Daily Papers

Building virtual embodied agents that operate in open-ended games like human players is a long-standing goal requiring both long-horizon autonomy and reliable native-interface control. As a procedurally generated open world, Minecraft provides a natural testbed for studying the integration of these capabilities. Existing agents typically provide either native visuomotor control without long-horizon autonomy or high-level planning executed through environment APIs or predefined skills. To bridge this gap, we propose HiSTEVE, a hierarchical VLA agent with a capability-aware agent harness. At the orchestration level, we equip the harness with structured memory for tracking progress and a VLM planner for selecting subtasks within the VLA's capabilities. To reliably determine subtask completion, we further introduce a policy-coupled task completion state detector that conditions on VLA policy context to signal candidate completion. At the control level, a single VLA executes all subtasks with vision-only perception and native keyboard-and-mouse actions. To mitigate interference between heterogeneous GUI and non-GUI interactions, we introduce regime-specific RMSNorm branches and separate mouse-movement token embeddings. We also train the VLA through world knowledge injection, imitation learning, and reinforcement learning with environment feedback to improve reliability and recovery. HiSTEVE achieves state-of-the-art atomic-task performance, scoring 85.0% on MineStudio Bench and a 37.4% average success rate on OpenHA, while also completing long-horizon tasks such as crafting an iron pickaxe from scratch like human players.

Layer normalization (LayerNorm) has been successfully applied to various deep neural networks to help stabilize training and boost model convergence because of its capability in handling re-centering and re-scaling of both inputs and weight matrix. However, the computational overhead introduced by LayerNorm makes these improvements expensive and significantly slows the underlying network, e.g. RNN in particular. In this paper, we hypothesize that re-centering invariance in LayerNorm is dispensable and propose root mean square layer normalization, or RMSNorm. RMSNorm regularizes the summed inputs to a neuron in one layer according to root mean square (RMS), giving the model re-scaling invariance property and implicit learning rate adaptation ability. RMSNorm is computationally simpler and thus more efficient than LayerNorm. We also present partial RMSNorm, or pRMSNorm where the RMS is estimated from p% of the summed inputs without breaking the above properties. Extensive experiments on several tasks using diverse network architectures show that RMSNorm achieves comparable performance against LayerNorm but reduces the running time by 7%~64% on different models. Source code is available at https://github.com/bzhangGo/rmsnorm.

RMSNorm is used by many LLMs such as Llama, Mistral, and OpenELM. This paper details FlashNorm, which is an exact but faster implementation of RMSNorm followed by linear layers. See https://huggingface.co/open-machine/FlashNorm for code and more transformer tricks.

Low-rank adaptation (LoRA) has become a standard approach for fine-tuning large foundation models. However, our theoretical understanding of LoRA remains limited as prior analyses of LoRA's training dynamics either rely on linearization arguments or consider highly simplified setups. In this work, we analyze the LoRA loss landscape without such restrictive assumptions. We define two regimes: a "special regime", which includes idealized setups where linearization arguments hold, and a "generic regime" representing more realistic setups where linearization arguments do not hold. In the generic regime, we show that LoRA training converges to a global minimizer with low rank and small magnitude, or a qualitatively distinct solution with high rank and large magnitude. Finally, we argue that the zero-initialization and weight decay in LoRA training induce an implicit bias toward the low-rank, small-magnitude region of the parameter space -- where global minima lie -- thus shedding light on why LoRA training usually succeeds in finding global minima.

Transformers have achieved great success in machine learning applications. Normalization techniques, such as Layer Normalization (LayerNorm, LN) and Root Mean Square Normalization (RMSNorm), play a critical role in accelerating and stabilizing the training of Transformers. While LayerNorm recenters and rescales input vectors, RMSNorm only rescales the vectors by their RMS value. Despite being more computationally efficient, RMSNorm may compromise the representation ability of Transformers. There is currently no consensus regarding the preferred normalization technique, as some models employ LayerNorm while others utilize RMSNorm, especially in recent large language models. It is challenging to convert Transformers with one normalization to the other type. While there is an ongoing disagreement between the two normalization types, we propose a solution to unify two mainstream Transformer architectures, Pre-LN and Pre-RMSNorm Transformers. By removing the inherent redundant mean information in the main branch of Pre-LN Transformers, we can reduce LayerNorm to RMSNorm, achieving higher efficiency. We further propose the Compressed RMSNorm (CRMSNorm) and Pre-CRMSNorm Transformer based on a lossless compression of the zero-mean vectors. We formally establish the equivalence of Pre-LN, Pre-RMSNorm, and Pre-CRMSNorm Transformer variants in both training and inference. It implies that Pre-LN Transformers can be substituted with Pre-(C)RMSNorm counterparts at almost no cost, offering the same arithmetic functionality along with free efficiency improvement. Experiments demonstrate that we can reduce the training and inference time of Pre-LN Transformers by 1% - 10%.

Sky-image irradiance studies often compare forecasting systems in which the image encoder, temporal model, fusion block, target definition, and training recipe all change together. We use a narrower protocol: the multimodal forecasting pipeline is fixed, and only the visual backbone is varied. The shared setup keeps preprocessing, clear-sky-index normalization, weather-history encoding, fusion, regression head, loss, optimizer schedule, seed, and chronological split policy unchanged. We compare ConvNeXt, Swin Transformer, VMamba, Spatial Mamba, and MambaVision backbones for 10min-ahead forecasting on Folsom and a strict matched NREL split. Forecast skill is measured against clear-sky-index smart persistence, and temporal-only rows are reported as weather-history diagnostics rather than as the main ranking criterion. On the Folsom strict split, all evaluated visual-backbone runs improve over smart persistence. In the evaluated single-seed strict runs, VMamba Small and Swin Base reach matched Folsom RMSE values of 65.39 W/m^2 and 65.50 W/m^2; the temporal-only diagnostic reaches 69.51 W/m^2. On the 313-sample NREL strict split, smart persistence remains strongest at 17.48 W/m^2, while the lowest visual RMSE is obtained by Swin Tiny at 23.76 W/m^2. These results provide a reproducible encoder comparison under one fixed multimodal operating point rather than establishing architecture-level dominance, statistically resolved ranking, or fully optimized forecasting performance. Code available here: https://github.com/Oshadha345/irradiance_benchmark

Normalization layer constitutes an essential component in neural networks. In transformers, the predominantly used RMSNorm constrains vectors to a unit hypersphere, followed by dimension-wise rescaling through a learnable scaling coefficient γ to maintain the representational capacity of the model. However, RMSNorm discards the input norm information in forward pass and a static scaling factor γ may be insufficient to accommodate the wide variability of input data and distributional shifts, thereby limiting further performance improvements, particularly in zero-shot scenarios that large language models routinely encounter. To address this limitation, we propose SeeDNorm, which enhances the representational capability of the model by dynamically adjusting the scaling coefficient based on the current input, thereby preserving the input norm information and enabling data-dependent, self-rescaled dynamic normalization. During backpropagation, SeeDNorm retains the ability of RMSNorm to dynamically adjust gradient according to the input norm. We provide a detailed analysis of the training optimization for SeedNorm and proposed corresponding solutions to address potential instability issues that may arise when applying SeeDNorm. We validate the effectiveness of SeeDNorm across models of varying sizes in large language model pre-training as well as supervised and unsupervised computer vision tasks. By introducing a minimal number of parameters and with neglligible impact on model efficiency, SeeDNorm achieves consistently superior performance compared to previously commonly used normalization layers such as RMSNorm and LayerNorm, as well as element-wise activation alternatives to normalization layers like DyT.

During lung radiotherapy, the position of infrared reflective objects on the chest can be recorded to estimate the tumor location. However, radiotherapy systems have a latency inherent to robot control limitations that impedes the radiation delivery precision. Prediction with online learning of recurrent neural networks (RNN) allows for adaptation to non-stationary respiratory signals, but classical methods such as RTRL and truncated BPTT are respectively slow and biased. This study investigates the capabilities of unbiased online recurrent optimization (UORO) to forecast respiratory motion and enhance safety in lung radiotherapy. We used 9 observation records of the 3D position of 3 external markers on the chest and abdomen of healthy individuals breathing during intervals from 73s to 222s. The sampling frequency was 10Hz, and the amplitudes of the recorded trajectories range from 6mm to 40mm in the superior-inferior direction. We forecast the 3D location of each marker simultaneously with a horizon value between 0.1s and 2.0s, using an RNN trained with UORO. We compare its performance with an RNN trained with RTRL, LMS, and offline linear regression. We provide closed-form expressions for quantities involved in the loss gradient calculation in UORO, thereby making its implementation efficient. Training and cross-validation were performed during the first minute of each sequence. On average over the horizon values considered and the 9 sequences, UORO achieves the lowest root-mean-square (RMS) error and maximum error among the compared algorithms. These errors are respectively equal to 1.3mm and 8.8mm, and the prediction time per time step was lower than 2.8ms (Dell Intel core i9-9900K 3.60 GHz). Linear regression has the lowest RMS error for the horizon values 0.1s and 0.2s, followed by LMS for horizon values between 0.3s and 0.5s, and UORO for horizon values greater than 0.6s.

Conformal prediction (CP) provides distribution-free prediction intervals for fixed forecasters, but its standard calibration procedure is often inefficient for time series data, where forecast errors are temporally dependent and change across time and operating conditions. Recent time series CP methods improve local calibration using recent, weighted, or localized residuals. Yet local calibration can remain indirect, since broad residual weighting or additional adaptation procedures may dilute the evidence most relevant to the current prediction. This motivates a simple retrieval and correction strategy that selects similar past residuals as local evidence and then corrects the coverage error left by retrieval. In this paper, we propose Retrieval--Corrected Conformal Prediction (RCCP), a retrieval-augmented calibration method for time series prediction intervals. RCCP builds an asymmetric interval from retrieved one-sided residuals and calibrates its normalized retrieval error with a scalar conformal correction. Thus, retrieval provides local residual evidence, while conformal correction determines the final scale needed for coverage. We provide a coverage-gap bound based on the stability of the normalized retrieval error distribution. Across standard benchmarks and backbone forecasters, RCCP attains the target coverage in every setting and achieves the lowest Winkler scores, with fewer severe misses. RCCP also achieves low calibration and inference overhead, showing that retrieval-corrected calibration is an effective and scalable approach to uncertainty quantification in time series forecasting. Code is available at https://github.com/jinsaaang/rccp.

Air pollution constitutes a global problem of paramount importance that affects not only human health, but also the environment. The existence of spatial and temporal data regarding the concentrations of pollutants is crucial for performing air pollution studies and monitor emissions. However, although observation data presents great temporal coverage, the number of stations is very limited and they are usually built in more populated areas. The main objective of this work is to create models capable of inferring pollutant concentrations in locations where no observation data exists. A machine learning model, more specifically the random forest model, was developed for predicting concentrations in the Iberian Peninsula in 2019 for five selected pollutants: NO_2, O_3 SO_2, PM10, and PM2.5. Model features include satellite measurements, meteorological variables, land use classification, temporal variables (month, day of year), and spatial variables (latitude, longitude, altitude). The models were evaluated using various methods, including station 10-fold cross-validation, in which in each fold observations from 10\% of the stations are used as testing data and the rest as training data. The R^2, RMSE and mean bias were determined for each model. The NO_2 and O_3 models presented good values of R^2, 0.5524 and 0.7462, respectively. However, the SO_2, PM10, and PM2.5 models performed very poorly in this regard, with R^2 values of -0.0231, 0.3722, and 0.3303, respectively. All models slightly overestimated the ground concentrations, except the O_3 model. All models presented acceptable cross-validation RMSE, except the O_3 and PM10 models where the mean value was a little higher (12.5934 mu g/m^3 and 10.4737 mu g/m^3, respectively).

QMSum provides no scorer, making query-focused meeting summarization results difficult to compare. We rescore or generate 15 systems under one implementation. Through a common inference port, a released 406M Fusion-in-Decoder specialist loses 6.30 ROUGE-1 when moved from capped long input to 2,000-word retrieved spans. Fine-tuning it on this span regime recovers the loss. On test it scores 36.33 ROUGE-1 versus 35.41 for our 1.2B system; the meeting-cluster 95% interval for the difference is [-0.27, +2.22], so QMSum does not statistically separate them. The smaller system uses about one-third as many total parameters and less than half the peak inference memory. Within the fixed 1.2B base, span-regime fine-tuning adds 5.29 [+4.02, +6.56], while replacing the first 4,500 transcript words with 2,000 retrieved words adds 1.55 on test and 0.29 on validation. Separately, under one concise prompt and reference-overlap scorer, a released 406M specialist exceeds five proprietary hosted models by at least 6.2 ROUGE-1, but output length and absent human or factuality evaluation limit this ordering. Conclusions are limited to QMSum and automatic metrics.

Cross-machine deployment of industrial world models requires transfer across changes in dynamics, sensing interfaces, sampling regimes, and control units. We study a schema-adaptive action-conditioned Joint-Embedding Predictive Architecture (SAAC-JEPA) for CNC dynamics, where the source machine has 17 canonical sensor channels and the target shares only 10. Evaluation uses group-disjoint source splits, source-only normalization, held-out self-supervised validation, unit audits, and a sealed target test after model locking. Across five seeds, JEPA pretraining gives no clean-source forecasting gain: scratch and pretrained-body models obtain \(RMSE=0.811\pm0.022\) and \(0.813\pm0.022\). A source-only search over 20 candidates selects a schema-consistent action-conditioned JEPA after seven-seed stability checks. On the confirmatory target pass, the locked model reaches zero-shot \(RMSE=0.546\), \(R^2=0.012\), and \(NLL=0.52\), outperforming persistence but not RevIN-equipped PatchTST and iTransformer baselines (\(0.503\) and \(0.498\)). A pre-declared paired ablation shows that RevIN in the same architecture improves RMSE to \(0.495\pm0.004\) over three seeds, but degrades target calibration (\(NLL=20.6\)) on stationary context windows. A pre-lock adaptation sweep further reduces RMSE to \(0.520\) with limited target support. These results show that source-domain forecasting accuracy alone is insufficient to assess industrial predictive representations, and that cross-machine adaptation under partial sensor overlap is a distinct evaluation axis.

The key of the out-of-distribution (OOD) generalization is to generalize invariance from training domains to target domains. The variance risk extrapolation (V-REx) is a practical OOD method, which depends on a domain-level regularization but lacks theoretical verifications about its motivation and utility. This article provides theoretical insights into V-REx by studying a variance-based regularizer. We propose Risk Variance Penalization (RVP), which slightly changes the regularization of V-REx but addresses the theory concerns about V-REx. We provide theoretical explanations and a theory-inspired tuning scheme for the regularization parameter of RVP. Our results point out that RVP discovers a robust predictor. Finally, we experimentally show that the proposed regularizer can find an invariant predictor under certain conditions.

Randomized smoothing (RS) is one of the prominent techniques to ensure the correctness of machine learning models, where point-wise robustness certificates can be derived analytically. While RS is well understood for classification, its application to generative models is unclear, since their outputs are sequences rather than labels. We resolve this by connecting generative outputs to an oracle classification task and showing that RS can still be enabled: the final response can be classified as a discrete action (e.g., service-robot commands in VLAs), as harmful vs. harmless (content moderation or toxicity detection in VLMs), or even applying oracles to cluster answers into semantically equivalent ones. Provided that the error rate for the oracle classifier comparison is bounded, we develop the theory that associates the number of samples with the corresponding robustness radius. We further derive improved scaling laws analytically relating the certified radius and accuracy to the number of samples, showing that the earlier result of 2 to 3 orders of magnitude fewer samples sufficing with minimal loss remains valid even under weaker assumptions. Together, these advances make robustness certification both well-defined and computationally feasible for state-of-the-art VLMs, as validated against recent jailbreak-style adversarial attacks.

We introduce a comprehensive framework for modeling single cell transcriptomic responses to perturbations, aimed at standardizing benchmarking in this rapidly evolving field. Our approach includes a modular and user-friendly model development and evaluation platform, a collection of diverse perturbational datasets, and a set of metrics designed to fairly compare models and dissect their performance. Through extensive evaluation of both published and baseline models across diverse datasets, we highlight the limitations of widely used models, such as mode collapse. We also demonstrate the importance of rank metrics which complement traditional model fit measures, such as RMSE, for validating model effectiveness. Notably, our results show that while no single model architecture clearly outperforms others, simpler architectures are generally competitive and scale well with larger datasets. Overall, this benchmarking exercise sets new standards for model evaluation, supports robust model development, and furthers the use of these models to simulate genetic and chemical screens for therapeutic discovery.

