What Are the Odds? Language Models Are Capable of Probabilistic Reasoning

Language models (LM) are capable of remarkably complex linguistic tasks; however, numerical reasoning is an area in which they frequently struggle. An important but rarely evaluated form of reasoning is understanding probability distributions. In this paper, we focus on evaluating the probabilistic reasoning capabilities of LMs using idealized and real-world statistical distributions. We perform a systematic evaluation of state-of-the-art LMs on three tasks: estimating percentiles, drawing samples, and calculating probabilities. We evaluate three ways to provide context to LMs 1) anchoring examples from within a distribution or family of distributions, 2) real-world context, 3) summary statistics on which to base a Normal approximation. Models can make inferences about distributions, and can be further aided by the incorporation of real-world context, example shots and simplified assumptions, even if these assumptions are incorrect or misspecified. To conduct this work, we developed a comprehensive benchmark distribution dataset with associated question-answer pairs that we will release publicly.

Towards a Personal Health Large Language Model

In health, most large language model (LLM) research has focused on clinical tasks. However, mobile and wearable devices, which are rarely integrated into such tasks, provide rich, longitudinal data for personal health monitoring. Here we present Personal Health Large Language Model (PH-LLM), fine-tuned from Gemini for understanding and reasoning over numerical time-series personal health data. We created and curated three datasets that test 1) production of personalized insights and recommendations from sleep patterns, physical activity, and physiological responses, 2) expert domain knowledge, and 3) prediction of self-reported sleep outcomes. For the first task we designed 857 case studies in collaboration with domain experts to assess real-world scenarios in sleep and fitness. Through comprehensive evaluation of domain-specific rubrics, we observed that Gemini Ultra 1.0 and PH-LLM are not statistically different from expert performance in fitness and, while experts remain superior for sleep, fine-tuning PH-LLM provided significant improvements in using relevant domain knowledge and personalizing information for sleep insights. We evaluated PH-LLM domain knowledge using multiple choice sleep medicine and fitness examinations. PH-LLM achieved 79% on sleep and 88% on fitness, exceeding average scores from a sample of human experts. Finally, we trained PH-LLM to predict self-reported sleep quality outcomes from textual and multimodal encoding representations of wearable data, and demonstrate that multimodal encoding is required to match performance of specialized discriminative models. Although further development and evaluation are necessary in the safety-critical personal health domain, these results demonstrate both the broad knowledge and capabilities of Gemini models and the benefit of contextualizing physiological data for personal health applications as done with PH-LLM.