Minjae Kim

James V. Roggeveen, Erik Y. Wang, Will Flintoft et al.

Large language models (LLMs) have shown remarkable progress in mathematical problem-solving, but evaluation has largely focused on problems that have exact analytical solutions or involve formal proofs, often overlooking approximation-based problems ubiquitous in applied science and engineering. To fill this gap, we build on prior work and present HARDMath2, a dataset of 211 original problems covering the core topics in an introductory graduate applied math class, including boundary-layer analysis, WKB methods, asymptotic solutions of nonlinear partial differential equations, and the asymptotics of oscillatory integrals. This dataset was designed and verified by the students and instructors of a core graduate applied mathematics course at Harvard. We build the dataset through a novel collaborative environment that challenges students to write and refine difficult problems consistent with the class syllabus, peer-validate solutions, test different models, and automatically check LLM-generated solutions against their own answers and numerical ground truths. Evaluation results show that leading frontier models still struggle with many of the problems in the dataset, highlighting a gap in the mathematical reasoning skills of current LLMs. Importantly, students identified strategies to create increasingly difficult problems by interacting with the models and exploiting common failure modes. This back-and-forth with the models not only resulted in a richer and more challenging benchmark but also led to qualitative improvements in the students' understanding of the course material, which is increasingly important as we enter an age where state-of-the-art language models can solve many challenging problems across a wide domain of fields.

Jun Seo, Hyeokjun Choe, Seohui Bae et al.

Time series forecasting is a critical task for artificial intelligence with numerous real-world applications. Traditional approaches primarily rely on historical time series data to predict the future values. However, in practical scenarios, this is often insufficient for accurate predictions due to the limited information available. To address this challenge, multimodal time series forecasting methods which incorporate additional data modalities, mainly text data, alongside time series data have been explored. In this work, we introduce the Adaptive Information Routing (AIR) framework, a novel approach for multimodal time series forecasting. Unlike existing methods that treat text data on par with time series data as interchangeable auxiliary features for forecasting, AIR leverages text information to dynamically guide the time series model by controlling how and to what extent multivariate time series information should be combined. We also present a text-refinement pipeline that employs a large language model to convert raw text data into a form suitable for multimodal forecasting, and we introduce a benchmark that facilitates multimodal forecasting experiments based on this pipeline. Experiment results with the real world market data such as crude oil price and exchange rates demonstrate that AIR effectively modulates the behavior of the time series model using textual inputs, significantly enhancing forecasting accuracy in various time series forecasting tasks.