Machine-learning-based parameterizations (i.e. representation of sub-grid processes) of global climate models or turbulent simulations have recently been proposed as a powerful alternative to physical, but empirical, representations, offering a lower computational cost and higher accuracy. Yet, those approaches still suffer from a lack of generalization and extrapolation beyond the training data, which is however critical to projecting climate change or unobserved regimes of turbulence. Here we show that a multi-fidelity approach, which integrates datasets of different accuracy and abundance, can provide the best of both worlds: the capacity to extrapolate leveraging the physically-based parameterization and a higher accuracy using the machine-learning-based parameterizations. In an application to climate modeling, the multi-fidelity framework yields more accurate climate projections without requiring major increase in computational resources. Our multi-fidelity randomized prior networks (MF-RPNs) combine physical parameterization data as low-fidelity and storm-resolving historical run's data as high-fidelity. To extrapolate beyond the training data, the MF-RPNs are tested on high-fidelity warming scenarios, +4K, data. We show the MF-RPN's capacity to return much more skillful predictions compared to either low- or high-fidelity (historical data) simulations trained only on one regime while providing trustworthy uncertainty quantification across a wide range of scenarios. Our approach paves the way for the use of machine-learning based methods that can optimally leverage historical observations or high-fidelity simulations and extrapolate to unseen regimes such as climate change.

Recent work has highlighted the complex influence training hyperparameters, e.g., the number of training epochs, can have on the prunability of machine learning models. Perhaps surprisingly, a systematic approach to predict precisely how adjusting a specific hyperparameter will affect prunability remains elusive. To address this gap, we introduce a phenomenological model grounded in the statistical mechanics of learning. Our approach uses temperature-like and load-like parameters to model the impact of neural network (NN) training hyperparameters on pruning performance. A key empirical result we identify is a sharp transition phenomenon: depending on the value of a load-like parameter in the pruned model, increasing the value of a temperature-like parameter in the pre-pruned model may either enhance or impair subsequent pruning performance. Based on this transition, we build a three-regime model by taxonomizing the global structure of the pruned NN loss landscape. Our model reveals that the dichotomous effect of high temperature is associated with transitions between distinct types of global structures in the post-pruned model. Based on our results, we present three case-studies: 1) determining whether to increase or decrease a hyperparameter for improved pruning; 2) selecting the best model to prune from a family of models; and 3) tuning the hyperparameter of the Sharpness Aware Minimization method for better pruning performance.

We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular Hansen (1982) (offline) GMM, and offers fast and scalable implementation with the ability to handle streaming datasets in real time. We establish the almost sure convergence, and the (functional) central limit theorem for the inefficient online 2SLS and the efficient SGMM. Moreover, we propose online versions of the Durbin-Wu-Hausman and Sargan-Hansen tests that can be seamlessly integrated within the SGMM framework. Extensive Monte Carlo simulations show that as the sample size increases, the SGMM matches the standard (offline) GMM in terms of estimation accuracy and gains over computational efficiency, indicating its practical value for both large-scale and online datasets. We demonstrate the efficacy of our approach by a proof of concept using two well known empirical examples with large sample sizes.

Selective state space models (SSMs), such as Mamba, achieve strong per-token expressivity by making the time discretization step TildeΔ a learned function of the input. However, in doing so, TildeΔ no longer equals the physical time gap Δ between consecutive observations, limiting the ability of these models to handle irregular time series. Continuous time SSMs, such as S5, keep TildeΔequivΔ and therefore handle irregular timestamps natively, but their dynamics remain linear time invariant (LTI), limiting per token expressivity. We propose TIDES, a selective SSM variant that reconciles selective and continuous architectures by moving input dependence off the step size and onto the diagonal state matrix. As a result, TildeΔequivΔ as in S5, allowing the model to handle irregular timestamps natively without sacrificing the per-token expressivity that makes selective SSMs effective. We show this on a novel Fading Flash experimental benchmark, a compact controlled diagnostic for sequence models that jointly tests input dependence and extrapolation to out-of-distribution Δ values, and isolates the distinct failure modes of current state-of-the-art architectures that TIDES avoids by construction. On large-scale benchmarks, TIDES sets the new best average rank on UEA time series classification and the Physiome ODE regression benchmark, and matches or exceeds the reference baseline model on 6 of 8 natively irregular datasets from astronomy, agriculture, neuromorphic sensing, and climate events. Code available at: https://github.com/TaylanSoydan/TIDES.

In lung radiotherapy, infrared cameras can track reflective objects on the chest to estimate tumor motion due to breathing, but treatment system latencies hinder radiation beam precision. Real-time recurrent learning (RTRL) is a potential solution that can learn patterns within non-stationary respiratory data but has high complexity. This study assesses the capabilities of resource-efficient online RNN algorithms, namely unbiased online recurrent optimization (UORO), sparse-1 step approximation (SnAp-1), and decoupled neural interfaces (DNI) to forecast respiratory motion during radiotherapy treatment accurately. We use time series containing the 3D positions of external markers on the chest of healthy subjects. We propose efficient implementations for SnAp-1 and DNI that compress the influence and immediate Jacobian matrices and accurately update the linear coefficients used in credit assignment estimation, respectively. Data was originally sampled at 10Hz; we resampled it at 3.33Hz and 30Hz to analyze the effect of the sampling rate on performance. We use UORO, SnAp-1, and DNI to forecast each marker's 3D position with horizons h<=2.1s (the time interval in advance for which the prediction is made) and compare them with RTRL, least mean squares, kernel support vector regression, and linear regression. RNNs trained online achieved similar or better accuracy than most previous works using larger training databases and deep learning, even though we used only the first minute of each sequence to predict motion within that exact sequence. SnAp-1 had the lowest normalized root mean square errors (nRMSEs) averaged over the horizon values considered, equal to 0.335 and 0.157, at 3.33Hz and 10.0Hz, respectively. Similarly, UORO had the lowest nRMSE at 30Hz, equal to 0.086. DNI's inference time (6.8ms per time step at 30Hz, Intel Core i7-13700 CPU) was the lowest among the RNN methods.

We introduce rd-spiral, an open-source Python library for simulating 2D reaction-diffusion systems using pseudo-spectral methods. The framework combines FFT-based spatial discretization with adaptive Dormand-Prince time integration, achieving exponential convergence while maintaining pedagogical clarity. We analyze three dynamical regimes: stable spirals, spatiotemporal chaos, and pattern decay, revealing extreme non-Gaussian statistics (kurtosis >96) in stable states. Information-theoretic metrics show 10.7% reduction in activator-inhibitor coupling during turbulence versus 6.5% in stable regimes. The solver handles stiffness ratios >6:1 with features including automated equilibrium classification and checkpointing. Effect sizes (delta=0.37--0.78) distinguish regimes, with asymmetric field sensitivities to perturbations. By balancing computational rigor with educational transparency, rd-spiral bridges theoretical and practical nonlinear dynamics.

We address the challenge of adapting pre-trained Large Language Models (LLMs) for multivariate time-series analysis, where their deployment is often hindered by prohibitive computational and memory demands. Our solution, One-for-All, introduces Gaussian Rank-Stabilized Low-Rank Adapters (rsLoRA) to enable parameter-efficient fine-tuning of frozen LLMs. While inspired by LoRA, rsLoRA introduces a mathematically grounded rank-stabilization mechanism that enables provable gradient stability at low ranks a novel contribution absent in prior PEFT methods. Our framework injects trainable rank decomposition matrices (rank 16) into positional embeddings and output layers, while keeping self-attention weights fixed. This design reduces trainable parameters by 6.8times (vs. TimesNet), 21times (vs. GPT4TS), and 11.8times (vs. TIME-LLM), while achieving a 168-1,776times smaller memory footprint (2.2MiB vs. 340MiB-4.18GiB in SOTA models). Rigorous evaluation across six time-series tasks demonstrates that One-for-All achieves state-of-the-art efficiency-accuracy trade-offs: 5.5times higher parameter efficiency (MSE=5.50) than TimesNet and 21times better than GPT4TS, while matching their forecasting accuracy (MSE=0.33). The framework's stability is validated through consistent performance across diverse horizons (96-720 steps) and datasets (ETT, Weather, M3, M4), with 98.3% fewer parameters than conventional transformers. These advances enable deployment on edge devices for healthcare, finance, and environmental monitoring without compromising performance.

The development of 0.1^{circ} global weather forecasting models based on machine learning (ML) is constrained by the limited availability of high-resolution data, as decades of reanalysis are only available at 0.25^{circ} resolution. While existing approaches fine-tune 0.25^{circ} forecast models on limited 0.1^{circ} samples, we show that this transfer is hindered by the irreversible information loss inherent in coarse-resolution forecasting. Therefore, we propose BaguanHR, a framework that shifts the focus from transferring models to transferring data. We first show that super-resolution (SR) has lower conditional entropy and input amplification than forecasting, making it a more robust vehicle for resolution transfer. By leveraging this advantage through variable-wise SR, we synthesize extensive 0.1^{circ} data from ERA5. BaguanHR's performance on the synthetic-plus-real dataset exceeds both ML-based methods and IFS-HRES, achieving superior performance across over 85% of the lead times within 72 hours. Furthermore, our findings highlight a power-law scaling effect, as a twofold increase in data reduces RMSE by 4.6% for 72-hour forecasting and 4.9% for 120-hour forecasting. Our results demonstrate that scaling high resolution ML-based forecasting is primarily a data bottleneck, and that variable-wise super-resolution provides a simple yet general solution to unlock long coarse-resolution reanalyses for high-resolution training.

Accurate, high-resolution vertical profiles of optical turbulence (C_n^2), which reflect local meteorology and topography, are crucial for ground-based optical astronomy and free-space optical communication. However, measuring these profiles or generating them with numerical weather models requires substantial operational or computational effort. In this work, we present OTProf, a deep-learning method that estimates high-resolution C_n^2 profiles from widely available coarse-resolution ERA5 reanalysis data. OTProf is based on the Squeezeformer architecture, modified for super-resolution by introducing grid-agnostic interpolation in the latent space. We train and evaluate OTProf in the Netherlands using high-resolution C_n^2 data obtained from the Weather Research and Forecasting (WRF) model. The commonly used Hufnagel-Valley model serves as the baseline. Overall, OTProf reproduces the vertical structure of WRF-based C_n^2 more accurately than Hufnagel-Valley and yields more accurate estimates of the Fried parameter r_0 and the scintillation index σ_I^2. Out-of-domain performance is assessed using a smaller WRF-based C_n^2 dataset covering the Canary Islands. Initial results indicate a performance drop because the orography differs markedly from the training domain. We show that output bias correction based on a few local simulations can help OTProf to adapt, but more work for domain adaptation is needed. OTProf is therefore primarily recommended for in-domain applications, e.g., generating C_n^2 climatologies from long ERA5 records.

We study how to predict the downstream closed-loop performance of a learned latent world model from validation-time diagnostics alone. Choosing the right checkpoint from a world-model training run is difficult: validation loss and multi-step prediction RMSE keep improving long after closed-loop performance has collapsed. We present a suite of structural validation-time diagnostics drawn from optimal-control theory and apply them to Gymnasium's LunarLander v3, which features shaped rewards. We train an RSSM [5, 4] world model on it and treat per checkpoint CEM-MPC return as the oracle for closed-loop quality. By evaluating 40 metrics against this oracle, we find that the strongest single predictor is the Reward Observability Fraction (ROF), which measures the reward predictor's dependence on the observable subspace. We combine ROF with three structural regularizers into a single-number offline checkpoint selection score, the Composite Reward Observability Fraction (CROF). The CROF-selected world model trains a model-based A2C policy that beats a fairly evaluated model-free A2C baseline by ~24.5 return points while using ~65x fewer real-environment interactions, and the same world model also drives a strong zero-shot CEM-MPC policy. Code and data: https://github.com/nsmoly/LunarLander_RSSM.

Motivated by recent advances in operational weather forecasting, we study the efficacy of low-precision arithmetic for climate simulations. We develop a framework to measure rounding error in a climate model which provides a stress-test for a low-precision version of the model, and we apply our method to a variety of models including the Lorenz system; a shallow water approximation for flow over a ridge; and a coarse resolution global atmospheric model with simplified parameterisations (SPEEDY). Although double precision (52 significant bits) is standard across operational climate models, in our experiments we find that single precision (23 sbits) is more than enough and that as low as half precision (10 sbits) is often sufficient. For example, SPEEDY can be run with 12 sbits across the entire code with negligible rounding error and this can be lowered to 10 sbits if very minor errors are accepted, amounting to less than 0.1 mm/6hr for the average grid-point precipitation, for example. Our test is based on the Wasserstein metric and this provides stringent non-parametric bounds on rounding error accounting for annual means as well as extreme weather events. In addition, by testing models using both round-to-nearest (RN) and stochastic rounding (SR) we find that SR can mitigate rounding error across a range of applications. Thus our results also provide evidence that SR could be relevant to next-generation climate models. While many studies have shown that low-precision arithmetic can be suitable on short-term weather forecasting timescales, our results give the first evidence that a similar low precision level can be suitable for climate.

In the era of mega-constellations, the need for accurate and publicly available information has become fundamental for satellite operators to guarantee the safety of spacecrafts and the Low Earth Orbit (LEO) space environment. This study critically evaluates the accuracy and reliability of publicly available ephemeris data for a LEO mega-constellation - Starlink. The goal of this work is twofold: (i) compare and analyze the quality of the data against high-precision numerical propagation. (ii) Leverage Physics-Informed Machine Learning to extract relevant satellite quantities, such as non-conservative forces, during the decay process. By analyzing two months of real orbital data for approximately 1500 Starlink satellites, we identify discrepancies between high precision numerical algorithms and the published ephemerides, recognizing the use of simplified dynamics at fixed thresholds, planned maneuvers, and limitations in uncertainty propagations. Furthermore, we compare data obtained from multiple sources to track and analyze deorbiting satellites over the same period. Empirically, we extract the acceleration profile of satellites during deorbiting and provide insights relating to the effects of non-conservative forces during reentry. For non-deorbiting satellites, the position Root Mean Square Error (RMSE) was approximately 300 m, while for deorbiting satellites it increased to about 600 m. Through this in-depth analysis, we highlight potential limitations in publicly available data for accurate and robust Space Situational Awareness (SSA), and importantly, we propose a data-driven model of satellite decay in mega-constellations.

This paper provides the first tight convergence analyses for RMSProp and Adam in non-convex optimization under the most relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. We first analyze RMSProp, which is a special case of Adam with adaptive learning rates but without first-order momentum. Specifically, to solve the challenges due to dependence among adaptive update, unbounded gradient estimate and Lipschitz constant, we demonstrate that the first-order term in the descent lemma converges and its denominator is upper bounded by a function of gradient norm. Based on this result, we show that RMSProp with proper hyperparameters converges to an epsilon-stationary point with an iteration complexity of mathcal O(epsilon^{-4}). We then generalize our analysis to Adam, where the additional challenge is due to a mismatch between the gradient and first-order momentum. We develop a new upper bound on the first-order term in the descent lemma, which is also a function of the gradient norm. We show that Adam with proper hyperparameters converges to an epsilon-stationary point with an iteration complexity of mathcal O(epsilon^{-4}). Our complexity results for both RMSProp and Adam match with the complexity lower bound established in arjevani2023lower.

This study presents the application of generative deep learning techniques to evaluate marine fog visibility nowcasting using the FATIMA (Fog and turbulence interactions in the marine atmosphere) campaign observations collected during July 2022 in the North Atlantic in the Grand Banks area and vicinity of Sable Island (SI), northeast of Canada. The measurements were collected using the Vaisala Forward Scatter Sensor model FD70 and Weather Transmitter model WXT50, and Gill R3A ultrasonic anemometer mounted on the Research Vessel Atlantic Condor. To perform nowcasting, the time series of fog visibility (Vis), wind speed, dew point depression, and relative humidity with respect to water were preprocessed to have lagged time step features. Generative nowcasting of Vis time series for lead times of 30 and 60 minutes were performed using conditional generative adversarial networks (cGAN) regression at visibility thresholds of Vis < 1 km and < 10 km. Extreme gradient boosting (XGBoost) was used as a baseline method for comparison against cGAN. At the 30 min lead time, Vis was best predicted with cGAN at Vis < 1 km (RMSE = 0.151 km) and with XGBoost at Vis < 10 km (RMSE = 2.821 km). At the 60 min lead time, Vis was best predicted with XGBoost at Vis < 1 km (RMSE = 0.167 km) and Vis < 10 km (RMSE = 3.508 km), but the cGAN RMSE was similar to XGBoost. Despite nowcasting Vis at 30 min being quite difficult, the ability of the cGAN model to track the variation in Vis at 1 km suggests that there is potential for generative analysis of marine fog visibility using observational meteorological parameters.

Constant-step stochastic approximation generally has a nonzero stationary mean error that persists under time averaging. This paper studies that error for nonlinear two-timescale recursions driven by an exogenous finite-state Markov chain. Under stated smoothness assumptions and conditions on the stationary distribution, we derive a first-order bias expansion whose error bound remains uniform as the slow step size becomes much smaller than the fast step size. Fast-manifold coordinates keep the associated covariance equation regular in this limit. For fast step η and slow step varepsilon, the expansion reveals a mixed contribution varepsilon^2/η alongside terms linear in each step size. This dependence matters for bias reduction: along power-law step-size paths, the bias exponents need not be integers, so Richardson--Romberg extrapolation requires weights matched to the path. An exactly solvable nonlinear Markov example verifies the coefficients. We verify localization for temporal-difference learning and compare finite-run extrapolation at equal update budgets. For finite runs, we bound the initialization error of tail averages on both timescales under an additional coupling assumption. In the special case of additive independent noise, signed third-moment cancellation yields a sharper remainder.

