Robustness Assessment of Mathematical Reasoning in the Presence of Missing and Contradictory Conditions

Large language models (LLMs) have demonstrated impressive performance on reasoning tasks, which can be further improved through few-shot prompting techniques. However, the current evaluation primarily focuses on carefully constructed benchmarks and neglects the consideration of real-world reasoning problems that present missing and contradictory conditions, known as ill-defined problems. Our observations suggest that existing few-shot prompting techniques are ineffective in such scenarios, often providing overconfident answers or hallucination. To further study this problem, we develop a benchmark called Problems with Missing and Contradictory conditions (PMC) and introduce two novel metrics to evaluate the performance of few-shot prompting methods in these scenarios. Our analysis using the PMC benchmark reveals a trade-off dilemma between the performance of mathematical reasoning for well-defined problems and the ability to recognize ill-defined problems. To address the challenges posed by PMC, we propose a novel few-shot prompting method called SMT-LIB Prompting (SLP), which utilizes the SMT-LIB language to model the problems instead of solving them directly. Subsequently, a double-check solving strategy checks the satisfiability and uniqueness of the solution and provides final feedback. Extensive experiments demonstrate the superiority of our SLP approach compared to existing few-shot prompting methods when dealing with problems with missing and contradictory conditions. We will open-source our benchmark and code to facilitate future research.

LAMDA-SSL: Semi-Supervised Learning in Python

LAMDA-SSL is open-sourced on GitHub and its detailed usage documentation is available at https://ygzwqzd.github.io/LAMDA-SSL/. This documentation introduces LAMDA-SSL in detail from various aspects and can be divided into four parts. The first part introduces the design idea, features and functions of LAMDA-SSL. The second part shows the usage of LAMDA-SSL by abundant examples in detail. The third part introduces all algorithms implemented by LAMDA-SSL to help users quickly understand and choose SSL algorithms. The fourth part shows the APIs of LAMDA-SSL. This detailed documentation greatly reduces the cost of familiarizing users with LAMDA-SSL toolkit and SSL algorithms.