Conformal Prediction Sets for Deep Generative Models via Reduction to Conformal Regression

We consider the problem of generating valid and small prediction sets by sampling outputs (e.g., software code and natural language text) from a black-box deep generative model for a given input (e.g., textual prompt). The validity of a prediction set is determined by a user-defined binary admissibility function depending on the target application. For example, requiring at least one program in the set to pass all test cases in code generation application. To address this problem, we develop a simple and effective conformal inference algorithm referred to as Generative Prediction Sets (GPS). Given a set of calibration examples and black-box access to a deep generative model, GPS can generate prediction sets with provable guarantees. The key insight behind GPS is to exploit the inherent structure within the distribution over the minimum number of samples needed to obtain an admissible output to develop a simple conformal regression approach over the minimum number of samples. Experiments on multiple datasets for code and math word problems using different large language models demonstrate the efficacy of GPS over state-of-the-art methods.

GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models

Recent advancements in Large Language Models (LLMs) have sparked interest in their formal reasoning capabilities, particularly in mathematics. The GSM8K benchmark is widely used to assess the mathematical reasoning of models on grade-school-level questions. While the performance of LLMs on GSM8K has significantly improved in recent years, it remains unclear whether their mathematical reasoning capabilities have genuinely advanced, raising questions about the reliability of the reported metrics. To address these concerns, we conduct a large-scale study on several SOTA open and closed models. To overcome the limitations of existing evaluations, we introduce GSM-Symbolic, an improved benchmark created from symbolic templates that allow for the generation of a diverse set of questions. GSM-Symbolic enables more controllable evaluations, providing key insights and more reliable metrics for measuring the reasoning capabilities of models.Our findings reveal that LLMs exhibit noticeable variance when responding to different instantiations of the same question. Specifically, the performance of all models declines when only the numerical values in the question are altered in the GSM-Symbolic benchmark. Furthermore, we investigate the fragility of mathematical reasoning in these models and show that their performance significantly deteriorates as the number of clauses in a question increases. We hypothesize that this decline is because current LLMs cannot perform genuine logical reasoning; they replicate reasoning steps from their training data. Adding a single clause that seems relevant to the question causes significant performance drops (up to 65%) across all state-of-the-art models, even though the clause doesn't contribute to the reasoning chain needed for the final answer. Overall, our work offers a more nuanced understanding of LLMs' capabilities and limitations in mathematical reasoning.