Long-term time-series forecasting needs models that are accurate yet efficient enough for commodity hardware. Lightweight linear forecasters are remarkably strong in this regime, yet they leave two openings: reversible instance normalization (RevIN) de-normalizes the entire horizon with a single lookback statistic, which is inaccurate under non-stationarity, and time-domain trend/seasonal decomposition relies on a fixed, non-adaptive filter. We present FreqLite, an ultra-lightweight, channel-independent frequency-decomposed linear forecaster: a learnable, lossless, partition-of-unity spectral filter splits the input into bands that are forecast by per-band linear heads and, unlike low-pass-truncation approaches, the high-frequency band is retained and modeled. FreqLite is the best lightweight model on the standard long-term forecasting benchmarks and, at long lookback (L=336), attains a lower average error than a PatchTST Transformer (0.3244 vs. 0.3587 MSE) while using 4x fewer parameters, 2.2x less memory, and 2.2x less time per epoch on a single 4 GB laptop GPU; although modest in magnitude, its improvements are statistically significant under paired Wilcoxon tests across all matched cells (p < 1e-5). We further introduce Adaptive Reversible Instance Normalization (A-RevIN), a regime-adaptive reversible normalization that strictly generalizes RevIN (recovered exactly when its gate is closed), engages under non-stationarity, and reduces to RevIN without harm on stationary data. We validate this on both a real strongly non-stationary dataset (ILI, up to ~5% MSE reduction) and a controlled synthetic drift sweep in which A-RevIN's benefit and its learned gate both rise monotonically with injected non-stationarity. Every component is independently ablatable (Linear and RLinear are special cases of FreqLite), and all results are reproducible on commodity hardware.

Approximating Stochastic Gradient Descent (SGD) as a Stochastic Differential Equation (SDE) has allowed researchers to enjoy the benefits of studying a continuous optimization trajectory while carefully preserving the stochasticity of SGD. Analogous study of adaptive gradient methods, such as RMSprop and Adam, has been challenging because there were no rigorously proven SDE approximations for these methods. This paper derives the SDE approximations for RMSprop and Adam, giving theoretical guarantees of their correctness as well as experimental validation of their applicability to common large-scaling vision and language settings. A key practical result is the derivation of a square root scaling rule to adjust the optimization hyperparameters of RMSprop and Adam when changing batch size, and its empirical validation in deep learning settings.

Multi-hop retrieval failures are not uniformly distributed across queries: they cluster in structurally predictable subpopulations. We prove two results formalizing this structure. First (CWAR Reducibility): confident-failure reduction is achievable if and only if retrieval features carry mutual information about success, a condition satisfied by LLM-judge pipelines but substantially weaker in dense-only settings, explaining the AUC-AC gap between regimes. Second (Feature Regime Complementarity): no single ANN score feature achieves best predictive performance across all failure regimes; the dominant feature differs between datasets (query length on MuSiQue, hop-1 concentration on HoVer), and a constructive witness pair shows each is necessary in one regime and non-contributory in the other. We instantiate these principles in RegimeAbstain, which computes a Retrieval Confidence Score (RCS), a logistic function of up to nine query-ANN structural features, all available without any additional LLM call, and uses it to implement a calibrated abstention policy. We define the Confident-Wrong-Answer Rate (CWAR) metric and evaluate across three multi-hop benchmarks (MuSiQue, 2WikiMultiHopQA, HoVer) and two retrieval architectures (LLM-judge and dense-only), covering five failure regimes with CWAR from 14.5% to 62.1%. RCS achieves best or co-best AUC-AC in all five conditions against eight confidence baselines. On MuSiQue (LLM-judge), RCS reduces CWAR from 39.5% to 20.6% at 50% coverage (47.8% relative reduction), with ECE=0.035. A model trained on MuSiQue transfers to 2WikiMultiHopQA with only -0.5pp AUC loss, confirming the domain-agnostic structure of regime features.

Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly. However, most existing studies remain in 2D, while 3D turbulence has fundamentally different physics and is far more costly to simulate. Existing 3D resources also typically provide only one realization per configuration, making it difficult to distinguish learning the dynamics from fitting the statistics of a single flow. In this paper, we introduce TIDE (Turbulent Incompressible DNS Ensembles), a 256^3 DNS corpus and benchmark for 3D incompressible turbulence, with 15 configurations on eight controlled axes, independent ensembles, pressure fields, and equation-level verification. The benchmark includes five tasks, standardized learned baselines, controlled generalization splits, and physical-fidelity metrics alongside pointwise error. Across the main forecasting configurations, current learned models barely outperform persistence and still make about twice the error of a spectral solver given the true equations. Moreover, lower pointwise error can coincide with severely distorted small-scale dynamics, showing that accuracy alone does not ensure physical fidelity. Generalization results further show that most regime shifts reflect limited training coverage, whereas forced-to-decay transfer exposes a missing conditioning variable: operators trained under forcing continue to predict driven evolution when the external drive is removed. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE.

We study estimation and clustering in Gaussian mixture models under variance misspecification. Observations are generated with true variance σ^2, while the component means are estimated using a likelihood with variance τ^2, yielding a family of mismatched likelihood functions parameterized by the ratio ρ=τ/σ. We show that the interplay between ρ and the signal-to-noise ratio (SNR) induces a sharp phase diagram. Under correct specification (ρ=1), maximum likelihood recovers the true means, independently of the SNR. However, once the model is misspecified, two different regimes emerge. Under under-smoothing (ρ<1), the estimated Gaussian means are displaced from the truth, and in low SNR this discrepancy grows as the SNR decreases: for every fixed ρ<1, the squared error scales as SNR^{-1}. Under over-smoothing (ρ>1), the fitted likelihood blurs the cluster separation, causing distinct component means to collapse towards the overall mixture center once ρ^2 exceeds a threshold of the form 1 + λ,SNR, where λ depends on the geometry of the true means. We further show that the hard assignment objective arises as the limit τto 0 of the same mismatched likelihood family, and derive corresponding low- and high-SNR results for hard-assignment mean estimation and latent-label recovery. Furthermore, in low SNR, Bayes-optimal clustering is close to random guessing, and the hard-assignment target remains far from the true means. These results show that in low-SNR applications, even mild variance misspecification or hard-assignment procedures can induce substantial bias, whereas in high SNR these effects are largely absent.

Large language models (LLMs) are increasingly deployed in high-stakes domains, where rare but severe failures can result in irreversible harm. However, prevailing evaluation benchmarks often reduce complex social risk to mean-centered scalar scores, thereby obscuring distributional structure, cross-dimensional interactions, and worst-case behavior. This paper introduces Social Harm Analysis via Risk Profiles (SHARP), a framework for multidimensional, distribution-aware evaluation of social harm. SHARP models harm as a multivariate random variable and integrates explicit decomposition into bias, fairness, ethics, and epistemic reliability with a union-of-failures aggregation reparameterized as additive cumulative log-risk. The framework further employs risk-sensitive distributional statistics, with Conditional Value at Risk (CVaR95) as a primary metric, to characterize worst-case model behavior. Application of SHARP to eleven frontier LLMs, evaluated on a fixed corpus of n=901 socially sensitive prompts, reveals that models with similar average risk can exhibit more than twofold differences in tail exposure and volatility. Across models, dimension-wise marginal tail behavior varies systematically across harm dimensions, with bias exhibiting the strongest tail severities, epistemic and fairness risks occupying intermediate regimes, and ethical misalignment consistently lower; together, these patterns reveal heterogeneous, model-dependent failure structures that scalar benchmarks conflate. These findings indicate that responsible evaluation and governance of LLMs require moving beyond scalar averages toward multidimensional, tail-sensitive risk profiling.

Classical estimators for ARIMA parameters (MLE, CSS, OLS) assume Gaussian innovations, an assumption frequently violated in financial and economic data exhibiting asymmetric distributions with heavy tails. We develop and validate the second-order polynomial maximization method (PMM2) for estimating ARIMA(p,d,q) models with non-Gaussian innovations. PMM2 is a semiparametric technique that exploits higher-order moments and cumulants without requiring full distributional specification. Monte Carlo experiments (128,000 simulations) across sample sizes N in {100, 200, 500, 1000} and four innovation distributions demonstrate that PMM2 substantially outperforms classical methods for asymmetric innovations. For ARIMA(1,1,0) with N=500, relative efficiency reaches 1.58--1.90 for Gamma, lognormal, and χ^2(3) innovations (37--47\% variance reduction). Under Gaussian innovations PMM2 matches OLS efficiency, avoiding the precision loss typical of robust estimators. The method delivers major gains for moderate asymmetry (|γ_3| geq 0.5) and N geq 200, with computational costs comparable to MLE. PMM2 provides an effective alternative for time series with asymmetric innovations typical of financial markets, macroeconomic indicators, and industrial measurements. Future extensions include seasonal SARIMA models, GARCH integration, and automatic order selection.

We study the parameter placement problem: given a fixed budget of k trainable entries within the B matrix of a LoRA adapter (A frozen), does the choice of which k matter? Under supervised fine-tuning, random and informed subsets achieve comparable performance. Under GRPO on base models, random placement fails to improve over the base model, while gradient-informed placement recovers standard LoRA accuracy. This regime dependence traces to gradient structure: SFT gradients are low-rank and directionally stable, so any subset accumulates coherent updates; GRPO gradients are high-rank and near-orthogonal across steps, so only elements with consistently signed gradients retain the learning signal. Our scoring procedure identifies these critical parameters in under 10 seconds at less than 0.5% of training cost. Selected parameters concentrate on residual-stream-writing projections (V, O, Down), stable across model families and scales (1.5B - 8B).

Large-scale traffic forecasting relies on fixed sensor networks that often exhibit blackouts: contiguous intervals of missing measurements caused by detector or communication failures. These outages are typically handled under a Missing At Random (MAR) assumption, even though blackout events may correlate with unobserved traffic conditions (e.g., congestion or anomalous flow), motivating a Missing Not At Random (MNAR) treatment. We propose a latent state-space framework that jointly models (i) traffic dynamics via a linear dynamical system and (ii) sensor dropout via a Bernoulli observation channel whose probability depends on the latent traffic state. Inference uses an Extended Kalman Filter with Rauch-Tung-Striebel smoothing, and parameters are learned via an approximate EM procedure with a dedicated update for detector-specific missingness parameters. On the Seattle inductive loop detector data, introducing latent dynamics yields large gains over naive baselines, reducing blackout imputation RMSE from 7.02 (LOCF) and 5.02 (linear interpolation + seasonal naive) to 4.23 (MAR LDS), corresponding to about a 64% reduction in MSE relative to LOCF. Explicit MNAR modeling provides a consistent but smaller additional improvement on real data (imputation RMSE 4.20; 0.8% RMSE reduction relative to MAR), with similar modest gains for short-horizon post-blackout forecasts (evaluated at 1, 3, and 6 steps). In controlled synthetic experiments, the MNAR advantage increases as the true missingness dependence on latent state strengthens. Overall, temporal dynamics dominate performance, while MNAR modeling offers a principled refinement that becomes most valuable when missingness is genuinely informative.

The main objective of Prognostics and Health Management is to estimate the Remaining Useful Lifetime (RUL), namely, the time that a system or a piece of equipment is still in working order before starting to function incorrectly. In recent years, numerous machine learning algorithms have been proposed for RUL estimation, mainly focusing on providing more accurate RUL predictions. However, there are many sources of uncertainty in the problem, such as inherent randomness of systems failure, lack of knowledge regarding their future states, and inaccuracy of the underlying predictive models, making it infeasible to predict the RULs precisely. Hence, it is of utmost importance to quantify the uncertainty alongside the RUL predictions. In this work, we investigate the conformal prediction (CP) framework that represents uncertainty by predicting sets of possible values for the target variable (intervals in the case of RUL) instead of making point predictions. Under very mild technical assumptions, CP formally guarantees that the actual value (true RUL) is covered by the predicted set with a degree of certainty that can be prespecified. We study three CP algorithms to conformalize any single-point RUL predictor and turn it into a valid interval predictor. Finally, we conformalize two single-point RUL predictors, deep convolutional neural networks and gradient boosting, and illustrate their performance on the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) data sets.

Foundation models (FMs) for the Earth system learn statistical relationships between physical variables across massive datasets to enable versatile downstream applications through finetuning, separating them from task-specific weather models. Here, we introduce Earth System Foundation Model (ESFM), a fully open model building on the 3D Swin UNet backbone of the pioneering Aurora model. ESFM introduces extensions that increase functionality and foster adoption in climate sciences. First, the encoding scheme and training protocols have been extended to handle diverse datasets, including those containing missing values across all spatio-temporal dimensions such as satellite data, as well as station data, all under one backbone. Axial attention is introduced to capture inter-variable dependencies. As a result ESFM skillfully predicts variables in regions or on pressure levels where no data is present at the initial time, while preserving inter-variable relationships, for example between temperature, pressure, and humidity. Individual variable tokenization enables different sets of variables to be shuffled during training and simplifies the process of building extensions for new downstream tasks. Adaptive layer norm-based ensembles allow for a simple yet effective way to transform deterministic ESFM to a probabilistic FM. We present findings using dense gridded data (ERA5, CMIP6), regionally masked dense data, sparse gridded MODIS satellite data, and station data. Results demonstrate competitive or superior performance relative to state-of-the-art benchmarks. Case studies of Super Typhoon Doksuri (2023) and 2024 sudden stratospheric warming events show accurate positional and magnitude estimations of extreme weather. ESFM retains the strengths of previous foundation models, such as long-term stability, but facilitates application to a variety of downstream tasks.

Fine-tuning a pretrained LLM into a vision-language model (VLM) can erode the backbone's text capability, with the damage concentrated on tasks that require following exact output rules, such as instruction following, chain-of-thought reasoning graded on a strictly parsed final answer, and similar evaluations with strict graders. We trace this gap to attention-sink corruption: VL fine-tuning perturbs the early sink position that anchors a large fraction of attention probability, and how well the base LLM preserves its sink tracks how much of the affected capability survives adaptation. Building on this view, we introduce Sink Strength, a single scalar computed on the base LLM in a few seconds on a single GPU that predicts post-VL degradation without any VL training. It consistently tracks relative degradation across the six VLM-LLM pairs and multiple format-sensitive tasks. Complementing this diagnostic, we find that post-pretraining QK-RMSNorm injection fails to reproduce the protection of native QK-RMSNorm, while several off-the-shelf weight-merging settings fail to recover the lost capability after VL training. These negative results underscore the value of screening backbones with Sink Strength before VL training and narrow the intervention space toward head-selective training-time protection.

Most of the world's offshore wind resource lies in waters too deep for fixed-bottom foundations, making floating offshore wind turbines (FOWTs) essential for deep-water deployment. As the industry scales toward 22 MW class designs, tower fatigue becomes increasingly critical because larger structures amplify the coupled aero-hydro-servo-elastic loads induced by continuous wind and wave excitation. Accurate fatigue-damage prediction is therefore central to certification, design optimization, and cost reduction. Yet the field lacks a shared surrogate benchmark: studies report different simulations, splits, and metrics, making methods difficult to compare. We present FLOATBench, a public tabular benchmark with 582{,}120 per-section fatigue-damage labels across three 22 MW FOWT tower geometries, derived from 19{,}404 high-fidelity OpenFAST simulations across the three towers (6{,}468 per tower: 1{,}078 aligned wind/wave operating points times six turbulence seeds), labeled at 30 cross-sections per tower. FLOATBench includes a regime-aware alpha-shape partition of the joint wind/wave operating envelope, stratifying test points into in-train, interpolation, and extrapolation regimes. It is paired with a reproducible evaluation harness covering three protocol levels: random validation (E1), within-tower regime-aware evaluation (E2), and cross-tower transfer (E3). The regime-aware protocol reveals rank shifts between global and extrapolation performance that random-split leaderboards cannot detect. To the authors' knowledge, FLOATBench is the first FOWT fatigue benchmark for tabular surrogate modeling, and offers an evaluation protocol that generalizes to engineering surrogates defined over physical operating envelopes. Dataset and code available at: https://github.com/Joao97ribeiro/FLOATBench.

