Beyond Positive Scaling: How Negation Impacts Scaling Trends of Language Models

Abstract: LLMs have been shown to exhibit positive scaling, where performance improves as models are scaled up in terms of size, compute, or data. In this work, we introduce NeQA, a dataset consisting of questions with negation in which LLMs do not exhibit straightforward positive scaling. We show that this task can exhibit inverse scaling, U-shaped scaling, or positive scaling, and the three scaling trends shift in this order as we use more powerful prompting methods or model families. We hypothesize that solving NeQA depends on two subtasks: question answering (task 1) and negation understanding (task 2). We find that task 1 has linear scaling, while task 2 has sigmoid-shaped scaling with an emergent transition point, and composing these two scaling trends yields the final scaling trend of NeQA. Our work reveals and provides a way to analyze the complex scaling trends of LLMs.