Reasoning LLMs such as OpenAI o1, o3 and DeepSeek R1 have made significant progress in mathematics and coding, yet find challenging advanced tasks such as International Mathematical Olympiad (IMO) combinatorics problems, Abstraction and Reasoning Corpus (ARC) puzzles, and Humanity's Last Exam (HLE) questions. We use a diverse inference approach that combines multiple models and methods at test time. We find that verifying mathematics and code problems, and rejection sampling on other problems is simple and effective. We automatically verify correctness of solutions to IMO problems by Lean, and ARC puzzles by code, and find that best-of-N effectively answers HLE questions. Our approach increases answer accuracy on IMO combinatorics problems from 33.3% to 77.8%, accuracy on HLE questions from 8% to 37%, and solves 80% of ARC puzzles that 948 humans could not and 26.5% of ARC puzzles that o3 high compute does not. Test-time simulations, reinforcement learning, and meta-learning with inference feedback improve generalization by adapting agent graph representations and varying prompts, code, and datasets. Our approach is reliable, robust, and scalable, and in the spirit of reproducible research, we will make it publicly available upon publication.

ABSTRACT The TESS mission produces a large amount of time series data, only a small fraction of which contain detectable exoplanetary transit signals. Deep learning techniques such as neural networks have proved effective at differentiating promising astrophysical eclipsing candidates from other phenomena such as stellar variability and systematic instrumental effects in an efficient, unbiased and sustainable manner. This paper presents a high quality dataset containing light curves from the Primary Mission and 1st Extended Mission full frame images and periodic signals detected via Box Least Squares (Kovács et al. 2002; Hartman 2012). The dataset was curated using a thorough manual review process then used to train a neural network called Astronet-Triage-v2. On our test set, for transiting/eclipsing events we achieve a 99.6% recall (true positives over all data with positive labels) at a precision of 75.7% (true positives over all predicted positives). Since 90% of our training data is from the Primary Mission, we also test our ability to generalize on held-out 1st Extended Mission data. Here, we find an area under the precision-recall curve of 0.965, a 4% improvement over Astronet-Triage (Yu et al. 2019). On the TESS Object of Interest (TOI) Catalog through April 2022, a shortlist of planets and planet candidates, Astronet-Triage-v2 is able to recover 3577 out of 4140 TOIs, while Astronet-Triage only recovers 3349 targets at an equal level of precision. In other words, upgrading to Astronet-Triage-v2 helps save at least 200 planet candidates from being lost. The new model is currently used for planet candidate triage in the Quick-Look Pipeline (Huang et al. 2020a,b; Kunimoto et al. 2021). INTRODUCTION ally requires extremely precise observations.

We demonstrate that a neural network pre-trained on text and fine-tuned on code solves Mathematics problems by program synthesis. We turn questions into programming tasks, automatically generate programs, and then execute them, perfectly solving university-level problems from MIT's large Mathematics courses (Single Variable Calculus 18.01, Multivariable Calculus 18.02, Differential Equations 18.03, Introduction to Probability and Statistics 18.05, Linear Algebra 18.06, and Mathematics for Computer Science 6.042), Columbia University's COMS3251 Computational Linear Algebra course, as well as questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems specifically designed to assess mathematical reasoning. We explore prompt generation methods that enable Transformers to generate question solving programs for these subjects, including solutions with plots. We generate correct answers for a random sample of questions in each topic. We quantify the gap between the original and transformed questions and perform a survey to evaluate the quality and difficulty of generated questions. This is the first work to automatically solve, grade, and generate university-level Mathematics course questions at scale. This represents a milestone for higher education.