Reinforcement learning (RL) has become central to training large language models (LLMs), yet the field lacks predictive scaling methodologies comparable to those established for pre-training. Despite rapidly rising compute budgets, there is no principled understanding of how to evaluate algorithmic improvements for scaling RL compute. We present the first large-scale systematic study, amounting to more than 400,000 GPU-hours, that defines a principled framework for analyzing and predicting RL scaling in LLMs. We fit sigmoidal compute-performance curves for RL training and ablate a wide range of common design choices to analyze their effects on asymptotic performance and compute efficiency. We observe: (1) Not all recipes yield similar asymptotic performance, (2) Details such as loss aggregation, normalization, curriculum, and off-policy algorithm primarily modulate compute efficiency without materially shifting the asymptote, and (3) Stable, scalable recipes follow predictable scaling trajectories, enabling extrapolation from smaller-scale runs. Combining these insights, we propose a best-practice recipe, ScaleRL, and demonstrate its effectiveness by successfully scaling and predicting validation performance on a single RL run scaled up to 100,000 GPU-hours. Our work provides both a scientific framework for analyzing scaling in RL and a practical recipe that brings RL training closer to the predictability long achieved in pre-training.

Forecasting urban phenomena such as housing prices and public health indicators requires the effective integration of various geospatial data. Current methods primarily utilize task-specific models, while recent foundation models for spatial representations often support only limited modalities and lack multimodal fusion capabilities. To overcome these challenges, we present UrbanFusion, a Geo-Foundation Model (GeoFM) that features Stochastic Multimodal Fusion (SMF). The framework employs modality-specific encoders to process different types of inputs, including street view imagery, remote sensing data, cartographic maps, and points of interest (POIs) data. These multimodal inputs are integrated via a Transformer-based fusion module that learns unified representations. An extensive evaluation across 41 tasks in 56 cities worldwide demonstrates UrbanFusion's strong generalization and predictive performance compared to state-of-the-art GeoAI models. Specifically, it 1) outperforms prior foundation models on location-encoding, 2) allows multimodal input during inference, and 3) generalizes well to regions unseen during training. UrbanFusion can flexibly utilize any subset of available modalities for a given location during both pretraining and inference, enabling broad applicability across diverse data availability scenarios. All source code is available at https://github.com/DominikM198/UrbanFusion.

Machine learning solvers for partial differential equations (PDEs) have attracted growing interest. However, most existing approaches, such as neural network solvers, rely on stochastic training, which is inefficient and typically requires a great many training epochs. Gaussian process (GP)/kernel-based solvers, while mathematical principled, suffer from scalability issues when handling large numbers of collocation points often needed for challenging or higher-dimensional PDEs. To overcome these limitations, we propose TGPS, a tensor-GP-based solver that models factor functions along each input dimension using one-dimensional GPs and combines them via tensor decomposition to approximate the full solution. This design reduces the task to learning a collection of one-dimensional GPs, substantially lowering computational complexity, and enabling scalability to massive collocation sets. For efficient nonlinear PDE solving, we use a partial freezing strategy and Newton's method to linerize the nonlinear terms. We then develop an alternating least squares (ALS) approach that admits closed-form updates, thereby substantially enhancing the training efficiency. We establish theoretical guarantees on the expressivity of our model, together with convergence proof and error analysis under standard regularity assumptions. Experiments on several benchmark PDEs demonstrate that our method achieves superior accuracy and efficiency compared to existing approaches.

A key question for adapting modern deep learning architectures to functional MRI (fMRI) is how to represent the data for model input. To bridge the modality gap between fMRI and natural images, we transform the 4D volumetric fMRI data into videos of 2D fMRI activity flat maps. We train Vision Transformers on 2.3K hours of fMRI flat map videos from the Human Connectome Project using the spatiotemporal masked autoencoder (MAE) framework. We observe that masked fMRI modeling performance improves with dataset size according to a strict power scaling law. Downstream classification benchmarks show that our model learns rich representations supporting both fine-grained state decoding across subjects, as well as subject-specific trait decoding across changes in brain state. This work is part of an ongoing open science project to build foundation models for fMRI data. Our code and datasets are available at https://github.com/MedARC-AI/fmri-fm.