We introduce Leap+Verify, a framework that applies speculative execution -- predicting future model weights and validating predictions before acceptance -- to accelerate neural network training. Inspired by speculative decoding in language model inference and by the Automatically Scalable Computation (ASC) architecture for program execution, Leap+Verify decomposes training into three dynamically detected regimes (chaotic, transition, stable) using activation-space cosine similarity as a real-time Lyapunov proxy signal. Within each regime, analytic weight predictors (momentum, linear, quadratic extrapolation) attempt to forecast model parameters K training steps ahead; predictions are accepted only when validated against a held-out loss criterion. We evaluate Leap+Verify on GPT-2 124M and Qwen 2.5-1.5B trained on WikiText-103 across five random seeds, sweeping prediction depth K in {5, 10, 25, 50, 75, 100}. Momentum-based prediction (Adam moment extrapolation) fails catastrophically at both scales, with predicted losses exceeding actuals by 100-10,000x -- a universal norm explosion in optimizer-state extrapolation. Finite-difference predictors (linear, quadratic) succeed where momentum fails: at 124M, they achieve 24% strict acceptance at K=5 in stable regimes; at 1.5B, they achieve 37% strict acceptance in transition regimes. The scale-dependent finding is in regime distribution: GPT-2 124M spends 34% of training in stable regime, while Qwen 1.5B spends 64% in chaotic regime and reaches stable in only 0-2 of 40 checkpoints. Larger models are more predictable when predictable, but less often predictable -- the practical bottleneck shifts from predictor accuracy to regime availability. Cross-seed results are highly consistent (less than 1% validation loss variance), and the three-regime framework produces identical phase boundaries (plus or minus 50 steps) across seeds.

Large Language Models (LLMs) achieve competitive performance across diverse natural language processing (NLP) tasks, yet pretraining is computationally demanding, making optimizer efficiency an important practical consideration. Muon accelerates LLM pretraining via orthogonal momentum updates that serve as a matrix analogue of the element-wise sign operator. Motivated by the recent perspective that Adam is a variance-adaptive sign update algorithm, we propose two variants of Muon, Muon-NSR and Muon-VS, which apply variance-adaptive normalization to momentum before orthogonalization. Muon-NSR applies noise-to-signal ratio (NSR) modulation, while Muon-VS performs variance-based scaling without introducing additional hyperparameters. Experiments on GPT-2 and LLaMA pretraining demonstrate that our proposed methods accelerate convergence and consistently achieve lower validation loss than both competitive, well-tuned AdamW and Muon baselines. For example, on the LLaMA-1.2B model, Muon-NSR and Muon-VS reduce the iterations required to reach the target validation loss by 1.36times relative to the well-tuned Muon following the recent benchmark.

Constant-stepsize stochastic approximation (SA) is widely used in learning for computational efficiency. For a fixed stepsize, the iterates typically admit a stationary distribution that is rarely tractable. Prior work shows that as the stepsize αdownarrow 0, the centered-and-scaled steady state converges weakly to a Gaussian random vector. However, for fixed α, this weak convergence offers no usable error bound for approximating the steady-state by its Gaussian limit. This paper provides explicit, non-asymptotic error bounds for fixed α. We first prove general-purpose theorems that bound the Wasserstein distance between the centered-scaled steady state and an appropriate Gaussian distribution, under regularity conditions for drift and moment conditions for noise. To ensure broad applicability, we cover both i.i.d. and Markovian noise models. We then instantiate these theorems for three representative SA settings: (1) stochastic gradient descent (SGD) for smooth strongly convex objectives, (2) linear SA, and (3) contractive nonlinear SA. We obtain dimension- and stepsize-dependent, explicit bounds in Wasserstein distance of order α^{1/2}log(1/α) for small α. Building on the Wasserstein approximation error, we further derive non-uniform Berry--Esseen-type tail bounds that compare the steady-state tail probability to Gaussian tails. We achieve an explicit error term that decays in both the deviation level and stepsize α. We adapt the same analysis for SGD beyond strongly convexity and study general convex objectives. We identify a non-Gaussian (Gibbs) limiting law under the correct scaling, which is validated numerically, and provide a corresponding pre-limit Wasserstein error bound.

Global climate models (GCMs) are the main tools for understanding and predicting climate change. However, due to limited numerical resolutions, these models suffer from major structural uncertainties; e.g., they cannot resolve critical processes such as small-scale eddies in atmospheric and oceanic turbulence. Thus, such small-scale processes have to be represented as a function of the resolved scales via closures (parametrization). The accuracy of these closures is particularly important for capturing climate extremes. Traditionally, such closures are based on heuristics and simplifying assumptions about the unresolved physics. Recently, supervised-learned closures, trained offline on high-fidelity data, have been shown to outperform the classical physics-based closures. However, this approach requires a significant amount of high-fidelity training data and can also lead to instabilities. Reinforcement learning is emerging as a potent alternative for developing such closures as it requires only low-order statistics and leads to stable closures. In Scientific Multi-Agent Reinforcement Learning (SMARL) computational elements serve a dual role of discretization points and learning agents. We leverage SMARL and fundamentals of turbulence physics to learn closures for prototypes of atmospheric and oceanic turbulence. The policy is trained using only the enstrophy spectrum, which is nearly invariant and can be estimated from a few high-fidelity samples (these few samples are far from enough for supervised/offline learning). We show that these closures lead to stable low-resolution simulations that, at a fraction of the cost, can reproduce the high-fidelity simulations' statistics, including the tails of the probability density functions. The results demonstrate the high potential of SMARL for closure modeling for GCMs, especially in the regime of scarce data and indirect observations.

Recent advancements in artificial intelligence (AI) for numerical weather prediction (NWP) have significantly transformed atmospheric modeling. AI NWP models outperform traditional physics-based systems, such as the Integrated Forecast System (IFS), across several global metrics while requiring fewer computational resources. However, existing AI NWP models face limitations related to training datasets and timestep choices, often resulting in artifacts that reduce model performance. To address these challenges, we introduce the Community Research Earth Digital Intelligence Twin (CREDIT) framework, developed at NSF NCAR. CREDIT provides a flexible, scalable, and user-friendly platform for training and deploying AI-based atmospheric models on high-performance computing systems. It offers an end-to-end pipeline for data preprocessing, model training, and evaluation, democratizing access to advanced AI NWP capabilities. We demonstrate CREDIT's potential through WXFormer, a novel deterministic vision transformer designed to predict atmospheric states autoregressively, addressing common AI NWP issues like compounding error growth with techniques such as spectral normalization, padding, and multi-step training. Additionally, to illustrate CREDIT's flexibility and state-of-the-art model comparisons, we train the FUXI architecture within this framework. Our findings show that both FUXI and WXFormer, trained on six-hourly ERA5 hybrid sigma-pressure levels, generally outperform IFS HRES in 10-day forecasts, offering potential improvements in efficiency and forecast accuracy. CREDIT's modular design enables researchers to explore various models, datasets, and training configurations, fostering innovation within the scientific community.

As opaque predictive models increasingly impact many areas of modern life, interest in quantifying the importance of a given input variable for making a specific prediction has grown. Recently, there has been a proliferation of model-agnostic methods to measure variable importance (VI) that analyze the difference in predictive power between a full model trained on all variables and a reduced model that excludes the variable(s) of interest. A bottleneck common to these methods is the estimation of the reduced model for each variable (or subset of variables), which is an expensive process that often does not come with theoretical guarantees. In this work, we propose a fast and flexible method for approximating the reduced model with important inferential guarantees. We replace the need for fully retraining a wide neural network by a linearization initialized at the full model parameters. By adding a ridge-like penalty to make the problem convex, we prove that when the ridge penalty parameter is sufficiently large, our method estimates the variable importance measure with an error rate of O(1{n}) where n is the number of training samples. We also show that our estimator is asymptotically normal, enabling us to provide confidence bounds for the VI estimates. We demonstrate through simulations that our method is fast and accurate under several data-generating regimes, and we demonstrate its real-world applicability on a seasonal climate forecasting example.

Data assimilation (DA) estimates the state of an evolving dynamical system from noisy, partial observations, and is widely used in scientific simulation as well as weather and climate science. In practice, filtering methods rely on frame-to-frame transition models. However, these models are fragile when observations are non-Markovian (when they form only a partial slice of a higher-dimensional latent state as in real-world weather data): they tend to accumulate errors over long horizons. At the same time, learned DA methods typically commit to a single regime, either filtering (nowcasting, real-time forecasting) or smoothing (retrospective reanalysis), which splits what should be a shared prior across application-specific pipelines. To address both issues, we introduce ForcingDAS, a unified and robust DA framework. Built on Diffusion Forcing with an independent noise level assigned to each frame, ForcingDAS learns a joint-trajectory prior instead of frame-to-frame transitions. This allows it to capture long-horizon temporal dependencies and reduce error accumulation. In addition, the same trained model spans the full filtering to smoothing spectrum at inference time. Specifically, nowcasting, fixed-lag smoothing, and batch reanalysis are selected through the inference schedule alone, without retraining. We evaluate ForcingDAS on 2D Navier-Stokes vorticity, precipitation nowcasting, and global atmospheric state estimation. Across all settings, a single model is competitive with or outperforms both learned and classical baselines that are specialized for individual regimes, with the largest gains observed on real-world weather benchmarks.

The objective of this study is to evaluate the potential for History Matching (HM) to tune a climate system with multi-scale dynamics. By considering a toy climate model, namely, the two-scale Lorenz96 model and producing experiments in perfect-model setting, we explore in detail how several built-in choices need to be carefully tested. We also demonstrate the importance of introducing physical expertise in the range of parameters, a priori to running HM. Finally we revisit a classical procedure in climate model tuning, that consists of tuning the slow and fast components separately. By doing so in the Lorenz96 model, we illustrate the non-uniqueness of plausible parameters and highlight the specificity of metrics emerging from the coupling. This paper contributes also to bridging the communities of uncertainty quantification, machine learning and climate modeling, by making connections between the terms used by each community for the same concept and presenting promising collaboration avenues that would benefit climate modeling research.

Earth system models suffer from various structural and parametric errors in their representation of nonlinear, multi-scale processes, leading to uncertainties in their long-term projections. The effects of many of these errors (particularly those due to fast physics) can be quantified in short-term simulations, e.g., as differences between the predicted and observed states (analysis increments). With the increase in the availability of high-quality observations and simulations, learning nudging from these increments to correct model errors has become an active research area. However, most studies focus on using neural networks, which while powerful, are hard to interpret, are data-hungry, and poorly generalize out-of-distribution. Here, we show the capabilities of Model Error Discovery with Interpretability and Data Assimilation (MEDIDA), a general, data-efficient framework that uses sparsity-promoting equation-discovery techniques to learn model errors from analysis increments. Using two-layer quasi-geostrophic turbulence as the test case, MEDIDA is shown to successfully discover various linear and nonlinear structural/parametric errors when full observations are available. Discovery from spatially sparse observations is found to require highly accurate interpolation schemes. While NNs have shown success as interpolators in recent studies, here, they are found inadequate due to their inability to accurately represent small scales, a phenomenon known as spectral bias. We show that a general remedy, adding a random Fourier feature layer to the NN, resolves this issue enabling MEDIDA to successfully discover model errors from sparse observations. These promising results suggest that with further development, MEDIDA could be scaled up to models of the Earth system and real observations.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

Time domain simulation, i.e., modeling the system's evolution over time, is a crucial tool for studying and enhancing power system stability and dynamic performance. However, these simulations become computationally intractable for renewable-penetrated grids, due to the small simulation time step required to capture renewable energy resources' ultra-fast dynamic phenomena in the range of 1-50 microseconds. This creates a critical need for solutions that are both fast and scalable, posing a major barrier for the stable integration of renewable energy resources and thus climate change mitigation. This paper explores operator learning, a family of machine learning methods that learn mappings between functions, as a surrogate model for these costly simulations. The paper investigates, for the first time, the fundamental concept of simulation time step-invariance, which enables models trained on coarse time steps to generalize to fine-resolution dynamics. Three operator learning methods are benchmarked on a simple test system that, while not incorporating practical complexities of renewable-penetrated grids, serves as a first proof-of-concept to demonstrate the viability of time step-invariance. Models are evaluated on (i) zero-shot super-resolution, where training is performed on a coarse simulation time step and inference is performed at super-resolution, and (ii) generalization between stable and unstable dynamic regimes. This work addresses a key challenge in the integration of renewable energy for the mitigation of climate change by benchmarking operator learning methods to model physical systems.

Reference-free faithfulness metrics verify each atomic claim a model makes against ground truth, and are increasingly used to evaluate grounded generation. We show they share a blind spot: they measure only precision -- are the stated claims supported? -- and therefore reward abstention, since a model can score near-perfect faithfulness by saying almost nothing. We make this measurable using Formula 1 telemetry, a domain where strategic ground truth is derived deterministically and, crucially, completely: for each decision we know the full set of facts that mattered. This completeness -- absent in open-domain faithfulness benchmarks -- lets us measure recall (coverage of the relevant facts) exactly, alongside precision. On a multilingual (EN/ES/PT) benchmark of 7,253 decision instances spanning 150 races, the most precise frontier model covers under half of the relevant facts and ranks last by F1, so requiring coverage reorders the systems; the same effect reappears in a second complete-oracle domain (NOAA weather forecasts). A prompt ablation shows the low coverage is not an under-prompting artifact: explicitly asking models to be thorough does not close the gap. We pair faithfulness with coverage into a single score, validate the metric (controlled perturbation; agreement across a model-free regex extractor and a cross-family LLM extractor, system-level Spearman 1.0), and give a verifier-guided generation method that improves precision and recall without references. We release the benchmark, structured annotations, metric, baselines, and an interactive demo.

Inferring atmospheric properties of exoplanets from observed spectra is key to understanding their formation, evolution, and habitability. Since traditional Bayesian approaches to atmospheric retrieval (e.g., nested sampling) are computationally expensive, a growing number of machine learning (ML) methods such as neural posterior estimation (NPE) have been proposed. We seek to make ML-based atmospheric retrieval (1) more reliable and accurate with verified results, and (2) more flexible with respect to the underlying neural networks and the choice of the assumed noise models. First, we adopt flow matching posterior estimation (FMPE) as a new ML approach to atmospheric retrieval. FMPE maintains many advantages of NPE, but provides greater architectural flexibility and scalability. Second, we use importance sampling (IS) to verify and correct ML results, and to compute an estimate of the Bayesian evidence. Third, we condition our ML models on the assumed noise level of a spectrum (i.e., error bars), thus making them adaptable to different noise models. Both our noise level-conditional FMPE and NPE models perform on par with nested sampling across a range of noise levels when tested on simulated data. FMPE trains about 3 times faster than NPE and yields higher IS efficiencies. IS successfully corrects inaccurate ML results, identifies model failures via low efficiencies, and provides accurate estimates of the Bayesian evidence. FMPE is a powerful alternative to NPE for fast, amortized, and parallelizable atmospheric retrieval. IS can verify results, thus helping to build confidence in ML-based approaches, while also facilitating model comparison via the evidence ratio. Noise level conditioning allows design studies for future instruments to be scaled up, for example, in terms of the range of signal-to-noise ratios.

Radio frequency (RF) signal mapping, which is the process of analyzing and predicting the RF signal strength and distribution across specific areas, is crucial for cellular network planning and deployment. Traditional approaches to RF signal mapping rely on statistical models constructed based on measurement data, which offer low complexity but often lack accuracy, or ray tracing tools, which provide enhanced precision for the target area but suffer from increased computational complexity. Recently, machine learning (ML) has emerged as a data-driven method for modeling RF signal propagation, which leverages models trained on synthetic datasets to perform RF signal mapping in "unseen" areas. In this paper, we present Geo2SigMap, an ML-based framework for efficient and high-fidelity RF signal mapping using geographic databases. First, we develop an automated framework that seamlessly integrates three open-source tools: OpenStreetMap (geographic databases), Blender (computer graphics), and Sionna (ray tracing), enabling the efficient generation of large-scale 3D building maps and ray tracing models. Second, we propose a cascaded U-Net model, which is pre-trained on synthetic datasets and employed to generate detailed RF signal maps, leveraging environmental information and sparse measurement data. Finally, we evaluate the performance of Geo2SigMap via a real-world measurement campaign, where three types of user equipment (UE) collect over 45,000 data points related to cellular information from six LTE cells operating in the citizens broadband radio service (CBRS) band. Our results show that Geo2SigMap achieves an average root-mean-square-error (RMSE) of 6.04 dB for predicting the reference signal received power (RSRP) at the UE, representing an average RMSE improvement of 3.59 dB compared to existing methods.

Recurrent fast-weight memories and selective state-space models compress an expanding context into a fixed-size recurrent state, making the state transition an online learning rule. We study this rule under read-after-write autoregressive semantics. For the prefix-prediction objective considered here, the local fast-memory example revealed at step t is the prefix-aligned pair (x_t,y_t)=(ϕ(k_{t-1}),v_t). The common same-step association (ϕ(k_t),v_t) remains causal, but optimizes a different internal objective. We derive normalized first-order updates for squared-error regression and negative inner-product objectives. The regression family comprises Falcon-1 (a scalar NLMS update), Falcon-2 (its per-column extension), and Falcon-3 (a sliding-window mini-batch update); Falcon-1A/Falcon-2A/Falcon-3A are the corresponding inner-product variants. We provide recurrent, masked-parallel, and chunk-parallel forms, together with numerically stable positive-decay renormalization. Representative variants remain competitive in language modeling and improve length extrapolation on variable-digit addition. This framework separates temporal alignment, plasticity, forgetting, and bounded rehearsal in recurrent sequence models.

