For a while now, companies like OpenAI and Google have been touting advanced "reasoning" capabilities as the next big step in their latest artificial intelligence models. Now, though, a new study from six Apple engineers shows that the mathematical "reasoning" displayed by advanced large language models can be extremely brittle and unreliable in the face of seemingly trivial changes to common benchmark problems. The fragility highlighted in these new results helps support previous research suggesting that LLMs' use of probabilistic pattern matching is missing the formal understanding of underlying concepts needed for truly reliable mathematical reasoning capabilities. "Current LLMs are not capable of genuine logical reasoning," the researchers hypothesize based on these results. "Instead, they attempt to replicate the reasoning steps observed in their training data."

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.