Beyond Positive Scaling: How Negation Impacts Scaling Trends of Language Models (2023)

Abstract: Language models 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 language models 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 language models.

## introduction language models have been shown to exhibit positive scaling, where task performance improves as models are scaled up in terms of size, compute, or data, like the blue curve in figure 1 @xcite @xcite @xcite . however, there are exceptions. recent works show that some tasks can exhibit inverse scaling @xcite , where the performance degrades as models are scaled up (green curve), or u-shaped scaling @xcite , where the performance degrades first but then improves as models are scaled up (red curve). analyzing tasks that exhibit different scaling trends, such as inverse and u-shaped scaling, is therefore useful for better understanding the behaviors of language models, identifying their limitations, and guiding future development. in this work, we introduce neqa, a new task of answering multiple-choice questions containing negation words, constructed by transforming questions from obqa @xcite and negatedlama @xcite . we conduct experiments on this task using 4 language model families and 3 prompting methods, and show that large language models do not follow straightforward positive scaling on this task. specifically, as we use more powerful prompting methods or model families, neqa exhibits a gradation from inverse scaling to u-shape to positive scaling. this result provides a unified view of when the three types of scaling trends (inverse, u-shaped, and positive scaling) occur for language models. our result indicates that the development of large language models' capability to process negation may be a complex and nuanced problem. to further understand this nuanced scaling trend of the neqa task, we decompose the task into two subtasks: question answering (task 1) and negation understanding (task 2). our empirical results show that task 1 has linearly positive scaling, while task 2 has sigmoid-shaped scaling with an emergent transition point, where the transition point is influenced by the prompt method and model family. combining these two scaling trends yields the final scaling trend observed in neqa. the task decomposition provides a new way to think of the scaling on a task in terms of a combination of its component skills. in summary, our contributions are (1) the neqa dataset that contains diverse distributions of texts about negation; ## dataset: neqa we develop neqa, a question answering dataset designed to evaluate the ability of models to process negation in natural language. each example of the dataset consists of a negated question and two answer choices, one correct and one incorrect. an example of neqa looks like: (question "child does not want?", correct choice "marriage", incorrect choice "love"). to construct this, we leveraged negatedlama @xcite and obqa @xcite . the negatedlama dataset includes negated questions from four subsets: conceptnet, googlere, squad, and trex. each subset comprises multiple files that represent different question distributions, such as questions about different entity relations. each question is associated with a negated question, an answer, and a misprimed question (i.e., a wrong answer followed by the question). for instance, when "child wants?" is the original question, "child does not want?" can be its associated negated question, "love" can be the answer, and "marriage? child wants?" can be its misprimed question. we turn it into a multiple choice question by setting the negated question as the question, and setting the wrong answer in the misprimed question in conjunction with the correct answer as the two choices. for instance, in the above example, we get "q: child does not want? a. love b. marriage" (appendix to be able to analyze the impact of different negation types, we also created additional data by applying diverse rules to transform questions in obqa @xcite into negated ones. we defined six types of negation transformations: action verb negation (e.g., "cause" → "does not/doesn't cause"), linking verb negation (e.g., "is" → "is not/isn't"), modal verb negation (e.g., "can" → "can not/can't"), conjunction negation (e.g., "because" → "not because"), negation prefix (e.g., "able" → "unable"), and negation prompt (e.g., add "choose the wrong answer"). for each type, we collected 50 questions by applying a rule-based transformation, sampling an incorrect answer as the correct answer, and treating the correct answer as the incorrect answer. for example, "pushing on a pedal is an example of" is an original question in obqa with the correct answer "force" and one of the incorrect answers "speed". we apply the rule-based transformation to change the verb "is" to "isn't" and get "q: pushing on a pedal isn't an 1,718 questions the following are multiple choice questions (with answers) about common sense. question: child does not want? a. love b. marriage answer: _ the following are multiple choice questions (with answers) about common sense. note that if there is a negation in the question, we should choose the wrong answer to the original question. question: child does not want? a. love b. marriage answer: _ the following are multiple choice questions (with answers) about common sense. question: if a cat has a body temp that is below average, it isn't in a. danger b. safe ranges answer: let's think step-by-step. first, let's answer non-negated question: "if a cat has a body temp that is below average, it is in?" for this non-negated question, we have a. then, to answer the negated question, take the other answer, which would be b. so the answer is b. … question: child does not want? a. love b. marriage answer: ______________ zero-shot zero-shot w/ hint few-shot w/ chain-of-thought (cot) neqa dataset question distribution example of? a. speed. b. force", where "a" is the answer (appendix we employ post-processing techniques such as redistributing labels evenly between "a" and "b" and balancing the use of negation words such as "not" and "n't". the validity of each question is ensured through manual examination and editing. our dataset comprises a total of 1718 questions sourced from conceptnet (150 questions), googlere (374 questions), squad (100 questions), trex (594 questions), and obqa (500 questions), providing a diverse range of negation types, text distributions, and prompts. we believe that this dataset serves as a valuable benchmark for assessing the ability of language models to process negation. data distributions are shown in figure 3 . out of the 1718 questions, we define a set of 944 questions from conceptnet, trex, and a subset of obqa that exhibit clear positive scaling on the corresponding original (non-negated) questions. for our experiments ( §3), we randomly select 100 questions from this positive set in order to make the scaling more obvious during our analysis. ## conclusion we introduced neqa, a new question answering dataset that yields different scaling trends of language models than traditional positive scaling. we then proposed task decomposition analysis, a general idea to decompose the task to better understand the complex scaling trends and their transitions. we hope that these insights can facilitate the understanding and development of language models.