Catastrophic regime shifts in complex natural systems may be averted through advanced detection. Recent work has provided a proof-of-principle that many systems approaching a catastrophic transition may be identified through the lens of early warning indicators such as rising variance or increased return times. Despite widespread appreciation of the difficulties and uncertainty involved in such forecasts, proposed methods hardly ever characterize their expected error rates. Without the benefits of replicates, controls, or hindsight, applications of these approaches must quantify how reliable different indicators are in avoiding false alarms, and how sensitive they are to missing subtle warning signs. We propose a model based approach in order to quantify this trade-off between reliability and sensitivity and allow comparisons between different indicators. We show these error rates can be quite severe for common indicators even under favorable assumptions, and also illustrate how a model-based indicator can improve this performance. We demonstrate how the performance of an early warning indicator varies in different data sets, and suggest that uncertainty quantification become a more central part of early warning predictions.

Forecasting weather and climate events is crucial for making appropriate measures to mitigate environmental hazards and minimize losses. However, existing environmental forecasting research focuses narrowly on predicting numerical meteorological variables (e.g., temperature), neglecting the translation of these variables into actionable textual narratives of events and their consequences. To bridge this gap, we proposed Weather and Climate Event Forecasting (WCEF), a new task that leverages numerical meteorological raster data and textual event data to predict weather and climate events. This task is challenging to accomplish due to difficulties in aligning multimodal data and the lack of supervised datasets. To address these challenges, we present CLLMate, the first multimodal dataset for WCEF, using 26,156 environmental news articles aligned with ERA5 reanalysis data. We systematically benchmark 23 existing MLLMs on CLLMate, including closed-source, open-source, and our fine-tuned models. Our experiments reveal the advantages and limitations of existing MLLMs and the value of CLLMate for the training and benchmarking of the WCEF task.

The state of the art for physical hazard prediction from weather and climate requires expensive km-scale numerical simulations driven by coarser resolution global inputs. Here, a generative diffusion architecture is explored for downscaling such global inputs to km-scale, as a cost-effective machine learning alternative. The model is trained to predict 2km data from a regional weather model over Taiwan, conditioned on a 25km global reanalysis. To address the large resolution ratio, different physics involved at different scales and prediction of channels beyond those in the input data, we employ a two-step approach where a UNet predicts the mean and a corrector diffusion (CorrDiff) model predicts the residual. CorrDiff exhibits encouraging skill in bulk MAE and CRPS scores. The predicted spectra and distributions from CorrDiff faithfully recover important power law relationships in the target data. Case studies of coherent weather phenomena show that CorrDiff can help sharpen wind and temperature gradients that co-locate with intense rainfall in cold front, and can help intensify typhoons and synthesize rain band structures. Calibration of model uncertainty remains challenging. The prospect of unifying methods like CorrDiff with coarser resolution global weather models implies a potential for global-to-regional multi-scale machine learning simulation.

Precise crop yield prediction is essential for improving agricultural practices and ensuring crop resilience in varying climates. Integrating weather data across the growing season, especially for different crop varieties, is crucial for understanding their adaptability in the face of climate change. In the MLCAS2021 Crop Yield Prediction Challenge, we utilized a dataset comprising 93,028 training records to forecast yields for 10,337 test records, covering 159 locations across 28 U.S. states and Canadian provinces over 13 years (2003-2015). This dataset included details on 5,838 distinct genotypes and daily weather data for a 214-day growing season, enabling comprehensive analysis. As one of the winning teams, we developed two novel convolutional neural network (CNN) architectures: the CNN-DNN model, combining CNN and fully-connected networks, and the CNN-LSTM-DNN model, with an added LSTM layer for weather variables. Leveraging the Generalized Ensemble Method (GEM), we determined optimal model weights, resulting in superior performance compared to baseline models. The GEM model achieved lower RMSE (5.55% to 39.88%), reduced MAE (5.34% to 43.76%), and higher correlation coefficients (1.1% to 10.79%) when evaluated on test data. We applied the CNN-DNN model to identify top-performing genotypes for various locations and weather conditions, aiding genotype selection based on weather variables. Our data-driven approach is valuable for scenarios with limited testing years. Additionally, a feature importance analysis using RMSE change highlighted the significance of location, MG, year, and genotype, along with the importance of weather variables MDNI and AP.

With the rapid deployment of SCADA systems, how to effectively analyze industrial signals and detect abnormal states is an urgent need for the industry. Due to the significant heterogeneity of these signals, which we summarize as the M5 problem, previous works only focus on small sub-problems and employ specialized models, failing to utilize the synergies between modalities and the powerful scaling law. However, we argue that the M5 signals can be modeled in a unified manner due to the intrinsic similarity. As a result, we propose FISHER, a Foundation model for multi-modal Industrial Signal compreHEnsive Representation. To support arbitrary sampling rates, FISHER considers the increment of sampling rate as the concatenation of sub-band information. Specifically, FISHER takes the STFT sub-band as the modeling unit and adopts a teacher student SSL framework for pre-training. We also develop the RMIS benchmark, which evaluates the representations of M5 industrial signals on multiple health management tasks. Compared with top SSL models, FISHER showcases versatile and outstanding capabilities with a general performance gain up to 5.03%, along with much more efficient scaling curves. We also investigate the scaling law on downstream tasks and derive potential avenues for future works. FISHER is now open-sourced on https://github.com/jianganbai/FISHER

Physiological time series signals reflect complex, multi-scale dynamical processes of the human body. Existing modeling studies focus on static tasks such as classification, event forecasting, or short-horizon next step prediction, while long-horizon signal-level forecasting and predictive nature of physiological signals remain underexplored. We introduce NormWear-2, a world model that encodes both multivariate physiological signals and clinical intervention variables into a shared latent space and models their joint temporal evolution as a dynamical system. Our approach combines inference from prior pre-trained knowledge (intuition) with instant non-parametric latent state transition adaptation (insight), enabling coherent forecasting across multiple temporal scales, conditioned on heterogeneous clinical interventions. During the pretraining phase, we find that chaos-theoretic balancing of dynamical regime diversity yields more robust representations, with a smaller balanced corpus outperforming one twice its size and capturing bifurcation regimes. We evaluate the world model performance across diverse real-world physiological datasets spanning heterogeneous temporal resolutions and intervention regimes, covering daily life, point-of-care, and clinical settings, including fitness planning, hemodialysis, diabetes management, and surgical monitoring. These evaluation datasets comprise records from 8,026 subjects, spanning study durations from 3.2 hours for high-resolution signal data to 2.3 years for longitudinal clinical biomarker tracking. NormWear-2 achieves the best overall forecasting performance across time, frequency, and latent representation domains, with significant improvements over state-of-the-art time series foundation models, while maintaining competitive downstream representation quality, providing a step toward general-purpose world models for physiological signals.

Models of many engineering and natural systems are imperfect. The discrepancy between the mathematical representations of a true physical system and its imperfect model is called the model error. These model errors can lead to substantial differences between the numerical solutions of the model and the state of the system, particularly in those involving nonlinear, multi-scale phenomena. Thus, there is increasing interest in reducing model errors, particularly by leveraging the rapidly growing observational data to understand their physics and sources. Here, we introduce a framework named MEDIDA: Model Error Discovery with Interpretability and Data Assimilation. MEDIDA only requires a working numerical solver of the model and a small number of noise-free or noisy sporadic observations of the system. In MEDIDA, first the model error is estimated from differences between the observed states and model-predicted states (the latter are obtained from a number of one-time-step numerical integrations from the previous observed states). If observations are noisy, a data assimilation (DA) technique such as ensemble Kalman filter (EnKF) is employed to provide the analysis state of the system, which is then used to estimate the model error. Finally, an equation-discovery technique, here the relevance vector machine (RVM), a sparsity-promoting Bayesian method, is used to identify an interpretable, parsimonious, and closed-form representation of the model error. Using the chaotic Kuramoto-Sivashinsky (KS) system as the test case, we demonstrate the excellent performance of MEDIDA in discovering different types of structural/parametric model errors, representing different types of missing physics, using noise-free and noisy observations.

We study the problem of robustly learning Gaussian Single Index Models (SIMs) in the presence of heavy-tailed noise and a constant fraction of adversarially corrupted covariates and responses. Prior work on robust recovery has considered settings such as linear regression (Pensia et al., JASA 2024), strictly monotonic link functions (Awasthi et al., NeurIPS 2022), and phase retrieval (Buna and Rebeschini, AISTATS 2025). However, these techniques do not extend to generic asymmetric non-monotonic link functions such as GeLU and Swish, which arise naturally as scalar primitives in modern gated neural architectures. We close this gap by giving the first robust recovery algorithm with near-linear sample and time complexity for generic non-monotonic link functions, thereby establishing the first robust recovery guarantees for a broad family of nonlinear SIMs for which no guarantees were previously known. Our central contribution is a new structural understanding of the Gaussian squared-loss landscape under adversarial contamination. Crucially, we prove that for a broad class of nonlinear non-monotonic SIMs, a dimension-independent, constant-radius convex basin exists around the ground truth and is efficiently reachable via robust spectral initialization even under adversarial contamination. Prior works fail to establish both guarantees simultaneously, thereby either breaking down under adversarial contamination or failing to handle generic non-monotonic link functions. Together, these structural insights yield a principled warm start for robust gradient descent that provably converges to a final estimation error of O(σsqrtε) in O(nd) time with O(d) samples, where ε is the contamination fraction.

Time series classification (TSC) performance depends not only on architectural design but also on the diversity of input representations. In this work, we propose a scalable multi-scale convolutional framework that systematically integrates structured multi-representation inputs for univariate time series. We introduce two architectures: MRMS-Net, a hierarchical multi-scale convolutional network optimized for robustness and calibration, and LMRMS-Net, a lightweight variant designed for efficiency-aware deployment. In addition, we adapt LiteMV -- originally developed for multivariate inputs -- to operate on multi-representation univariate signals, enabling cross-representation interaction. We evaluate all models across 142 benchmark datasets under a unified experimental protocol. Critical Difference (CD) analysis confirms statistically significant performance differences among the top models. Results show that LiteMV achieves the highest mean accuracy, MRMS-Net provides superior probabilistic calibration (lowest NLL), and LMRMS-Net offers the best efficiency-accuracy tradeoff. Pareto analysis further demonstrates that multi-representation multi-scale modeling yields a flexible design space that can be tuned for accuracy-oriented, calibration-oriented, or resource-constrained settings. These findings establish scalable multi-representation multi-scale learning as a principled and practical direction for modern TSC. Reference implementation of MRMS-Net and LMRMS-Net is available at: https://github.com/alagoz/mrmsnet-tsc

This paper presents a differentially private approach to Kaplan-Meier estimation that achieves accurate survival probability estimates while safeguarding individual privacy. The Kaplan-Meier estimator is widely used in survival analysis to estimate survival functions over time, yet applying it to sensitive datasets, such as clinical records, risks revealing private information. To address this, we introduce a novel algorithm that applies time-indexed Laplace noise, dynamic clipping, and smoothing to produce a privacy-preserving survival curve while maintaining the cumulative structure of the Kaplan-Meier estimator. By scaling noise over time, the algorithm accounts for decreasing sensitivity as fewer individuals remain at risk, while dynamic clipping and smoothing prevent extreme values and reduce fluctuations, preserving the natural shape of the survival curve. Our results, evaluated on the NCCTG lung cancer dataset, show that the proposed method effectively lowers root mean squared error (RMSE) and enhances accuracy across privacy budgets (epsilon). At epsilon = 10, the algorithm achieves an RMSE as low as 0.04, closely approximating non-private estimates. Additionally, membership inference attacks reveal that higher epsilon values (e.g., epsilon geq 6) significantly reduce influential points, particularly at higher thresholds, lowering susceptibility to inference attacks. These findings confirm that our approach balances privacy and utility, advancing privacy-preserving survival analysis.

Reinforcement learning (RL) is essential for adaptive decision-making, e.g., robust Meta-RL and domain randomization (DR), and efficient post-training of large language models (LLMs), where tasks are commonly structured as Markov decision processes or prompts. A central bottleneck in all these settings is the cost of agent-environment interactions required for task selection and policy optimization. Model predictive task sampling (MPTS) has emerged as a promising approach to improve sample efficiency by querying informative tasks via a risk predictive model (RPM) trained on optimization history. However, existing RPMs suffer from two failure modes: (i) sparse optimization histories, which limit RPMs' generalization across the task space, and (ii) a one-step lag in risk approximation, which causes biased difficulty estimation as the policy evolves. This work formalizes these failure modes, derives lagged-risk decompositions that expose the resulting temporal bias, and recasts risk prediction as an in-context sequence modeling problem. The developed RPM integrates a one-step look-ahead mechanism with a temporal-weighted sliding window to mitigate data non-stationarity and scarcity, without requiring additional rollouts. Empirically, our approach yields more reliable difficulty estimates and consistent performance gains across robust Meta-RL, DR, and prompt curriculum RL post-training of LLMs.

Data-driven models now rival numerical weather prediction in the medium range, but extending them to sub-seasonal lead times raises challenges absent at shorter horizons. Errors accumulate over long autoregressive rollouts, systematic biases grow with lead time, and several years of data must be held out for independent verification, even though machine-learning models otherwise benefit from longer training records. To address these challenges, we adapt ECMWF's AIFS-CRPS medium-range model. AIFS-SUBS adopts a 24h autoregressive time step to reduce error accumulation, adds stratospheric levels and top-of-atmosphere thermal radiation as predictors, and reserves 2007--2011 as an independent verification window. We evaluate two config-durations: AIFS-SUBS, fine-tuned on operational analyses, and AIFS-SUBS-ERA5, trained on ERA5 alone. Across weeks 2--6, AIFS-SUBS matches the operational Integrated Forecasting System (IFS) in probabilistic skill while reducing systematic biases. For the convective (OLR) component of the Madden--Julian Oscillation (MJO), AIFS-SUBS extends skilful forecasts (correlation > 0.5) by eight days relative to the IFS, while matching or exceeding the IFS for the full multivariate RMM index. AIFS-SUBS also reproduces the observed MJO modulation of tropical cyclone activity comparably. Stratospheric skill is particularly strong with AIFS-SUBS reproducing sudden stratospheric warming (SSW) frequency and surface impact. In the AI Weather Quest, AIFS-SUBS-ERA5 attains a variable-averaged ranked probability skill score slightly ahead of the IFS at weeks 3 and 4. At inference, AIFS-SUBS uses about 200 times less energy than the IFS, opening the door to much larger real-time ensembles. AIFS-SUBS is ECMWF's first machine-learning model targeted at sub-seasonal time-scales.

Machine learning weather prediction (MLWP) models have demonstrated remarkable potential in delivering accurate forecasts at significantly reduced computational cost compared to traditional numerical weather prediction (NWP) systems. However, challenges remain in ensuring the physical consistency of MLWP outputs, particularly in deterministic settings. This study presents FastNet, a graph neural network (GNN)-based global prediction model, and investigates the impact of alternative loss function designs on improving the physical realism of its forecasts. We explore three key modifications to the standard mean squared error (MSE) loss: (1) a modified spherical harmonic (MSH) loss that penalises spectral amplitude errors to reduce blurring and enhance small-scale structure retention; (2) inclusion of horizontal gradient terms in the loss to suppress non-physical artefacts; and (3) an alternative wind representation that decouples speed and direction to better capture extreme wind events. Results show that while the MSH and gradient-based losses alone may slightly degrade RMSE scores, when trained in combination the model exhibits very similar MSE performance to an MSE-trained model while at the same time significantly improving spectral fidelity and physical consistency. The alternative wind representation further improves wind speed accuracy and reduces directional bias. Collectively, these findings highlight the importance of loss function design as a mechanism for embedding domain knowledge into MLWP models and advancing their operational readiness.

We propose an approach to estimate the number of samples required for a model to reach a target performance. We find that the power law, the de facto principle to estimate model performance, leads to large error when using a small dataset (e.g., 5 samples per class) for extrapolation. This is because the log-performance error against the log-dataset size follows a nonlinear progression in the few-shot regime followed by a linear progression in the high-shot regime. We introduce a novel piecewise power law (PPL) that handles the two data regimes differently. To estimate the parameters of the PPL, we introduce a random forest regressor trained via meta learning that generalizes across classification/detection tasks, ResNet/ViT based architectures, and random/pre-trained initializations. The PPL improves the performance estimation on average by 37% across 16 classification and 33% across 10 detection datasets, compared to the power law. We further extend the PPL to provide a confidence bound and use it to limit the prediction horizon that reduces over-estimation of data by 76% on classification and 91% on detection datasets.

