arXiv subjects

Dan Schwarz

Publications and source records attributed to Dan Schwarz.

7 recordsLinked to original sources

arXiv2026

Negative Latin-Square-Type Partial Difference Sets in Non-Elementary Abelian 2-Groups

Using cubic cyclotomic classes, character theory, and product constructions motivated by generalized Denniston partial difference sets, we construct negative Latin-square-type partial difference sets in $\mathbb{F}_{2^6}^{+}\times\mathbb{Z}_4^4$, $\mathbb{Z}_4^4\times\mathbb{F}_{2^{10}}^{+}$, $\mathbb{F}_{2^{10}}^{+}\times\mathbb{Z}_8^4$, $\mathbb{Z}_8^4\times\mathbb{F}_{2^{14}}^{+}$, and $\mathbb{Z}_4^4\times\mathbb{Z}_{16}^2$. The first four constructions replace cubic cyclotomic partitions by partitions of non-elementary abelian 2-groups having the same character-value patterns. To the best of our knowledge, these are the first partial difference sets with the stated parameters in the indicated groups.

math.CO↗

arXiv2026

Evaluating Strategic Reasoning in Forecasting Agents

Forecasting benchmarks produce accuracy leaderboards but little insight into why some forecasters are more accurate than others. We introduce Bench to the Future 2 (BTF-2), 1,417 pastcasting questions with a frozen 15M-document research corpus in which agents reproducibly research and forecast offline, producing full reasoning traces. BTF-2 detects accuracy differences of 0.004 Brier score, and can distinguish differential agent strengths in research vs. judgment. We build a forecaster 0.011 Brier more accurate than any single frontier agent, and use it to evaluate agent strategic reasoning without hindsight bias. We find the better forecaster differs primarily in its pre-mortem analysis of its blind spots and consideration of black swans. Expert human forecasters found the dominant strategic reasoning failures of frontier agents are in assessing political and business leaders' incentives, judging their likelihood to follow through on stated plans, and modeling institutional processes.

cs.AI↗

arXiv2026

Automating Forecasting Question Generation and Resolution for AI Evaluation

Forecasting future events is highly valuable in decision-making and is a robust measure of general intelligence. As forecasting is probabilistic, developing and evaluating AI forecasters requires generating large numbers of diverse and difficult questions, and accurately resolving them. Previous efforts to automate this laborious work relied on recurring data sources (e.g., weather, stocks), limiting diversity and utility. In this work, we present a system for generating and resolving high-quality forecasting questions automatically and at scale using LLM-powered web research agents. We use this system to generate 1499 diverse, real-world forecasting questions, and to resolve them several months later. We estimate that our system produces verifiable, unambiguous questions approximately 96% of the time, exceeding the rate of Metaculus, a leading human-curated forecasting platform. We also find that our system resolves questions at approximately 95% accuracy. We verify that forecasting agents powered by more intelligent LLMs perform better on these questions (Brier score of 0.134 for Gemini 3 Pro, 0.149 for GPT-5, and 0.179 for Gemini 2.5 Flash). Finally, we demonstrate how our system can be leveraged to directly improve forecasting, by evaluating a question decomposition strategy on a generated question set, yielding a significant improvement in Brier scores (0.132 vs. 0.141).

cs.LG↗

arXiv2025

Excursions in Sylvester-Gallai land

The Sylvester-Gallai theorem states that for a finite set of points in the plane, if every line determined by any two of these points also contains a third, then the set is necessarily made of collinear points. In this paper, we first provide a counterexample in the plane when the point set is countably infinite but bounded. Then we consider a variant of the Sylvester-Gallai theorem where instead of a finite point set we have a finite family of convex sets in $\mathbb{R}^d$ ($d\geq 2$). Finally, we present another variant of the Sylvester-Gallai theorem, when instead of point sets we have a finite family of line-segments in the plane.

math.CO↗

arXiv2025

Bench to the Future: A Pastcasting Benchmark for Forecasting Agents

Forecasting is a challenging task that offers a clearly measurable way to study AI systems. Forecasting requires a large amount of research on the internet, and evaluations require time for events to happen, making the development of forecasting benchmarks challenging. To date, no forecasting benchmark provides a realistic, hermetic, and repeatable environment for LLM forecasters. We introduce Bench To the Future (BTF), a "pastcasting" benchmark with hundreds of high-quality questions for which the resolution is already known. Each question is accompanied by a large offline corpus of tens of thousands of relevant web pages, enabling a way to elicit realistic "forecasts" on past events from LLMs. Results suggest that our pastcasting environment can produce results comparable to those based on forecasts using the internet on at-the-time unresolved questions. We show results benchmarking agent and chain-of-thought forecasting approaches using several LLMs, including the recently-released Claude 4 models, and demonstrate BTF's ability to track steady forecasting capability progress over time. We intend this to be a living benchmark, with new questions added continually to account for increasing training data cutoff dates. We invite researchers to contact us at hello@futuresearch.ai to utilize our benchmark or tooling for their own research.

cs.CL↗

arXiv2025

Deep Research Bench: Evaluating AI Web Research Agents

Amongst the most common use cases of modern AI is LLM chat with web search enabled. However, no direct evaluations of the quality of web research agents exist that control for the continually-changing web. We introduce Deep Research Bench, consisting of 89 multi-step web research task instances of varying difficulty across 8 diverse task categories, with the answers carefully worked out by skilled humans. We provide a "RetroSearch" environment with a large frozen set of scraped web pages, and demonstrate that offline "RetroSearch" agents perform comparably to "live web" agents, enabling reliable evaluations of models over time. We provide robust agent tooling and scaffolding to benchmark major LLMs as they are released, including "thinking" models like o3 and Gemini 2.5 Pro. We include automated evaluations of the lengthy agent traces to report progress over time in hallucinations, tool use, and forgetting. Finally, we evaluate the major web research products branded as "Deep Research", "Deep Search", "Search", or "Research." Results are available on a public leaderboard at https://drb.futuresearch.ai/.

cs.AI↗

arXiv2019

Cal X-1: an absolute in-orbit calibrator for current and future X-ray observatories

We describe Cal X-1, a SmallSat mission concept to establish X-ray standard candles in the sky, which will enable absolute calibration of the current and future X-ray observatories. It consists of two CubeSats flying in formation, one containing an absolutely calibrated X-ray source and another, 1-2 km away, a simple X-ray telescope.

astro-ph.IM↗