Machine unlearning is a promising solution for efficiently removing specific knowledge by post hoc modifying models.

This is the Picard rank one analogue to Proposition 5.3 in the main text. The number in each dimension is given in Table 1.

Algebraic varieties are the geometric shapes defined by systems of polynomial equations; they are ubiquitous across mathematics and science.

This is the Picard rank one analogue to Proposition 5.3 in the main text. The number in each dimension is given in Table 1.

M1: Chunking long documents into max-context-length chunks, and averaging all-mini-LM-v6 embeddings across chunks to produce a final document embedding.

A great white shark was spotted this week swimming in the area of Scarborough, Maine. A drone video captured a great white shark lurking in the waters of a vacation spot in the Northeast. Police in Scarborough, Maine, which is located just south of Portland, confirmed this week that the shark was spotted off the state's coastline. "On Monday, August 11, 2025, Scarborough's Marine Resource Officer received a report of what appeared to be a large shark near Richmond Island and Scarborough Beach," the town wrote on its Facebook page. "Follow-up observations were conducted, and on Tuesday, August 12, 2025, the Marine Resource Officer obtained drone video footage showing a possible great white shark, estimated to be 10–12 feet in length, off the southern end of Richmond Island in the vicinity of Higgins Beach and Scarborough Beach," it added.

We introduce MentalChat16K, an English benchmark dataset combining a synthetic mental health counseling dataset and a dataset of anonymized transcripts from interventions between Behavioral Health Coaches and Caregivers of patients in palliative or hospice care. Covering a diverse range of conditions like depression, anxiety, and grief, this curated dataset is designed to facilitate the development and evaluation of large language models for conversational mental health assistance. By providing a high-quality resource tailored to this critical domain, MentalChat16K aims to advance research on empathetic, personalized AI solutions to improve access to mental health support services. The dataset prioritizes patient privacy, ethical considerations, and responsible data usage. MentalChat16K presents a valuable opportunity for the research community to innovate AI technologies that can positively impact mental well-being.

Performing interventions is a major challenge in economic policy-making. We propose causal strategic inference as a framework for conducting interventions and apply it to large, networked microfinance economies. The basic solution platform consists of modeling a microfinance market as a networked economy, learning the parameters of the model from the real-world microfinance data, and designing algorithms for various causal questions. For a special case of our model, we show that an equilibrium point always exists and that the equilibrium interest rates are unique. For the general case, we give a constructive proof of the existence of an equilibrium point. Our empirical study is based on the microfinance data from Bangladesh and Bolivia, which we use to first learn our models. We show that causal strategic inference can assist policy-makers by evaluating the outcomes of various types of interventions, such as removing a loss-making bank from the market, imposing an interest rate cap, and subsidizing banks.