Multimodal Large Language Models (MLLMs) struggle with precise reasoning for structured visuals like charts and diagrams, as pixel-based perception lacks a mechanism for verification. To address this, we propose to leverage derendering -- the process of reverse-engineering visuals into executable code -- as a new modality for verifiable visual reasoning. Specifically, we propose RECODE, an agentic framework that first generates multiple candidate programs to reproduce the input image. It then uses a critic to select the most faithful reconstruction and iteratively refines the code. This process not only transforms an ambiguous perceptual task into a verifiable, symbolic problem, but also enables precise calculations and logical inferences later on. On various visual reasoning benchmarks such as CharXiv, ChartQA, and Geometry3K, RECODE significantly outperforms methods that do not leverage code or only use code for drawing auxiliary lines or cropping. Our work demonstrates that grounding visual perception in executable code provides a new path toward more accurate and verifiable multimodal reasoning.

Chat assistants increasingly integrate web search functionality, enabling them to retrieve and cite external sources. While this promises more reliable answers, it also raises the risk of amplifying misinformation from low-credibility sources. In this paper, we introduce a novel methodology for evaluating assistants' web search behavior, focusing on source credibility and the groundedness of responses with respect to cited sources. Using 100 claims across five misinformation-prone topics, we assess GPT-4o, GPT-5, Perplexity, and Qwen Chat. Our findings reveal differences between the assistants, with Perplexity achieving the highest source credibility, whereas GPT-4o exhibits elevated citation of non-credibility sources on sensitive topics. This work provides the first systematic comparison of commonly used chat assistants for fact-checking behavior, offering a foundation for evaluating AI systems in high-stakes information environments.

Large language model (LLM)-based reasoning systems have recently achieved gold medal-level performance in the IMO 2025 competition, writing mathematical proofs where, to receive full credit, each step must be not only correct but also sufficiently supported. To train LLM-based reasoners in such challenging, open-ended settings, strong verifiers capable of catching step-level mistakes are necessary prerequisites. We introduce Hard2V erify, a human-annotated, step-level verification benchmark produced with over 500 hours of human labor. Hard2V erify is designed to rigorously assess step-level verifiers at the frontier: V erifiers must provide step-level annotations or identify the first error in responses generated by frontier LLMs for very recent, challenging, and open-ended math questions. We evaluate 29 generative critics and process reward models, demonstrating that, beyond a few standouts, open-source verifiers lag closed source models. We subsequently analyze what drives poor performance in step-level verification, the impacts of scaling verifier compute, as well as fundamental questions such as self-verification and verification-generation dynamics.Figure 1: Comparison of models evaluated on both ProcessBench (Zheng et al., 2024a) and our Hard2V erify benchmark. Past benchmarks do not sufficiently evaluate in the frontier-level math settings that Hard2V erify does; On the same error identification task, Qwen2.5-Math-PRM-72B Mathematical reasoning serves as a gold-standard evaluation setting for benchmarking reasoning progress in large language models (LLMs). Over the past half-decade, benchmarks have been introduced to assess LLMs at the grade-school (Cobbe et al., 2021), high-school (Hendrycks et al., 2021), university (Zhang et al., 2023), and competition math level (MMA, 2025; He et al., 2024a; Gao et al., 2024). However, the progress of mathematical reasoning ability of LLMs has outpaced benchmark creation, with every subsequent release of a frontier LLM saturating new benchmarks, most recently with GPT -5 Pro achieving 96.5%+ on AIME 2024. As a result, recent efforts (Glazer et al., 2024; Phan et al., 2025) have written novel, unseen mathematical questions to test LLMs. 1 This paradigm requires training data with solutions that are easily verifiable, i.e., have solutions that can be easily checked against a known ground-truth by string matching or symbolic checkers. Math benchmarks, for the most part, also adopt the verifiable setup, where a model response is considered correct if its final answer matches the established ground-truth.

