforms ChatGPT-3.5 and Claude-3 on fine-grained hallucination detection and substantially boosts the performance of LLMs on GSM8K and MATH benchmarks.

Neural models, including large language models (LLMs), achieve superior performance on multi-hop question-answering. To elicit reasoning capabilities from LLMs, recent works propose using the chain-of-thought (CoT) mechanism to generate both the reasoning chain and the answer, which enhances the model's capabilities in conducting multi-hop reasoning. However, several challenges still remain: such as struggling with inaccurate reasoning, hallucinations, and lack of interpretability. On the other hand, information extraction (IE) identifies entities, relations, and events grounded to the text. The extracted structured information can be easily interpreted by humans and machines (Grishman, 2019). In this work, we investigate constructing and leveraging extracted semantic structures (graphs) for multi-hop question answering, especially the reasoning process. Empirical results and human evaluations show that our framework: generates more faithful reasoning chains and substantially improves the QA performance on two benchmark datasets. Moreover, the extracted structures themselves naturally provide grounded explanations that are preferred by humans, as compared to the generated reasoning chains and saliency-based explanations.

Nowadays, the quality of responses generated by different modern large language models (LLMs) are hard to evaluate and compare automatically. Recent studies suggest and predominantly use LLMs as a reference-free metric for open-ended question answering. More specifically, they use the recognized "strongest" LLM as the evaluator, which conducts pairwise comparisons of candidate models' answers and provides a ranking score. However, this intuitive method has multiple problems, such as bringing in self-enhancement (favoring its own answers) and positional bias. We draw insights and lessons from the educational domain (Cho and MacArthur, 2011; Walsh, 2014) to improve LLM-based evaluations. Specifically, we propose the (1) peer rank (PR) algorithm that takes into account each peer LLM's pairwise preferences of all answer pairs, and outputs a final ranking of models; and (2) peer discussion (PD), where we prompt two LLMs to discuss and try to reach a mutual agreement on preferences of two answers. We conduct experiments on two benchmark datasets. We find that our approaches achieve higher accuracy and align better with human judgments, respectively. Interestingly, PR can induce a relatively accurate self-ranking of models under the anonymous setting, where each model's name is unrevealed. Our work provides space to explore evaluating models that are hard to compare for humans.