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byAK and the research community

Jul 30

One Example Shown, Many Concepts Known! Counterexample-Driven Conceptual Reasoning in Mathematical LLMs

Leveraging mathematical Large Language Models (LLMs) for proof generation is a fundamental topic in LLMs research. We argue that the ability of current LLMs to prove statements largely depends on whether they have encountered the relevant proof process during training. This reliance limits their deeper understanding of mathematical theorems and related concepts. Inspired by the pedagogical method of "proof by counterexamples" commonly used in human mathematics education, our work aims to enhance LLMs' ability to conduct mathematical reasoning and proof through counterexamples. Specifically, we manually create a high-quality, university-level mathematical benchmark, CounterMATH, which requires LLMs to prove mathematical statements by providing counterexamples, thereby assessing their grasp of mathematical concepts. Additionally, we develop a data engineering framework to automatically obtain training data for further model improvement. Extensive experiments and detailed analyses demonstrate that CounterMATH is challenging, indicating that LLMs, such as OpenAI o1, have insufficient counterexample-driven proof capabilities. Moreover, our exploration into model training reveals that strengthening LLMs' counterexample-driven conceptual reasoning abilities is crucial for improving their overall mathematical capabilities. We believe that our work offers new perspectives on the community of mathematical LLMs.

Hostile Counterspeech Drives Users From Hate Subreddits

Counterspeech -- speech that opposes hate speech -- has gained significant attention recently as a strategy to reduce hate on social media. While previous studies suggest that counterspeech can somewhat reduce hate speech, little is known about its effects on participation in online hate communities, nor which counterspeech tactics reduce harmful behavior. We begin to address these gaps by identifying 25 large hate communities ("subreddits") within Reddit and analyzing the effect of counterspeech on newcomers within these communities. We first construct a new public dataset of carefully annotated counterspeech and non-counterspeech comments within these subreddits. We use this dataset to train a state-of-the-art counterspeech detection model. Next, we use matching to evaluate the causal effects of hostile and non-hostile counterspeech on the engagement of newcomers in hate subreddits. We find that, while non-hostile counterspeech is ineffective at keeping users from fully disengaging from these hate subreddits, a single hostile counterspeech comment substantially reduces both future likelihood of engagement. While offering nuance to the understanding of counterspeech efficacy, these results a) leave unanswered the question of whether hostile counterspeech dissuades newcomers from participation in online hate writ large, or merely drives them into less-moderated and more extreme hate communities, and b) raises ethical considerations about hostile counterspeech, which is both comparatively common and might exacerbate rather than mitigate the net level of antagonism in society. These findings underscore the importance of future work to improve counterspeech tactics and minimize unintended harm.