Scientific machine learning is limited less by model size than by the data it is trained on. Observational data records what happened but not why; template synthetic data has a known generating process but only for the simulator's template, not the case a user faces. We argue a third option is now operationally feasible: instrumented data, in which every datum carries the mechanistic model that produced it, an explicit uncertainty over that model, and an executable family of counterfactuals. Verification-and-validation (V&V) instrumented image-to-simulation pipelines are one realisation: a sensor observation becomes a fully specified, solver-backed simulation with explicit, editable parameters and a propagated aleatoric/epistemic uncertainty. The substrate is case-specific, mechanistically supervised, and supports causal interventions through Pearl's do-operator.

Pretrained models are often evaluated on multi-task leaderboards to measure their applicability in diverse contexts. However, current methods for aggregating performance across tasks into leaderboard-level rankings do not address the uncertainty and variability at the task level. While recent works have proposed interval-based model rankings, the principled aggregation of uncertainty from individual tasks to leaderboard-level rankings remains unaddressed, and variation in models' performance across tasks is frequently obscured. In this work, we introduce a hierarchical framework that constructs model rank intervals with statistical guarantees at both levels: task-level rank confidence intervals from pairwise comparisons, and leaderboard-level rank prediction intervals using a conformal approach. This enables reliable quantification of model rank for each observed task and for new potential tasks. Experiments on simulated data and the TabArena and PromptEval (MMLU) benchmarks show that our method yields statistically valid and informative intervals, enabling reliable, uncertainty-aware model ranking on leaderboards.

Real-world datasets across image and text domains are often characterized by skewed class distributions and noisy annotations, which jointly degrade model performance, particularly on minority classes. Among existing solutions, active learning offers an effective and efficient paradigm by selectively querying the most informative and balanced samples for annotation. We propose an innovative active learning framework that mitigates class imbalance and selects the most informative samples to annotate. Leveraging foundation model priors, our algorithm enables imbalance-aware co-decisions between foundation model and small model to tackle noisy and imbalanced labels across various domains. We introduce the first study to systematically explore active learning under the dual challenges of label noise and class imbalance across image and text domains. Extensive experiments on imbalanced datasets demonstrate that our method achieves substantial annotation savings-over 50% compared to the best active learning baseline-while preserving performance and robustness to label noise.

Accurate vessel traffic flow prediction is crucial for smart port operations and navigational safety. However, maritime traffic flow data are often highly sparse with intermittent bursts, making robust forecasting challenging. Under such conditions, conventional spatio-temporal graph neural networks (ST-GNNs) can degrade toward conservative near-zero predictions and fail to capture non-zero activity. Although zero-inflated negative binomial (ZINB) models partially address excess zeros, their two-part formulation can still remain conservative around abrupt transitions. To address these issues, we propose a model-agnostic learnable Tweedie head that can be attached as a plug-and-play output module to arbitrary ST-GNN backbones. Instead of likelihood-based Tweedie training, which typically requires surrogate objectives, our approach optimizes the closed-form Tweedie unit deviance and predicts the mean for point forecasting while learning a node-level variance power to capture heterogeneous variability across port areas. Experiments on a maritime traffic graph constructed from real-world AIS data in the Port of Los Angeles and Long Beach show that the proposed head consistently improves RMSE across multiple ST-GNN backbones, especially on non-zero events, leading to more reliable forecasts for practical maritime traffic control.

We expect it to leak so we're just announcing it. Exactly a week after Anthropic announced its plan to go public, OpenAI has followed suit. The company said on Monday that it confidentially submitted a S-1 form with the Securities and Exchange Commission. No date or offer price has been set by OpenAI yet for the initial public offering. We recently submitted a confidential S-1. We expect it to leak so we're just announcing it.

The subscription now starts at $5 per month. Google is lowering the cost of its cheapest AI subscription to make Gemini models even easier to access. The Google AI Plus plan will now cost $5 per month, according to a post from Vikas Kansal, the company's Product Lead focused on Gemini AI subscriptions, down from its original $8 per month price. It now also comes with double the storage, 400GB instead of 200GB. The subscription plan became available in January 2026 as a cheaper way to access Google's Gemini 3 Pro model, Nano Banana Pro and Deep Research.

The Download: how the World Cup ball will fly and OpenAI's "super app" Plus: OpenAI plans to turn ChatGPT into a'super app' before its IPO. Why this year's World Cup ball may not fly as far Much is new about this month's FIFA World Cup tournament. It hosts more teams than ever before. It's the first to occur in three different host countries. And, like every World Cup for over half a century, it will employ a football with a brand-new design. Through wind-tunnel experiments, researchers found that long-distance kicks with Adidas's new Trionda ball might not travel as far as they did in the past.

A central mystery in deep learning is how neural networks, despite being highly non-convex and heavily overparameterized, are able to achieve near-zero training error while still generalizing well to unseen data. This paradox has sparked a surge of research aimed at understanding the convergence and generalization behavior of neural networks [1, 2, 6, 7, 15, 38, 41, 49]. The Neural Tangent Kernel (NTK), introduced by [20], has become one of a foundational tool for understanding the behavior of training dynamics for neural networks, especially those trained using gradient-based methods such as gradient descent (GD) and stochastic gradient descent (SGD). The core idea here is to linearize the neural network around its random initialization, which enables the evolution of the network during training to be closely approximated by a kernel method associated with the corresponding NTK. This framework establishes a powerful connection between the evolution of a neural network during training process and the behavior of kernel methods in a reproducing kernel Hilbert space (RKHS) induced by the NTK, allowing insights from the kernel methods to inform our understanding of neural networks. Following this perspective, the influential work [34] showed that for regression problems, shallow neural networks trained by SGD can achieve generalization performance on par with their kernel counterparts.

Predicting outputs that are located in non-Euclidean spaces, such as probability distributions, networks, and symmetric positive-definite matrices, is becoming increasingly important in modern data analysis, particularly when inputs are high-dimensional. We propose DeSI (Deep Single-Index Fréchet Regression), a semiparametric framework for regression with metric space-valued outputs and multivariate inputs that assumes a single-index structure for the conditional Fréchet mean. DeSI estimates an interpretable index direction, which quantifies the relative importance of inputs, using a deep neural network, and performs Fréchet regression along the resulting one-dimensional index in the target metric space. This structure mitigates the curse of dimensionality while retaining interpretability, which stands in contrast to standard deep neural networks. We establish theoretical guarantees for DeSI, including uniform approximation and convergence rates, and demonstrate its strong predictive performance through simulations on distributions, networks, and symmetric positive-definite matrices, as well as an application to compositional mood data from New Jersey.

Recent progress has been made in understanding the statistical generalization performance of gradient descent methods for overparameterized neural networks within the neural tangent kernel (NTK) regime. However, most of the existing work on regression problems is limited to shallow network architectures, leaving a notable gap in the theory of deep neural networks. This paper addresses this gap by presenting a comprehensive generalization analysis for deep ReLU networks trained using gradient descent (GD) and stochastic gradient descent (SGD). Specifically, we establish the first known minimax-optimal rates of excess population risk for both GD and SGD with deep ReLU networks, under the assumption that the network width scales polynomially with respect to the network depth and training sample size. Our results demonstrate that with sufficient width, gradient descent methods for deep ReLU networks can achieve optimal generalization rates on par with kernel methods.