We present HiRO-ACEv2 (High Resolution Output Ai2 Climate Emulator), a two-stage framework for AI emulation of the 3~km resolution X-SHiELD global storm-resolving model (GSRM), and highlight its ability to generate large ensembles of data for studying the characteristics of tropical cyclones and extreme events in high-resolution simulations at an inference computational cost over 300 times lower than that of traditional numerical GSRMs. HiRO-ACEv2 expands upon the precipitation-only HiRO-ACEv1 model to generate coherent precipitation, 10~m winds, and sea level pressure outputs, enabling a broader range of events to be simulated at high-resolution. Fine-resolution predictions are generated by running an autoregressive emulator of coarsened X-SHiELD at 100 km, whose multivariate outputs are regionally downscaled to 3~km resolution via a separately trained diffusion model. Particular importance is placed on capturing the statistics of extreme events during the diffusion downscaling step. Our ability to match the tails of distributions and generate realistic-looking extreme events in both the `perfect prediction' case as well as in free-running emulator rollouts is improved via the use of multiple denoisers at inference time and several updates to the data sampling, noise sampling, and loss weighting during training. HiRO-ACEv2 closely matches the high-resolution reference distributions of precipitation and near-surface winds out to their 99.9999th percentile values, and broadly tracks the reference distribution of tropical cyclone intensities.

End-to-end weather forecasting systems produce skillful global gridded and station forecasts directly from raw Earth observations, replacing the numerical weather prediction pipeline, including data assimilation, at a fraction of its cost. These systems are deterministic and issue no uncertainty. Here we render the Aardvark Weather model probabilistic by attaching one stochastic mechanism to each component: learned, input-dependent noise at the observation encoder, capturing aleatoric uncertainty inherited from the observing system, and Monte Carlo dropout in the processor, capturing epistemic uncertainty in the learned dynamics. The resulting nested ensemble attributes forecast spread to the two sources through a law-of-total-variance decomposition, cross-checked by withholding observation streams. Probabilistic finetuning significantly improves the mean forecast, by 4.2% on average across variables and lead times. The ensemble is calibrated against ERA5 through the medium range (spread-skill ratio 0.98), keeps station RMSE within 2.4% of the deterministic model while beating it in CRPS at every lead time, and trails the operational ECMWF ensemble. The encoder branch behaves as observation-driven uncertainty. Component-attributed uncertainty makes end-to-end forecasts more transparent, a step toward observation-driven digital twins of the atmosphere.

Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed β-NLL, in which each data point's contribution to the loss is weighted by the β-exponentiated variance estimate. We show that using an appropriate β largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.

Data-driven modeling based on machine learning (ML) is showing enormous potential for weather forecasting. Rapid progress has been made with impressive results for some applications. The uptake of ML methods could be a game-changer for the incremental progress in traditional numerical weather prediction (NWP) known as the 'quiet revolution' of weather forecasting. The computational cost of running a forecast with standard NWP systems greatly hinders the improvements that can be made from increasing model resolution and ensemble sizes. An emerging new generation of ML models, developed using high-quality reanalysis datasets like ERA5 for training, allow forecasts that require much lower computational costs and that are highly-competitive in terms of accuracy. Here, we compare for the first time ML-generated forecasts with standard NWP-based forecasts in an operational-like context, initialized from the same initial conditions. Focusing on deterministic forecasts, we apply common forecast verification tools to assess to what extent a data-driven forecast produced with one of the recently developed ML models (PanguWeather) matches the quality and attributes of a forecast from one of the leading global NWP systems (the ECMWF IFS). The results are very promising, with comparable skill for both global metrics and extreme events, when verified against both the operational analysis and synoptic observations. Increasing forecast smoothness and bias drift with forecast lead time are identified as current drawbacks of ML-based forecasts. A new NWP paradigm is emerging relying on inference from ML models and state-of-the-art analysis and reanalysis datasets for forecast initialization and model training.

Refusal rates are a poor proxy for LLM safety, i.e., a model may over-refuse benign prompts while still complying with harmful ones. We audit both failure modes across 21 open-weight LLMs on four safety benchmarks (OR-Bench, XSTest, ToxiGen, BOLD), using a composition adjustment to isolate model sensitivity from dataset toxicity confounds. We report three findings. First, models adopt fundamentally different calibration strategies: conservative ecosystems such as Llama suppress unsafe outputs at the cost of elevated over-refusals, while permissive ecosystems such as DeepSeek and Qwen preserve helpfulness but tolerate higher harmful compliance. Second, demographic protection is unequal: models over-protect prominent racial and religious groups, frequently refusing even benign prompts about them, while providing substantially weaker protection against disability-targeted attacks. Third, refusal and compliance tendencies are stable within model families across generations and scales, suggesting that post-training objectives shape safety behavior more than architecture. Our results call for joint, demographically-aware, and multi-judge safety evaluation.

Machine learning (ML)-based weather models have rapidly risen to prominence due to their greater accuracy and speed than traditional forecasts based on numerical weather prediction (NWP), recently outperforming traditional ensembles in global probabilistic weather forecasting. This paper presents FGN, a simple, scalable and flexible modeling approach which significantly outperforms the current state-of-the-art models. FGN generates ensembles via learned model-perturbations with an ensemble of appropriately constrained models. It is trained directly to minimize the continuous rank probability score (CRPS) of per-location forecasts. It produces state-of-the-art ensemble forecasts as measured by a range of deterministic and probabilistic metrics, makes skillful ensemble tropical cyclone track predictions, and captures joint spatial structure despite being trained only on marginals.

Given a task described by a few examples, how should a model be specialized to it? Four mechanisms are available -- zero-shot, in-context attention, test-time gradient adaptation, and emitting specialist weights from a hypernetwork -- yet the operating regime of the last is rarely mapped. We run the identical four-way comparison across six tasks spanning regression, generation, language modeling, reinforcement learning, and clinical and genomic classification, holding the specialist, the context, and (where we can) the training budget fixed. The clearest wins for emission are about cost at matched quality: it ties the state-of-the-art amortized tabular model (TabPFN) on clinical few-shot classification while emitting a reusable specialist instead of re-attending the support set per query, and reaches noise-floor shape generation with a 132-float per-instance program. On few-shot sinusoid regression it is 2--3 orders of magnitude below MAML at zero test-time gradient steps -- a margin that narrows to sim30times but persists once training budgets are equalized. Emission cannot match in-context attention on high-dimensional sequence modeling: under matched-budget pre-training a one-pass adapter recovers only a minority of the in-context gain (14.0pm0.9% at 5M, 11.2pm0.5% at 15M), and a LoRA-rank sweep shows this shortfall is a partial capacity limit -- capture climbs from 5% to 21% as rank grows but plateaus far below full recovery. Mechanism ablations confirm the emitted specialist is genuinely task-conditioned, not a memorized prior; and, more speculatively, emitted specialists compose in weight space -- interpolating two of them tracks the corresponding blend of their functions. We close with a falsifiable thesis, operationalized through a per-task resolution measure, bounding when each conditioning mechanism should be preferred.

This study focuses on forecasting major (>=M-class) solar flares that can severely impact the near-Earth environment. We construct two types of datasets using the Space Weather HMI Active Region Patches (SHARP), and develop a flare prediction network based on large language model (LLMFlareNet). We apply SHapley Additive exPlanations (SHAP) to explain the model predictions. We develop an operational forecasting system based on the LLMFlareNet model. We adopt a daily mode for performance comparison across various operational forecasting systems under identical active region (AR) number and prediction date, using daily operational observational data. The main results are as follows. (1) Through ablation experiments and comparison with baseline models, LLMFlareNet achieves the best TSS scores of 0.720 +/- 0.040 on the ten cross-validation (CV) dataset with mixed ARs. (2) By both global and local SHAP analyses, we identify that R_VALUE is the most influential physical feature for the prediction of LLMFlareNet, aligning with flare magnetic reconnection theory. (3) In daily mode, LLMFlareNet achieves TSS scores of 0.680/0.571 (0.689/0.661, respectively) on the dataset with single/mixed ARs, markedly outperforming NASA/CCMC (SolarFlareNet, respectively). This work introduces the first application of a large language model as a universal computation engine with explainability method in this domain, and presents the first comparison between operational flare forecasting systems in daily mode. The proposed LLMFlareNet-based system demonstrates substantial improvements over existing systems.

Sequential trial emulation (STE) estimates the effect of a sustained treatment by stacking nested emulated trials with inverse-probability weighting. Additive-hazards STE estimators of the marginal risk difference recommend the nonparametric bootstrap without evaluating its coverage. Using a correctly-specifiable mechanism (up to a small, disclosed residual), we compare analytic and bootstrap standard errors for both estimands. Exploiting the closed-form linearity of the additive-hazards estimating equation, we derive the influence functions and prove the default row-level robust variance inconsistent for the marginal risk-difference curve, and show the same failure empirically for the constant hazard difference: the row-level variance omits a within-subject cross-trial covariance that is positive under a sign condition we verify across our mechanisms, and is anticonservative at every horizon except the first - only there, where the covariance is zero, is the row-level standard error unimpaired. The subject-clustered variance and multiplier bootstrap are consistent for the fixed-weight linearisation and support simultaneous confidence bands, whose measured coverage is 0.88. Across our simulations the model-based and row-level robust intervals are anticonservative and worsen with sample size, coverage falling to 0.71 at n=5000; clustering leaves the constant-hazard-difference coverage near 0.86 at n=5000, and the multiplier bootstrap leaves the risk-difference-curve coverage near 0.90 (0.86 at the longest horizon). The STE constant hazard difference is a design-weighted summary of a time-varying effect, dependent on the trial structure. We illustrate on the Stanford heart transplant data and provide them in the steCI R package.

Single-optimizer training is a poor fit for the distinct phases of deep network optimization: adaptive methods handle noisy early gradients well but overshoot flat minima, while SGD with momentum generalizes better in the late phase but converges slowly early on. We introduce AOS-R (Adaptive Optimizer Switching, Rule-Based), a lightweight controller that monitors six online gradient-space signals -- gradient noise scale (GNS), Hutchinson curvature trace, loss stagnation, update stability ratio, gradient stability index (GSI), and loss improvement ratio (LIR) -- and switches among AdamW, SGD-M, and Lion as the optimization landscape evolves. State-preserving momentum transfer and a 400-step learning-rate bridge prevent accuracy degradation at every transition point. On CIFAR-100/WRN-28x10, AOS-R reaches 78% top-1 in 81 epochs -- 26% fewer than AdamW (109), 43% fewer than SGD-M (143), and 16% fewer than Lion (96). Across eight model-dataset benchmarks, AOS-R achieves best accuracy on 6 of 8 combinations with a mean +0.4 pp gain and 0.80x convergence speedup over AdamW under a single shared hyperparameter configuration.

Gravitational-wave approximants are essential for gravitational-wave astronomy, allowing the coverage binary black hole parameter space for inference or match filtering without costly numerical relativity (NR) simulations, but generally trading some accuracy for computational efficiency. To reduce this trade-off, NR surrogate models can be constructed using interpolation within NR waveform space. We present a 2-stage training approach for neural network-based NR surrogate models. Initially trained on approximant-generated waveforms and then fine-tuned with NR data, these dual-stage artificial neural surrogate (DANSur) models offer rapid and competitively accurate waveform generation, generating millions in under 20ms on a GPU while keeping mean mismatches with NR around 10^{-4}. Implemented in the bilby framework, we show they can be used for parameter estimation tasks.

In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.

We develop a rigorous walk-forward validation framework for algorithmic trading designed to mitigate overfitting and lookahead bias. Our methodology combines interpretable hypothesis-driven signal generation with reinforcement learning and strict out-of-sample testing. The framework enforces strict information set discipline, employs rolling window validation across 34 independent test periods, maintains complete interpretability through natural language hypothesis explanations, and incorporates realistic transaction costs and position constraints. Validating five market microstructure patterns across 100 US equities from 2015 to 2024, the system yields modest annualized returns (0.55%, Sharpe ratio 0.33) with exceptional downside protection (maximum drawdown -2.76%) and market-neutral characteristics (beta = 0.058). Performance exhibits strong regime dependence, generating positive returns during high-volatility periods (0.60% quarterly, 2020-2024) while underperforming in stable markets (-0.16%, 2015-2019). We report statistically insignificant aggregate results (p-value 0.34) to demonstrate a reproducible, honest validation protocol that prioritizes interpretability and extends naturally to advanced hypothesis generators, including large language models. The key empirical finding reveals that daily OHLCV-based microstructure signals require elevated information arrival and trading activity to function effectively. The framework provides complete mathematical specifications and open-source implementation, establishing a template for rigorous trading system evaluation that addresses the reproducibility crisis in quantitative finance research. For researchers, practitioners, and regulators, this work demonstrates that interpretable algorithmic trading strategies can be rigorously validated without sacrificing transparency or regulatory compliance.

Machine-learning (ML) models, such as the AIFS at the ECMWF, have revolutionised weather forecasting in recent years. We present an extension of the AIFS that jointly models the atmosphere and surface ocean, including ocean waves and sea ice. The primary objective of this extension is to enhance machine-learning medium-range forecasting and enable new use cases by expanding the weather state to better capture coupled surface processes. Our approach departs from traditional numerical models by not having two separate models for the atmosphere and marine components. The joint model instead learns correlations across the entire atmosphere-ocean interface in a component-agnostic way, and can exploit the expressive capacity of ML architectures to learn cross-component relationships directly from the data. We leverage tailored and targeted datasets and solve model design challenges such as missing values over land, multi-scale temporal dynamics, and physical realism of forecast fields and demonstrate the utility of loss scaling in guiding the learning process. We evaluate how representing the surface ocean affects medium-range weather forecasts. We also assess the model's ability to predict surface-ocean fields, including wave swell and tropical-cyclone cold wakes. For nearly all evaluated marine variables, we observe an improvement of approximately one day in forecast skill at medium-range lead times compared to physics-based models. Furthermore, we demonstrate that the model is robust to idealised initial conditions outside the training distribution and responds to them in a physically consistent way. Overall, our findings suggest that the joint AIFS modelling approach offers significant potential for combined atmosphere-ocean forecasting. Our work provides a solid foundation for future development of data-driven coupled Earth system models with greater flexibility and physical fidelity.

Scaling laws predict loss from compute but not how capabilities interact. We measure the coupling between reasoning and truthfulness across 63 base models from 16 families and find a regime change invisible to loss curves: below a family-dependent critical scale N_c, capabilities anticorrelate; above it, they cooperate. N_c approx 3.5B parameters [2.9B, 13.4B] (bootstrap 95% CI), but model size is not the only variable that determines phase. Architecture, data curation, and training recipe each shift N_c independently: curated training eliminated the coupling dip between Qwen generations (0.025 to 0.830 at matched scale), Gemma-4 at 4B achieves coupling 0.871, characteristic of 13B+ standard-trained models, through distillation and architectural innovation, and Phi at 1B matches web-trained coupling at 10B through data curation alone. Width normalization eliminates the anticorrelation across all tested families, supporting an output-projection bottleneck. Internally, 38 of 40 models show zero competing attention heads. A sparse-regression ODE cross-predicts held-out Llama-2 at 5.6% error. The diagnostic requires no model internals -- only public benchmark scores across a model family. The cooperative regime extends to the frontier (r = +0.72, 34 models, 10 labs). Code, data, and an open-source activation-steering tool for any open-weight model are released alongside an interactive dashboard that diagnoses any model's coupling phase, suggests concrete interventions (data curation, width, benchmark rotation), and provides ODE scaling predictions, frontier diagnostics, and eigenstructure analysis: https://zehenlabs.com/cape/.

Tropical cyclones are growing more destructive in a changing climate, and efficient forecasting of their structure and track has become a necessity. Deep generative models promise an alternative to computationally expensive numerical weather prediction (NWP), yet current systems produce either satellite imagery or atmospheric fields, never both; they need many sampling steps, putting them out of reach of modest hardware; and their storm tracks come from regression heads with no physical link to the generated atmosphere. This work presents a single-pass model that jointly forecasts GRIDSAT-B1 infrared imagery and four ERA5 atmospheric fields (U-wind, V-wind, air temperature, and surface pressure) out to nine hours. A five-channel variational autoencoder compresses each 5 x 256 x 256 frame to a 4 x 64 x 64 latent, and a conditional rectified-flow UNet with a factorized temporal-attention module predicts the next three frames from three past frames, their best-track coordinates, and timestamps. The model is then reward-fine-tuned (DRaFT) against a differentiable track error derived from the predicted winds through a steering-flow calculation. On held-out 2022 storms the model reaches 16.35 dB PSNR and 0.759 SSIM, ahead of a reproduced cascaded-diffusion baseline at every lead time (+0.84 dB at +9 h) while sampling ~30x faster (56 ms vs. 1673 ms). Track error at +9 h is 62.4 km, 15% below the baseline, and a reward fine-tuning study demonstrates a further 8-11% track-error reduction across sampler budgets.

