Alvin Li | Searcharxiv

arXiv2026

Solving Is Not Drawing: A Benchmark for Diagrammatic Reasoning in Olympiad Geometry

Foundation models such as GPT and Claude now solve olympiad-level mathematics with remarkable proficiency, so much so that geometry problem solving has become a standard proxy for their mathematical reasoning. Yet solving a geometry problem and drawing the figure it depends on are not the same skill: progress often hinges on a faithful diagram with the right auxiliary constructions and incidences, and it is unclear that a model which reasons its way to the answer can also produce one. A growing collection of benchmarks, including MathVista, and MathVerse, measures whether models reach the correct answer, but to our knowledge, none isolate the distinct ability to construct the diagram itself, leaving this capability unmeasured. We introduce an open-source benchmark that targets this gap: 954 self-contained olympiad geometry problems, with a 297-problem hard subset, each paired with its solution and a human-authored, high-fidelity diagram in renderable Asymptote code, together with a suite of text-, code-, image-, VLM-, and constraint-based metrics for what we term diagrammatic reasoning. Evaluating current foundation models reveals a pronounced gap between solving and drawing: their diagrams are markedly less faithful, with an average compile success rate of only 36.14\%. Strong mathematical reasoning, we find, does not imply the ability to construct accurate geometric diagrams. Our benchmark and dataset can be accessed at https://huggingface.co/datasets/max98765/hard_geometry_problems_with_diagrams.

cs.AI↗

arXiv2024

A neural network-based gravitational wave interpolant with applications to low-latency analyses

Matched-filter based gravitational-wave search pipelines identify candidate events within seconds of their arrival on Earth, offering a chance to guide electromagnetic follow-up and observe multi-messenger events. Understanding the detectors' response to an astrophysical transient across the searched signal manifold is paramount to inferring the parameters of the progenitor and deciding which candidates warrant telescope time. We describe a framework that uses artificial neural networks to interpolate gravitational waves and, equivalently, the signal-to noise ratio (SNR) across sufficiently local patches of the signal manifold. Our machine-learning based model generates a single waveform in 6 milliseconds on a CPU and 0.4 milliseconds on a GPU. When using a GPU to generate batches of waveforms simultaneously, we find that we can produce $10^4$ waveforms in $\lesssim 1$ ms. This is achieved while remaining faithful, on average, to 1 part in $10^4$ (1 part in $10^5$) for binary black hole (binary neutron star) waveforms. The model we present is designed to directly utilize intermediate detection pipeline outputs in the hopes of facilitating a better real-time understanding of gravitational-wave candidates.

astro-ph.IM↗