Educators have started to turn to Generative AI (GenAI) to help create new course content, but little is known about how they should do so. In this project, we investigated the first steps for optimizing content creation for advanced math. In particular, we looked at the ability of GenAI to produce high-quality practice problems that are relevant to the course content. We conducted two studies to: (1) explore the capabilities of current versions of publicly available GenAI and (2) develop an improved framework to address the limitations we found. Our results showed that GenAI can create math problems at various levels of quality with minimal support, but that providing examples and relevant content results in better quality outputs. This research can help educators decide the ideal way to adopt GenAI in their workflows, to create more effective educational experiences for students.

Machine learning (ML) primarily evolved to solve "prediction problems." The first stage of two-stage least squares (2SLS) is a prediction problem, suggesting potential gains from ML first-stage assistance. However, little guidance exists on when ML helps 2SLS$\unicode{x2014}$or when it hurts. We investigate the implications of inserting ML into 2SLS, decomposing the bias into three informative components. Mechanically, ML-in-2SLS procedures face issues common to prediction and causal-inference settings$\unicode{x2014}$and their interaction. Through simulation, we show linear ML methods (e.g., post-Lasso) work well, while nonlinear methods (e.g., random forests, neural nets) generate substantial bias in second-stage estimates$\unicode{x2014}$potentially exceeding the bias of endogenous OLS.

Providing personalized, detailed feedback at scale in large undergraduate STEM courses remains a persistent challenge. We present an empirically evaluated practice exam system that integrates AI generated feedback with targeted textbook references, deployed in a large introductory biology course. Our system encourages metacognitive behavior by asking students to explain their answers and declare their confidence. It uses OpenAI's GPT-4o to generate personalized feedback based on this information, while directing them to relevant textbook sections. Through interaction logs from consenting participants across three midterms (541, 342, and 413 students respectively), totaling 28,313 question-student interactions across 146 learning objectives, along with 279 surveys and 23 interviews, we examined the system's impact on learning outcomes and engagement. Across all midterms, feedback types showed no statistically significant performance differences, though some trends suggested potential benefits. The most substantial impact came from the required confidence ratings and explanations, which students reported transferring to their actual exam strategies. About 40 percent of students engaged with textbook references when prompted by feedback -- far higher than traditional reading rates. Survey data revealed high satisfaction (mean rating 4.1 of 5), with 82.1 percent reporting increased confidence on practiced midterm topics, and 73.4 percent indicating they could recall and apply specific concepts. Our findings suggest that embedding structured reflection requirements may be more impactful than sophisticated feedback mechanisms.

Diffusion models hold great potential in robotics due to their ability to capture complex, high-dimensional data distributions. However, their lack of constraint-awareness limits their deployment in safety-critical applications. We propose Constraint-Aware Diffusion Guidance (CoDiG), a data-efficient and general-purpose framework that integrates barrier functions into the denoising process, guiding diffusion sampling toward constraint-satisfying outputs. CoDiG enables constraint satisfaction even with limited training data and generalizes across tasks. We evaluate our framework in the challenging setting of miniature autonomous racing, where real-time obstacle avoidance is essential. Real-world experiments show that CoDiG generates safe outputs efficiently under dynamic conditions, highlighting its potential for broader robotic applications. A demonstration video is available at https://youtu.be/KNYsTdtdxOU.

The continued rise of neural networks and large language models in the more recent past has altered the natural language processing landscape, enabling new approaches towards typical language tasks and achieving mainstream success. Despite the huge success of large language models, many disadvantages still remain and through this work we assess the state of the art in five application scenarios with a particular focus on the future perspectives and sensible application scenarios of traditional and older approaches and techniques. In this paper we survey recent publications in the application scenarios classification, information and relation extraction, text simplification as well as text summarization. After defining our terminology, i.e., which features are characteristic for traditional techniques in our interpretation for the five scenarios, we survey if such traditional approaches are still being used, and if so, in what way they are used. It turns out that all five application scenarios still exhibit traditional models in one way or another, as part of a processing pipeline, as a comparison/baseline to the core model of the respective paper, or as the main model(s) of the paper. For the complete statistics, see https://zenodo.org/records/13683801

We present PyFCG, an open source software library that ports Fluid Construction Grammar (FCG) to the Python programming language. PyFCG enables its users to seamlessly integrate FCG functionality into Python programs, and to use FCG in combination with other libraries within Python's rich ecosystem. Apart from a general description of the library, this paper provides three walkthrough tutorials that demonstrate example usage of PyFCG in typical use cases of FCG: (i) formalising and testing construction grammar analyses, (ii) learning usage-based construction grammars from corpora, and (iii) implementing agent-based experiments on emergent communication.

Conformal symmetries, i.e.\ coordinate transformations that preserve angles, play a key role in many fields, including physics, mathematics, computer vision and (geometric) machine learning. Here we build a neural network that is equivariant under general conformal transformations. To achieve this, we lift data from flat Euclidean space to Anti de Sitter (AdS) space. This allows us to exploit a known correspondence between conformal transformations of flat space and isometric transformations on the AdS space. We then build upon the fact that such isometric transformations have been extensively studied on general geometries in the geometric deep learning literature. We employ message-passing layers conditioned on the proper distance, yielding a computationally efficient framework. We validate our model on tasks from computer vision and statistical physics, demonstrating strong performance, improved generalization capacities, and the ability to extract conformal data such as scaling dimensions from the trained network.

Recent advances in Generative Artificial Intelligence (GenAI) have transformed educational content creation, particularly in developing tutor training materials. However, biases embedded in AI-generated content--such as gender, racial, or national stereotypes--raise significant ethical and educational concerns. Despite the growing use of GenAI, systematic methods for detecting and evaluating such biases in educational materials remain limited. This study proposes an automated bias assessment approach that integrates the Contextualized Embedding Association Test with a prompt-engineered word extraction method within a Retrieval-Augmented Generation framework. We applied this method to AI-generated texts used in tutor training lessons. Results show a high alignment between the automated and manually curated word sets, with a Pearson correlation coefficient of r = 0.993, indicating reliable and consistent bias assessment. Our method reduces human subjectivity and enhances fairness, scalability, and reproducibility in auditing GenAI-produced educational content.

Foundation models have shown remarkable success across scientific domains, yet their impact in chemistry remains limited due to the absence of diverse, large-scale, high-quality datasets that reflect the field's multifaceted nature. We present the ChemPile, an open dataset containing over 75 billion tokens of curated chemical data, specifically built for training and evaluating general-purpose models in the chemical sciences. The dataset mirrors the human learning journey through chemistry -- from educational foundations to specialized expertise -- spanning multiple modalities and content types including structured data in diverse chemical representations (SMILES, SELFIES, IUPAC names, InChI, molecular renderings), scientific and educational text, executable code, and chemical images. ChemPile integrates foundational knowledge (textbooks, lecture notes), specialized expertise (scientific articles and language-interfaced data), visual understanding (molecular structures, diagrams), and advanced reasoning (problem-solving traces and code) -- mirroring how human chemists develop expertise through diverse learning materials and experiences. Constructed through hundreds of hours of expert curation, the ChemPile captures both foundational concepts and domain-specific complexity. We provide standardized training, validation, and test splits, enabling robust benchmarking. ChemPile is openly released via HuggingFace with a consistent API, permissive license, and detailed documentation. We hope the ChemPile will serve as a catalyst for chemical AI, enabling the development of the next generation of chemical foundation models.

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.