#01Oct 29, 2026
cs.LG
Training Foundation Models with a Single Algorithm
Yuda Song, Alvin Zhang, Fahim Tajwar and 7 more
Foundation models are typically trained in stages: pretraining, midtraining, supervised fine-tuning (SFT), and reinforcement learning (RL), with changes in both data and learning algorithms. We show that this algorithmic separation is not fundamental. By deriving suitable RL objectives as maximum-likelihood fitting to model-generated target distributions, we place all of these stages under a single likelihood-based training algorithm, unified training. This perspective turns the foundation-model training lifecycle into a problem of choosing which data to train on, in what proportions, and when, with conventional staged training as a special case. We instantiate this framework in a unified training system that mixes static data and RL generations within a single trainer. Across controlled and real-world experiments, unified training improves the accuracy-compute tradeoff and task coverage while preserving broader capabilities, and provides a stronger starting point for continual learning. This work lays the groundwork for a unified science of foundation-model training, connecting mathematical principles, training infrastructure, and the development of model capabilities.
#02Oct 29, 2026
math.ST
Self-regularization and structural adaptation of NPMLE for Gaussian mixture models in all dimensions
Yanjun Han, Yandi Shen, Yihong Wu
We establish structural properties of the nonparametric maximum likelihood estimator (NPMLE) for $d$-dimensional Gaussian mixtures whose means lie in a hypercube. We show that, with high probability, the NPMLE based on $n$ independent observations self-regularizes by fitting a mixture model with $O((\frac{\log n}{\log\log n})^d)$ components, achieving the optimal model complexity without explicit model selection. Furthermore, the NPMLE exhibits a structural adaptation property: For data drawn from a finite mixture, the number of fitted components is bounded in probability as $n\to\infty$. Our proof applies a multivariate Jensen-type bound to control the typical number of critical points of the KKT function associated with the first-order optimality conditions. The key step is to lower bound its gradient norm uniformly on complex spheres. We establish this lower bound by decomposing the KKT function into an empirical fluctuation term and a relative density estimation error term, combining small-ball probability estimates for the former with polynomial approximation and Hellinger error bounds for the latter.
#03Oct 29, 2026
physics.ao-ph
From extreme weather to agricultural consequences with agentic AI
Minghan Yu, Mengyu Dai, Yixin Wen and 1 more
Extreme weather is forecast days ahead, yet its consequences for agriculture remain hard to predict: a forecast says where a storm will strike, not which crops will suffer or how much is at risk, and the records that could tell span many sources. We present WxCrop, the first agent that judges agricultural hazards from physically interpretable weather indices examined by causal analysis, and the first that combines weather and agricultural information to predict crop loss reliably for past and forecast dates. We demonstrate it in Florida on hurricanes, freezes and dry heat, with a loss model calibrated on insurance records for each, and the same procedure extends to other hazards and areas. Three checks show reliability: the hurricane index detects recorded cyclone days with an AUC of 0.98, recorded losses in held-out years are reproduced to within 2%, and independent production records confirm the county rankings (rank correlation 0.63). Users ask the agent for each crop group's loss as a fraction of expected season value, every number sourced, so that governments, growers and scientists respond to agricultural disasters quickly.
#04Oct 29, 2026
cs.AI
Ramanujan Challenge Results: AI-Assisted Evaluation Pipeline for Multi-Format Proofs
Alan Sorani, Ashvni Narayanan, Michael Shalyt and 8 more
As AI's mathematical capabilities rapidly improve, meaningful benchmarks are shifting from university-level problems and math olympiads to research-level mathematics. The Ramanujan Challenge is a benchmark comprised of research-level problems in number theory, including unpublished results and open conjectures. It presented concrete formulas for mathematical constants whose correctness can be checked numerically, while their proofs may require non-obvious mathematics. Here, we analyze the Challenge submissions, measuring the relative success of different AI models, Computer Algebra Systems (CAS), and formal tools. We find correct submissions that are conceptually distinct from the official solutions, and a proof of one of the published open conjectures. Evaluating the submissions exposed a second challenge: judging complex proofs reliably at scale. We introduce an AI-assisted evaluation pipeline for natural language proofs, CAS code, and Lean formalizations that assesses semantic and logical correctness. Compared with the conventional one-shot LLM judgment, our pipeline reduces false-positive verdicts on natural language proofs from 23% to 6% and improves judgment accuracy on supporting code from 46% to 58%. This approach provides a methodology for evaluating research-level mathematics at scale, with potential applications across mathematics and AI for science.
#05Oct 29, 2026
cs.CE
TRACER, a time-to-event EHR foundation model for disease detection across health systems
Mara Pleasure, Ekaterina Redekop, Vedrana Ivezic and 4 more
Foundation models trained on longitudinal electronic health records (EHRs) can predict clinical diagnoses years in the future, making them a potential tool for disease screening. We developed TRACER (Temporal Risk Assessment with Clinical EHR Representations), a decoder-based foundation model pretrained on data from over 4.5 million patients from four health systems, and evaluated it on 16 incident diseases at 1-, 2-, and 5-year horizons in more than 2 million patients from two health systems excluded from model development. In contrast to typical evaluations that focus on global metrics (e.g., AUROC), we measured performance at the low false-positive rates that are realistic for screening. We found that TRACER retained its discrimination in external health systems, and at 95% specificity, the patients it flagged were up to eight times more likely to be diagnosed within a year than unselected patients. Evaluating at this operating point also revealed what global metrics alone did not: detection and false-alert burden varied across diseases and health systems, even when discrimination appeared stable. Our results illustrate the potential of foundation models for screening and underscore the need for evaluation in health systems excluded from development to assess disease detection and false-alert burden at levels appropriate for intended clinical use.}