Addressing the challenge of automated geometry math problem-solving in artificial intelligence (AI) involves understanding multi-modal information and mathematics. blackCurrent methods struggle with accurately interpreting geometry diagrams, which hinders effective problem-solving. To tackle this issue, we present the Geometry problem sOlver with natural Language Description (GOLD) model. GOLD enhances the extraction of geometric relations by separately processing symbols and geometric primitives within the diagram. Subsequently, it converts the extracted relations into natural language descriptions, efficiently utilizing large language models to solve geometry math problems. Experiments show that the GOLD model outperforms the Geoformer model, the previous best method on the UniGeo dataset, by achieving accuracy improvements of 12.7% and 42.1% in calculation and proving subsets. Additionally, it surpasses the former best model on the PGPS9K and Geometry3K datasets, PGPSNet, by obtaining accuracy enhancements of 1.8% and 3.2%, respectively.

In recent years, large language models (LLMs) have become increasingly prevalent, offering remarkable text generation capabilities. However, a pressing challenge is their tendency to make confidently wrong predictions, highlighting the critical need for uncertainty quantification (UQ) in LLMs. While previous works have mainly focused on addressing aleatoric uncertainty, the full spectrum of uncertainties, including epistemic, remains inadequately explored. Motivated by this gap, we introduce a novel UQ method, sampling with perturbation for UQ (SPUQ), designed to tackle both aleatoric and epistemic uncertainties. The method entails generating a set of perturbations for LLM inputs, sampling outputs for each perturbation, and incorporating an aggregation module that generalizes the sampling uncertainty approach for text generation tasks. Through extensive experiments on various datasets, we investigated different perturbation and aggregation techniques. Our findings show a substantial improvement in model uncertainty calibration, with a reduction in Expected Calibration Error (ECE) by 50% on average. Our findings suggest that our proposed UQ method offers promising steps toward enhancing the reliability and trustworthiness of LLMs.

Hallucination detection is a critical step toward understanding the trustworthiness of modern language models (LMs). To achieve this goal, we re-examine existing detection approaches based on the self-consistency of LMs and uncover two types of hallucinations resulting from 1) question-level and 2) model-level, which cannot be effectively identified through self-consistency check alone. Building upon this discovery, we propose a novel sampling-based method, i.e., semantic-aware cross-check consistency (SAC³) that expands on the principle of self-consistency checking. Our SAC³ approach incorporates additional mechanisms to detect both question-level and model-level hallucinations by leveraging advances including semantically equivalent question perturbation and cross-model response consistency checking. Through extensive and systematic empirical analysis, we demonstrate that SAC³ outperforms the state of the art in detecting both non-factual and factual statements across multiple question-answering and open-domain generation benchmarks.