Vision graph neural networks (ViG) have demonstrated promise in vision tasks as a competitive alternative to conventional convolutional neural nets (CNN) and transformers (ViTs); however, common graph construction methods, such as k-nearest neighbor (KNN), can be expensive on larger images. While methods such as Sparse Vision Graph Attention (SVGA) have shown promise, SVGA's fixed step scale can lead to over-squashing and missing multiple connections to gain the same information that could be gained from a long-range link. Through this observation, we propose a new graph construction method, Logarithmic Scalable Graph Construction (LSGC) to enhance performance by limiting the number of long-range links. To this end, we propose LogViG, a novel hybrid CNN-GNN model that utilizes LSGC. Furthermore, inspired by the successes of multi-scale and high-resolution architectures, we introduce and apply a high-resolution branch and fuse features between our high-resolution and low-resolution branches for a multi-scale high-resolution Vision GNN network. Extensive experiments show that LogViG beats existing ViG, CNN, and ViT architectures in terms of accuracy, GMACs, and parameters on image classification and semantic segmentation tasks. Our smallest model, Ti-LogViG, achieves an average top-1 accuracy on ImageNet-1K of 79.9% with a standard deviation of 0.2%, 1.7% higher average accuracy than Vision GNN with a 24.3% reduction in parameters and 35.3% reduction in GMACs. Our work shows that leveraging long-range links in graph construction for ViGs through our proposed LSGC can exceed the performance of current state-of-the-art ViGs. Code is available at https://github.com/mmunir127/LogViG-Official.

Generative AI systems are increasingly assisting and acting on behalf of end users in practical settings, from digital shopping assistants to next-generation autonomous cars. In this context, safety is no longer about blocking harmful content, but about preempting downstream hazards like financial or physical harm. Yet, most AI guardrails continue to rely on output classification based on labeled datasets and human-specified criteria,making them brittle to new hazardous situations. Even when unsafe conditions are flagged, this detection offers no path to recovery: typically, the AI system simply refuses to act--which is not always a safe choice. In this work, we argue that agentic AI safety is fundamentally a sequential decision problem: harmful outcomes arise from the AI system's continually evolving interactions and their downstream consequences on the world. We formalize this through the lens of safety-critical control theory, but within the AI model's latent representation of the world. This enables us to build predictive guardrails that (i) monitor an AI system's outputs (actions) in real time and (ii) proactively correct risky outputs to safe ones, all in a model-agnostic manner so the same guardrail can be wrapped around any AI model. We also offer a practical training recipe for computing such guardrails at scale via safety-critical reinforcement learning. Our experiments in simulated driving and e-commerce settings demonstrate that control-theoretic guardrails can reliably steer LLM agents clear of catastrophic outcomes (from collisions to bankruptcy) while preserving task performance, offering a principled dynamic alternative to today's flag-and-block guardrails.

Kilometer-scale weather data is crucial for real-world applications but remains computationally intensive to produce using traditional weather simulations. An emerging solution is to use deep learning models, which offer a faster alternative for climate downscaling. However, their reliability is still in question, as they are often evaluated using standard machine learning metrics rather than insights from atmospheric and weather physics. This paper benchmarks recent state-of-the-art deep learning models and introduces physics-inspired diagnostics to evaluate their performance and reliability, with a particular focus on geographic generalization and physical consistency. Our experiments show that, despite the seemingly strong performance of models such as CorrDiff, when trained on a limited set of European geographies (e.g., central Europe), they struggle to generalize to other regions such as Iberia, Morocco in the south, or Scandinavia in the north. They also fail to accurately capture second-order variables such as divergence and vorticity derived from predicted velocity fields. These deficiencies appear even in in-distribution geographies, indicating challenges in producing physically consistent predictions. We propose a simple initial solution: introducing a power spectral density loss function that empirically improves geographic generalization by encouraging the reconstruction of small-scale physical structures. The code for reproducing the experimental results can be found at https://github.com/CarloSaccardi/PSD-Downscaling