Reinforcement learning from human feedback (RLHF) has emerged as the primary method for aligning large language models (LLMs) with human preferences. The RLHF process typically starts by training a reward model (RM) using human preference data. Conventional RMs are trained on pairwise responses to the same user request, with relative ratings indicating which response humans prefer. The trained RM serves as a proxy for human preferences. However, due to the black-box nature of RMs, their outputs lack interpretability, as humans cannot intuitively understand why an RM thinks a response is good or not. As RMs act as human preference proxies, we believe they should be human-interpretable to ensure that their internal decision processes are consistent with human preferences and to prevent reward hacking in LLM alignment. To build RMs with interpretable preferences, we propose a two-stage approach: i) train an Absolute-Rating Multi-Objective Reward Model (ArmoRM) with multi-dimensional absolute-rating data, each dimension corresponding to a human-interpretable objective (e.g., honesty, verbosity, safety); ii) employ a Mixture-of-Experts (MoE) strategy with a gating network that automatically selects the most suitable reward objectives based on the context. We efficiently trained an ArmoRM with Llama-3 8B and a gating network consisting of a shallow MLP on top of the ArmoRM. Our trained model, ArmoRM-Llama3-8B, obtains state-of-the-art performance on RewardBench, a benchmark evaluating RMs for language modeling. Notably, the performance of our model surpasses the LLM-as-a-judge method with GPT-4 judges by a margin, and approaches the performance of the much larger Nemotron-4 340B reward model.

Arabic large language models must refuse harmful prompts without over-refusing benign or sensitive prompts, yet a single refusal rate hides this trade-off. We evaluate it using benign refusal B and harmful-prompt refusal H, where H measures refusal rather than harmful compliance. Across five Arabic-capable models and 130 runs on the full human-written AraSafe set, refusal-only supervised fine-tuning (SFT) collapses toward blanket refusal, whereas selected mixed-SFT configurations reach H = 90% to 93% at B = 14% to 23%; four selected configurations exceed the H = 90% target in all three runs, while Fanar does so in two of three. Direct Preference Optimization (DPO) and inference guards change B and H differently across models rather than acting as uniform upgrades. In a blinded 300-response audit, annotator binary-refusal agreement is 89.0% (kappa = 0.78); Qwen3Guard and Aya Expanse 32B reach 88.7% and 91.0% accuracy, respectively, with no conclusive paired difference. Selected SFT raises H on Arabizi for all five models, but none reaches 90%, showing only partial transfer from Modern Standard Arabic. Overall, the results support model-specific operating-point selection: set a deployment target and retain only interventions that improve it.

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the high-dimensional regime. Motivated by the recent stream of results on the Gaussian universality of the test and training errors in generalized linear estimation, we ask ourselves the question: "when is a single Gaussian enough to characterize the error?". Our formula allow us to give sharp answers to this question, both in the positive and negative directions. More precisely, we show that the sufficient conditions for Gaussian universality (or lack of thereof) crucially depend on the alignment between the target weights and the means and covariances of the mixture clusters, which we precisely quantify. In the particular case of least-squares interpolation, we prove a strong universality property of the training error, and show it follows a simple, closed-form expression. Finally, we apply our results to real datasets, clarifying some recent discussion in the literature about Gaussian universality of the errors in this context.

Accurate Above-Ground Biomass (AGB) mapping at both large scale and high spatio-temporal resolution is essential for applications ranging from climate modeling to biodiversity assessment, and sustainable supply chain monitoring. At present, fine-grained AGB mapping relies on costly airborne laser scanning acquisition campaigns usually limited to regional scales. Initiatives such as the ESA CCI map attempt to generate global biomass products from diverse spaceborne sensors but at a coarser resolution. To enable global, high-resolution (HR) mapping, several works propose to regress AGB from HR satellite observations such as ESA Sentinel-1/2 images. We propose a novel way to address HR AGB estimation, by leveraging both HR satellite observations and existing low-resolution (LR) biomass products. We cast this problem as Guided Super-Resolution (GSR), aiming at upsampling LR biomass maps (sources) from 100 to 10 m resolution, using auxiliary HR co-registered satellite images (guides). We compare super-resolving AGB maps with and without guidance, against direct regression from satellite images, on the public BioMassters dataset. We observe that Multi-Scale Guidance (MSG) outperforms direct regression both for regression (-780 t/ha RMSE) and perception (+2.0 dB PSNR) metrics, and better captures high-biomass values, without significant computational overhead. Interestingly, unlike the RGB+Depth setting they were originally designed for, our best-performing AGB GSR approaches are those that most preserve the guide image texture. Our results make a strong case for adopting the GSR framework for accurate HR biomass mapping at scale. Our code and model weights are made publicly available (https://github.com/kaankaramanofficial/GSR4B).

Background and Objective: Radiation pneumonitis (RP) is a side effect of thoracic radiation therapy. Recently, Machine learning (ML) models enhanced with radiomic and dosiomic features provide better predictions by incorporating spatial information beyond DVHs. However, to improve the clinical decision process, we propose to use uncertainty quantification (UQ) to improve the confidence in model prediction. This study evaluates the impact of post hoc UQ methods on the discriminative performance and calibration of ML models for RP prediction. Methods: This study evaluated four ML models: logistic regression (LR), support vector machines (SVM), extreme gradient boosting (XGB), and random forest (RF), using radiomic, dosiomic, and dosimetric features to predict RP. We applied UQ methods, including Patt scaling, isotonic regression, Venn-ABERS predictor, and Conformal Prediction, to quantify uncertainty. Model performance was assessed through Area Under the Receiver Operating Characteristic curve (AUROC), Area Under the Precision-Recall Curve (AUPRC), and Adaptive Calibration Error (ACE) using Leave-One-Out Cross-Validation (LOO-CV). Results: UQ methods enhanced predictive performance, particularly for high-certainty predictions, while also improving calibration. Radiomic and dosiomic features increased model accuracy but introduced calibration challenges, especially for non-linear models like XGB and RF. Performance gains from UQ methods were most noticeable at higher certainty thresholds. Conclusion: Integrating UQ into ML models with radiomic and dosiomic features improves both predictive accuracy and calibration, supporting more reliable clinical decision-making. The findings emphasize the value of UQ methods in enhancing applicability of predictive models for RP in healthcare settings.

Prediction of stock prices plays a significant role in aiding the decision-making of investors. Considering its importance, a growing literature has emerged trying to forecast stock prices with improved accuracy. In this study, we introduce an innovative approach for forecasting stock prices with greater accuracy. We incorporate external economic environment-related information along with stock prices. In our novel approach, we improve the performance of stock price prediction by taking into account variations due to future expected macroeconomic policy changes as investors adjust their current behavior ahead of time based on expected future macroeconomic policy changes. Furthermore, we incorporate macroeconomic variables along with historical stock prices to make predictions. Results from this strongly support the inclusion of future economic policy changes along with current macroeconomic information. We confirm the supremacy of our method over the conventional approach using several tree-based machine-learning algorithms. Results are strongly conclusive across various machine learning models. Our preferred model outperforms the conventional approach with an RMSE value of 1.61 compared to an RMSE value of 1.75 from the conventional approach.

Should prediction models always deliver a prediction? In the pursuit of maximum predictive performance, critical considerations of reliability and fairness are often overshadowed, particularly when it comes to the role of uncertainty. Selective regression, also known as the "reject option," allows models to abstain from predictions in cases of considerable uncertainty. Initially proposed seven decades ago, approaches to selective regression have mostly focused on distribution-based proxies for measuring uncertainty, particularly conditional variance. However, this focus neglects the significant influence of model-specific biases on a model's performance. In this paper, we propose a novel approach to selective regression by leveraging conformal prediction, which provides grounded confidence measures for individual predictions based on model-specific biases. In addition, we propose a standardized evaluation framework to allow proper comparison of selective regression approaches. Via an extensive experimental approach, we demonstrate how our proposed approach, conformalized selective regression, demonstrates an advantage over multiple state-of-the-art baselines.

Time-series forecasting research has been moving steadily toward larger architectures, from specialized transformers to general-purpose foundation models, on the assumption that capacity is what unlocks accuracy. We take the opposite position: most of the gap can be closed at far lower cost by tuning preprocessing rather than scaling models. We use Ridge regression as the testbed, since it has a closed-form solution and interpretable weights, which let the optimal hyperparameters be read off the search directly. We search over context length, local normalization, regularization, and augmentation on eight standard benchmarks and find three patterns. (1) Optimal lookback is strongly series-specific and often non-monotonic in forecast horizon, with fitted power-law exponents ranging from +0.46 on ETTm2 to -0.19 on Exchange and Traffic, challenging the convention that longer horizons need longer history. (2) Normalizing over a learned trailing fraction of the context, rather than its entirety, is almost universally preferred. (3) Series within the same dataset often disagree on hyperparameters; the optimal degree of cross-series sharing varies from fully shared to fully per-series. The resulting models beat prior linear forecasters on most dataset-horizon entries and exceed Transformer, MLP, and CNN baselines on six of eight benchmarks. The optimized hyperparameters also serve as a diagnostic on the data itself, revealing structures that larger models absorb silently into their learned parameters.

Multimodal Reward Models (MM-RMs) are crucial for aligning Large Language Models (LLMs) with human preferences, particularly as LLMs increasingly interact with multimodal data. However, we find that MM-RMs trained on existing datasets often struggle to generalize to out-of-distribution data due to their reliance on unimodal spurious correlations, primarily text-only shortcuts within the training distribution, which prevents them from leveraging true multimodal reward functions. To address this, we introduce a Shortcut-aware MM-RM learning algorithm that mitigates this issue by dynamically reweighting training samples, shifting the distribution toward better multimodal understanding, and reducing dependence on unimodal spurious correlations. Our experiments demonstrate significant improvements in generalization, downstream task performance, and scalability, establishing a more robust framework for multimodal reward modeling.

General circulation models (GCMs) are the foundation of weather and climate prediction. GCMs are physics-based simulators which combine a numerical solver for large-scale dynamics with tuned representations for small-scale processes such as cloud formation. Recently, machine learning (ML) models trained on reanalysis data achieved comparable or better skill than GCMs for deterministic weather forecasting. However, these models have not demonstrated improved ensemble forecasts, or shown sufficient stability for long-term weather and climate simulations. Here we present the first GCM that combines a differentiable solver for atmospheric dynamics with ML components, and show that it can generate forecasts of deterministic weather, ensemble weather and climate on par with the best ML and physics-based methods. NeuralGCM is competitive with ML models for 1-10 day forecasts, and with the European Centre for Medium-Range Weather Forecasts ensemble prediction for 1-15 day forecasts. With prescribed sea surface temperature, NeuralGCM can accurately track climate metrics such as global mean temperature for multiple decades, and climate forecasts with 140 km resolution exhibit emergent phenomena such as realistic frequency and trajectories of tropical cyclones. For both weather and climate, our approach offers orders of magnitude computational savings over conventional GCMs. Our results show that end-to-end deep learning is compatible with tasks performed by conventional GCMs, and can enhance the large-scale physical simulations that are essential for understanding and predicting the Earth system.

Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of {ell_2} certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension d, proportionally decreasing at a rate of 1/d. This paper explores the feasibility of providing {ell_2} certified robustness for high-dimensional input through the utilization of dual smoothing in the lower-dimensional space. The proposed Dual Randomized Smoothing (DRS) down-samples the input image into two sub-images and smooths the two sub-images in lower dimensions. Theoretically, we prove that DRS guarantees a tight {ell_2} certified robustness radius for the original input and reveal that DRS attains a superior upper bound on the {ell_2} robustness radius, which decreases proportionally at a rate of (1/sqrt m + 1/sqrt n ) with m+n=d. Extensive experiments demonstrate the generalizability and effectiveness of DRS, which exhibits a notable capability to integrate with established methodologies, yielding substantial improvements in both accuracy and {ell_2} certified robustness baselines of RS on the CIFAR-10 and ImageNet datasets. Code is available at https://github.com/xiasong0501/DRS.

Predicting how a patient's vital signs respond to an intervention is a central question in intensive care. World models can do so by learning dynamics as a function of prior actions. However, such models tend to be brittle outside of training data. Clinicians choose drug dosages based on the patient's state, so the association a model learns between dose and outcome runs opposite to the drug's effect, generalizing poorly to out-of-distribution (OOD) dosing practices. Yet, pharmacological information provides the directional effects of different drugs, which are invariant to OOD shifts. To resolve the OOD sensitivity of current ICU world models, we introduce PHYSIO WORLD, which isolates an intervention's effect by evaluating a forward pass twice: once under recorded doses, and once with those doses set to zero. The difference is projected onto pharmacologically admissible effect directions stated by 70 rules over 28 drugs, leaving the magnitude to be learned from data. Across five distribution-shift parameters over cohorts from three intensive-care databases, and against forecasters, counterfactual models, and invariance objectives, PHYSIO WORLD attains the lowest OOD RMSE in every setting, improving on the strongest external baseline by 8-12%, while matching the in-distribution error of its backbone. Reversing the pharmacological directions degrades accuracy below the backbone, and data-mined directions recover almost no gain, indicating the improvement derives from the content of the pharmacological knowledge. The construction may extend to other settings where the sign of an effect is known in advance and its magnitude is confounded by treatment assignment.

Single-cell perturbation atlases rarely measure every intervention in every cellular context: a query perturbation is often observed in one or more source contexts but missing in the recipient context where its effect is needed. Ignoring those measured responses discards query-specific experimental evidence, whereas copying or weakly calibrating them across contexts risks transferring the wrong signal. We propose PerturbMap, which predicts a missing recipient-context effect by combining a recipient-local low-rank base with accepted proposals that transport the same perturbation's measured source responses through source-to-recipient ridge experts fit on paired training perturbations, with proposal weights determined by route reliability estimated on validation anchors. On the Perturb-CITE-seq melanoma cohort, PerturbMap improves full-effect MSE by 4.1\% over a recipient-local low-rank base and achieves lower MSE than FedAvg, zero-response, raw-copy, calibrated-copy, and identity-shuffled affine controls. It remains within 2.82times10^{-6} MSE of our centralized token-matched pooled reference, which uses a stronger training interface. A condition-mean specificity diagnostic shows the same direction: same-recipient top-10 counterpart retrieval by cosine increases from 74.5\% for the low-rank base to 80.5\% for PerturbMap.

We present a comprehensive evaluation of proprietary and open-weights large language models using the first astronomy-specific benchmarking dataset. This dataset comprises 4,425 multiple-choice questions curated from the Annual Review of Astronomy and Astrophysics, covering a broad range of astrophysical topics. Our analysis examines model performance across various astronomical subfields and assesses response calibration, crucial for potential deployment in research environments. Claude-3.5-Sonnet outperforms competitors by up to 4.6 percentage points, achieving 85.0% accuracy. For proprietary models, we observed a universal reduction in cost every 3-to-12 months to achieve similar score in this particular astronomy benchmark. Open-source models have rapidly improved, with LLaMA-3-70b (80.6%) and Qwen-2-72b (77.7%) now competing with some of the best proprietary models. We identify performance variations across topics, with non-English-focused models generally struggling more in exoplanet-related fields, stellar astrophysics, and instrumentation related questions. These challenges likely stem from less abundant training data, limited historical context, and rapid recent developments in these areas. This pattern is observed across both open-weights and proprietary models, with regional dependencies evident, highlighting the impact of training data diversity on model performance in specialized scientific domains. Top-performing models demonstrate well-calibrated confidence, with correlations above 0.9 between confidence and correctness, though they tend to be slightly underconfident. The development for fast, low-cost inference of open-weights models presents new opportunities for affordable deployment in astronomy. The rapid progress observed suggests that LLM-driven research in astronomy may become feasible in the near future.

The inherent rigidity of fixed-size benchmarks makes them an inefficient tool for model evaluation. Diverse evaluation objectives, including model ranking, model selection and testing throughout development, demand varying levels of statistical power. The mismatch between fixed sample sizes and these diverse needs results in either excessive computational cost or compromised reliability - a critical concern for model evaluation. To overcome these limitations, we call for adoption of sequential testing in our field. We provide an adaptive evaluation framework, that provides a principled way to navigate the trade-off between efficiency and reliability in model evaluation. Our framework combines the established statistical paradigm of sequential testing with stopping criteria tailored to common evaluation needs such as diminishing returns detection, and minimum detectable effect size. We demonstrate its ability to adaptively manage the efficiency-reliability trade-off on the Open VLM Leaderboard, including, for example, a 80% reduction in computational cost compared to fixed-size evaluation (with a 2.5-point CI width allowance) while maintaining statistical significance.

Large language models are increasingly used for content moderation, but most evaluations still report aggregate accuracy on individual benchmarks. We introduce Safety-Flag, which places seven widely used safety benchmarks (BeaverTails, XSTest, Ethics, WildGuard, Aegis, ToxiChat, and ToxiGen) into a single balanced flag / do-not-flag protocol. We release item-level decisions and confidence scores for six general-purpose LLMs and four dedicated guards, together with three reference models, evaluated on the same items. Safety-Flag measures three dimensions of moderator reliability: error direction, probability calibration, and confidence-based error ranking for human review. They often disagree. Aggregate accuracy does not reveal error direction: one model flags 85% of benign content, whereas another misses 54% of harmful content. All six general-purpose models are overconfident; fitting one temperature per model reduces calibration error by 2.8--6.0times without changing predicted labels or confidence ordering. Confidence-based abstention lowers selective risk for every model, although the gains depend on how well confidence ranks errors. Dedicated guards produce fewer false alarms and are better calibrated, but several have higher miss rates outside their documented coverage. We release the benchmark, fixed item lists, evaluation code, per-item model outputs, and leaderboard at: https://github.com/yibo-hu-lab/safety-flag-benchmark.

Data pruning algorithms are commonly used to reduce the memory and computational cost of the optimization process. Recent empirical results reveal that random data pruning remains a strong baseline and outperforms most existing data pruning methods in the high compression regime, i.e., where a fraction of 30% or less of the data is kept. This regime has recently attracted a lot of interest as a result of the role of data pruning in improving the so-called neural scaling laws; in [Sorscher et al.], the authors showed the need for high-quality data pruning algorithms in order to beat the sample power law. In this work, we focus on score-based data pruning algorithms and show theoretically and empirically why such algorithms fail in the high compression regime. We demonstrate ``No Free Lunch" theorems for data pruning and present calibration protocols that enhance the performance of existing pruning algorithms in this high compression regime using randomization.

Loss Given Default (LGD) modeling faces a fundamental data quality constraint: 90% of available training data consists of proxy estimates based on pre-distress balance sheets rather than actual recovery outcomes from completed bankruptcy proceedings. We demonstrate that this mixture-contaminated training structure causes systematic failure of recursive partitioning methods, with Random Forest achieving negative r-squared (-0.664, worse than predicting the mean) on held-out test data. Information-theoretic approaches based on Shannon entropy and mutual information provide superior generalization, achieving r-squared of 0.191 and RMSE of 0.284 on 1,218 corporate bankruptcies (1980-2023). Analysis reveals that leverage-based features contain 1.510 bits of mutual information while size effects contribute only 0.086 bits, contradicting regulatory assumptions about scale-dependent recovery. These results establish practical guidance for financial institutions deploying LGD models under Basel III requirements when representative outcome data is unavailable at sufficient scale. The findings generalize to medical outcomes research, climate forecasting, and technology reliability-domains where extended observation periods create unavoidable mixture structure in training data.

Deep learning weather models now match numerical weather prediction accuracy while running orders of magnitude faster, but produce deterministic forecasts without uncertainty estimates, a critical gap for high-stakes decisions during extreme weather events. This paper proposes Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) using last-layer empirical features. Theoretical analysis predicts that UQ quality is architecture-dependent through two mechanisms. First, a variance collapse mechanism explains when UQ fails: when the eigenvalue truncation rank approaches the effective rank of the feature space, the GP correction term consumes nearly all prior variance, destroying discrimination between tropical cyclones and routine conditions; architectures with concentrated spectra (spectral operators) require aggressive truncation (k leq 10), while attention-based models tolerate full-rank computation. Second, decomposition performance depends on the non-Gaussian, heavy-tailed structure of extreme weather: Independent Component Analysis exploits higher-order statistics (kurtosis, negentropy) to isolate heavy-tailed extreme-event features, achieving higher discrimination than singular value decomposition, which captures only second-order variance. A data-driven selection rule chooses ICA or SVD from the feature eigenspectrum concentration ratio, correctly prescribing the superior decomposition for all four evaluated architectures. Compared to split conformal prediction (the natural post-hoc baseline), NTK-UQ achieves 31--37\% sharper prediction intervals at 90\% coverage, and uniquely produces adaptive intervals that scale with extreme event severity, which conformal prediction cannot achieve by construction. The framework requires no retraining; inference-time uncertainty requires only a single matrix-vector product per sample.

Foundation models are often used as fixed black-box predictors for downstream tasks with limited labeled data, but their predictions may be biased and unsafe to trust blindly. We study this setting through black-box assisted nonparametric regression: a learner observes labeled samples and can query a fixed predictor f_0, while the target f^* is close to f_0 in L_2(P_X) up to an unknown radius δ. We give a finite-sample minimax characterization showing a phase transition at δ_c(n) asymp n^{-β/(2β+d)}, with leading risk min{δ^2, n^{-2β/(2β+d)}}. We then analyze a Safe Residual Estimator: it learns a correction around f_0, initializes the residual head at zero so the initial predictor equals f_0, and uses holdout selection to revert to f_0 when the learned correction is not supported by validation data. Here, "safe" means avoiding negative transfer, i.e., performing worse than the black-box predictor alone. The estimator matches the leading minimax term up to an additive validation-selection cost. Synthetic regression experiments verify the predicted phase transition, while CIFAR-100 with CLIP and AG News with Qwen3-8B provide practice-facing evidence that the same residual-correction tradeoff is useful beyond the formal squared-loss regression setting.

This study aims to improve the accuracy of weather predictions by discovering spatial correlations between Earth observations and atmospheric states. Existing numerical weather prediction (NWP) systems predict future atmospheric states at fixed locations, which are called NWP grid points, by analyzing previous atmospheric states and newly acquired Earth observations. However, the shifting locations of observations and the surrounding meteorological context induce complex, dynamic spatial correlations that are difficult for traditional NWP systems to capture, since they rely on strict statistical and physical formulations. To handle complicated spatial correlations, which change dynamically, we employ a spatiotemporal graph neural networks (STGNNs) with structure learning. However, structure learning has an inherent limitation that this can cause structural information loss and over-smoothing problem by generating excessive edges. To solve this problem, we regulate edge sampling by adaptively determining node degrees and considering the spatial distances between NWP grid points and observations. We validated the effectiveness of the proposed method (CloudNine-v2) using real-world atmospheric state and observation data from East Asia, achieving up to 15\% reductions in RMSE over existing STGNN models. Even in areas with high atmospheric variability, CloudNine-v2 consistently outperformed baselines with and without structure learning.

Time series foundation models (TSFMs) are transforming the forecasting paradigm through large-scale cross-domain pretraining. However, most existing TSFMs remain univariate, and recent efforts to enable cross-variate modeling still operate directly within the raw variate space. This design introduces fundamental limitations in semantic alignment and relational expressivity. Specifically, raw-space group mixing lacks a dedicated mechanism to align heterogeneous physical quantities, while standard non-negative attention fails to capture the complex synergistic and antagonistic interactions ubiquitous in real-world systems. To address these challenges, we propose Falcon-X, decouples variates from the raw space and maps them into a unified latent prototype space. Falcon-X employs a Unified Prototype Diff-Attention mechanism that explicitly evaluates both positive and negative semantic affinities to explicitly align heterogeneous variates. Cross-variate interactions are then efficiently performed within this shared space via Latent Entity Attention, naturally facilitating zero-shot structural transfer. Finally, a Variate Reassembly Router robustly reconstructs variate-specific trajectories via a request-and-dispatch mechanism. Extensive evaluations on the GIFT-Eval and fev-bench benchmarks demonstrate that Falcon-X achieves state-of-the-art forecasting performance, offering a principled and scalable paradigm for complex multivariate environments. Falcon-X is publicly released to support future research.

Reward models (RMs) are fundamental to aligning Large Language Models (LLMs) via human feedback, yet they often suffer from reward hacking. They tend to latch on to superficial or spurious attributes, such as response length or formatting, mistaking these cues learned from correlations in training data for the true causal drivers of quality (e.g., factuality, relevance). This occurs because standard training objectives struggle to disentangle these factors, leading to brittle RMs and misaligned policies. We introduce Crome (Causally Robust Reward Modeling), a novel framework grounded in an explicit causal model designed to mitigate reward hacking. Crome employs the following synthetic targeted augmentations during training: (1) Causal Augmentations, which are pairs that differ along specific causal attributes, to enforce sensitivity along each causal attribute individually, and (2) Neutral Augmentations, which are tie-label pairs varying primarily in spurious attributes, to enforce invariance along spurious attributes. Notably, our augmentations are produced without any knowledge of spurious factors, via answer interventions only along causal rubrics, that are identified by querying an oracle LLM. Empirically, Crome significantly outperforms standard baselines on RewardBench, improving average accuracy by up to 5.4% and achieving gains of up to 13.2% and 7.2% in specific categories. The robustness of Crome is further testified by the consistent gains obtained in a Best-of-N inference setting across increasing N, across various benchmarks, including the popular RewardBench (covering chat, chat-hard, safety, and reasoning tasks), the safety-focused WildGuardTest, and the reasoning-specific GSM8k.

One of the major limits of kernel ridge regression (KRR) is that storing and manipulating the kernel matrix K_n for n samples requires O(n^2) space, which rapidly becomes unfeasible for large n. Nystrom approximations reduce the space complexity to O(nm) by sampling m columns from K_n. Uniform sampling preserves KRR accuracy (up to epsilon) only when m is proportional to the maximum degree of freedom of K_n, which may require O(n) columns for datasets with high coherence. Sampling columns according to their ridge leverage scores (RLS) gives accurate Nystrom approximations with m proportional to the effective dimension, but computing exact RLS also requires O(n^2) space. (Calandriello et al. 2016) propose INK-Estimate, an algorithm that processes the dataset incrementally and updates RLS, effective dimension, and Nystrom approximations on-the-fly. Its space complexity scales with the effective dimension but introduces a dependency on the largest eigenvalue of K_n, which in the worst case is O(n). In this paper we introduce SQUEAK, a new algorithm that builds on INK-Estimate but uses unnormalized RLS. As a consequence, the algorithm is simpler, does not need to estimate the effective dimension for normalization, and achieves a space complexity that is only a constant factor worse than exact RLS sampling.

Two-hop QA retrieval splits queries into two regimes determined by whether the hop-2 entity is explicitly named in the question (Q-dominant) or only in the bridge passage (B-dominant). We formalize this split with three theorems: (T1) per-query AUC is a monotone function of the cosine separation margin, with R^2 >= 0.90 for six of eight type-encoder pairs; (T2) regime is characterized by two surface-text predicates, with P1 decisive for routing and P2 qualifying the B-dominant case, holding across three encoders and three datasets; and (T3) bridge advantage requires the relation-bearing sentence, not entity name alone, with removal causing an 8.6-14.1 pp performance drop (p < 0.001). Building on this theory, we propose RegimeRouter, a lightweight binary router that selects between question-only and question-plus-relation-sentence retrieval using five text features derived directly from the predicate definitions. Trained on 2WikiMultiHopQA (n = 881, 5-fold cross-fitted) and applied zero-shot to MuSiQue and HotpotQA, RegimeRouter achieves +5.6 pp (p < 0.001), +5.3 pp (p = 0.002), and +1.1 pp (non-significant, no-regret) R@5 improvement, respectively, with artifact-driven.

Reward Models (RMs) are crucial for aligning language models with human preferences. Currently, the evaluation of RMs depends on measuring accuracy against a validation set of manually annotated preference data. Although this method is straightforward and widely adopted, the relationship between RM accuracy and downstream policy performance remains under-explored. In this work, we conduct experiments in a synthetic setting to investigate how differences in RM measured by accuracy translate into gaps in optimized policy performance. Our findings reveal that while there is a weak positive correlation between accuracy and downstream performance, policies optimized towards RMs with similar accuracy can exhibit quite different performance. Moreover, we discover that the way of measuring accuracy significantly impacts its ability to predict the final policy performance. Through the lens of the Regressional Goodhart effect, we recognize that accuracy, when used for measuring RM quality, can fail to fully capture the potential RM overoptimization. This underscores the inadequacy of relying solely on accuracy to reflect their impact on policy optimization.

The rapid advancement of large language models (LLMs) introduces dual-use capabilities that could both threaten and bolster national security and public safety (NSPS). Models implement safeguards to protect against potential misuse relevant to NSPS and allow for benign users to receive helpful information. However, current benchmarks often fail to test safeguard robustness to potential NSPS risks in an objective, robust way. We introduce FORTRESS: 500 expert-crafted adversarial prompts with instance-based rubrics of 4-7 binary questions for automated evaluation across 3 domains (unclassified information only): Chemical, Biological, Radiological, Nuclear and Explosive (CBRNE), Political Violence & Terrorism, and Criminal & Financial Illicit Activities, with 10 total subcategories across these domains. Each prompt-rubric pair has a corresponding benign version to test for model over-refusals. This evaluation of frontier LLMs' safeguard robustness reveals varying trade-offs between potential risks and model usefulness: Claude-3.5-Sonnet demonstrates a low average risk score (ARS) (14.09 out of 100) but the highest over-refusal score (ORS) (21.8 out of 100), while Gemini 2.5 Pro shows low over-refusal (1.4) but a high average potential risk (66.29). Deepseek-R1 has the highest ARS at 78.05, but the lowest ORS at only 0.06. Models such as o1 display a more even trade-off between potential risks and over-refusals (with an ARS of 21.69 and ORS of 5.2). To provide policymakers and researchers with a clear understanding of models' potential risks, we publicly release FORTRESS at https://huggingface.co/datasets/ScaleAI/fortress_public. We also maintain a private set for evaluation.

This paper studies the use of randomized neural networks for the estimation of exposure profiles and unilateral CVA of American options within a Monte Carlo framework. The analysis is carried out separately under both Black-Scholes and Heston dynamics, combining American option valuation, expected exposure and potential future exposure estimation, and unilateral CVA calculation with portfolio netting effects. The numerical experiment compares this approach with the classical Least-Squares Monte Carlo (LSM) used as a benchmark in both low-dimensional single-asset and high-dimensional multi-asset scenarios, and also includes a path convergence test and a sensitivity analysis. The results show that the randomized feedforward neural network approach preserves convergence to the LSM benchmark when it is extended from pricing to exposure and CVA estimation, while its main advantage appears in high-dimensional problems, where it scales more efficiently and leads to lower computational cost. These results support the use of randomized neural networks as a useful alternative for exposure and CVA estimation in high-dimensional American-style options.

Score-based generative models (SGMs) are a powerful class of generative models that exhibit remarkable empirical performance. Score-based generative modelling (SGM) consists of a ``noising'' stage, whereby a diffusion is used to gradually add Gaussian noise to data, and a generative model, which entails a ``denoising'' process defined by approximating the time-reversal of the diffusion. Existing SGMs assume that data is supported on a Euclidean space, i.e. a manifold with flat geometry. In many domains such as robotics, geoscience or protein modelling, data is often naturally described by distributions living on Riemannian manifolds and current SGM techniques are not appropriate. We introduce here Riemannian Score-based Generative Models (RSGMs), a class of generative models extending SGMs to Riemannian manifolds. We demonstrate our approach on a variety of manifolds, and in particular with earth and climate science spherical data.

When a steering intervention changes a language model's behavior, which part of the intervention deserves the credit? We test this question for a target-centered, scaled conceptor complement by removing its fitted covariance filter while preserving the same target-specific center and gain. At the original aperture α=.05 and gain β=2, all 21 fitted maps across three models and seven targets expand every direction at the generation intervention layers. The matrix correction is 0.093%--7.815% of the matched-control displacement on held-out extraction activations. In 480 paired comparisons within a 1,920-response study, retaining the matrix changes many individual texts but does not establish a consistent additional target-suppression benefit on the four-target panel. A geometric aperture sweep shows that the operating regime changes with the filter setting. Separately, an invertible soft filter preserves what an unrestricted affine readout can recover, whereas dedicated erasure methods reduce prediction by newly fitted probes. Together, the results show why a whole-intervention comparison cannot by itself attribute generated behavior to the fitted matrix: analyze the complete transformation, hold shared components fixed, and test its output consequences directly.

With the success of machine learning (ML) applied to climate reaching further every day, emulators have begun to show promise not only for weather but for multi-year time scales in the atmosphere. Similar work for the ocean remains nascent, with state-of-the-art limited to models running for shorter time scales or only for regions of the globe. In this work, we demonstrate high-skill global emulation for surface ocean fields over 5-8 years of model rollout, accurately representing modes of variability for two different ML architectures (ConvNext and Transformers). In addition, we address the outstanding question of generalization, an essential consideration if the end-use of emulation is to model warming scenarios outside of the model training data. We show that 1) generalization is not an intrinsic feature of a data-driven emulator, 2) fine-tuning the emulator on only small amounts of additional data from a distribution similar to the test set can enable the emulator to perform well in a warmed climate, and 3) the forced emulators are robust to noise in the forcing.

Selective Classification, wherein models can reject low-confidence predictions, promises reliable translation of machine-learning based classification systems to real-world scenarios such as clinical diagnostics. While current evaluation of these systems typically assumes fixed working points based on pre-defined rejection thresholds, methodological progress requires benchmarking the general performance of systems akin to the AUROC in standard classification. In this work, we define 5 requirements for multi-threshold metrics in selective classification regarding task alignment, interpretability, and flexibility, and show how current approaches fail to meet them. We propose the Area under the Generalized Risk Coverage curve (AUGRC), which meets all requirements and can be directly interpreted as the average risk of undetected failures. We empirically demonstrate the relevance of AUGRC on a comprehensive benchmark spanning 6 data sets and 13 confidence scoring functions. We find that the proposed metric substantially changes metric rankings on 5 out of the 6 data sets.