Daily Papers

Best-of-N (BoN) Average Displacement Error (ADE)/ Final Displacement Error (FDE) is the most used metric for evaluating trajectory prediction models. Yet, the BoN does not quantify the whole generated samples, resulting in an incomplete view of the model's prediction quality and performance. We propose a new metric, Average Mahalanobis Distance (AMD) to tackle this issue. AMD is a metric that quantifies how close the whole generated samples are to the ground truth. We also introduce the Average Maximum Eigenvalue (AMV) metric that quantifies the overall spread of the predictions. Our metrics are validated empirically by showing that the ADE/FDE is not sensitive to distribution shifts, giving a biased sense of accuracy, unlike the AMD/AMV metrics. We introduce the usage of Implicit Maximum Likelihood Estimation (IMLE) as a replacement for traditional generative models to train our model, Social-Implicit. IMLE training mechanism aligns with AMD/AMV objective of predicting trajectories that are close to the ground truth with a tight spread. Social-Implicit is a memory efficient deep model with only 5.8K parameters that runs in real time of about 580Hz and achieves competitive results. Interactive demo of the problem can be seen at https://www.abduallahmohamed.com/social-implicit-amdamv-adefde-demo . Code is available at https://github.com/abduallahmohamed/Social-Implicit .

Understanding drivers' decision-making is crucial for road safety. Although predicting the ego-vehicle's path is valuable for driver-assistance systems, existing methods mainly focus on external factors like other vehicles' motions, often neglecting the driver's attention and intent. To address this gap, we infer the ego-trajectory by integrating the driver's gaze and the surrounding scene. We introduce RouteFormer, a novel multimodal ego-trajectory prediction network combining GPS data, environmental context, and the driver's field-of-view, comprising first-person video and gaze fixations. We also present the Path Complexity Index (PCI), a new metric for trajectory complexity that enables a more nuanced evaluation of challenging scenarios. To tackle data scarcity and enhance diversity, we introduce GEM, a comprehensive dataset of urban driving scenarios enriched with synchronized driver field-of-view and gaze data. Extensive evaluations on GEM and DR(eye)VE demonstrate that RouteFormer significantly outperforms state-of-the-art methods, achieving notable improvements in prediction accuracy across diverse conditions. Ablation studies reveal that incorporating driver field-of-view data yields significantly better average displacement error, especially in challenging scenarios with high PCI scores, underscoring the importance of modeling driver attention. All data and code are available at https://meakbiyik.github.io/routeformer.

Safety and robustness are crucial factors in developing trustworthy autonomous vehicles. One essential aspect of addressing these factors is to equip vehicles with the capability to predict future trajectories for all moving objects in the surroundings and quantify prediction uncertainties. In this paper, we propose the Sequential Neural Variational Agent (SeNeVA), a generative model that describes the distribution of future trajectories for a single moving object. Our approach can distinguish Out-of-Distribution data while quantifying uncertainty and achieving competitive performance compared to state-of-the-art methods on the Argoverse 2 and INTERACTION datasets. Specifically, a 0.446 meters minimum Final Displacement Error, a 0.203 meters minimum Average Displacement Error, and a 5.35% Miss Rate are achieved on the INTERACTION test set. Extensive qualitative and quantitative analysis is also provided to evaluate the proposed model. Our open-source code is available at https://github.com/PurdueDigitalTwin/seneva.

Multi-modal trajectory forecasting methods commonly evaluate using single-agent metrics (marginal metrics), such as minimum Average Displacement Error (ADE) and Final Displacement Error (FDE), which fail to capture joint performance of multiple interacting agents. Only focusing on marginal metrics can lead to unnatural predictions, such as colliding trajectories or diverging trajectories for people who are clearly walking together as a group. Consequently, methods optimized for marginal metrics lead to overly-optimistic estimations of performance, which is detrimental to progress in trajectory forecasting research. In response to the limitations of marginal metrics, we present the first comprehensive evaluation of state-of-the-art (SOTA) trajectory forecasting methods with respect to multi-agent metrics (joint metrics): JADE, JFDE, and collision rate. We demonstrate the importance of joint metrics as opposed to marginal metrics with quantitative evidence and qualitative examples drawn from the ETH / UCY and Stanford Drone datasets. We introduce a new loss function incorporating joint metrics that, when applied to a SOTA trajectory forecasting method, achieves a 7% improvement in JADE / JFDE on the ETH / UCY datasets with respect to the previous SOTA. Our results also indicate that optimizing for joint metrics naturally leads to an improvement in interaction modeling, as evidenced by a 16% decrease in mean collision rate on the ETH / UCY datasets with respect to the previous SOTA.

We present a novel approach for long-term human trajectory prediction in indoor human-centric environments, which is essential for long-horizon robot planning in these environments. State-of-the-art human trajectory prediction methods are limited by their focus on collision avoidance and short-term planning, and their inability to model complex interactions of humans with the environment. In contrast, our approach overcomes these limitations by predicting sequences of human interactions with the environment and using this information to guide trajectory predictions over a horizon of up to 60s. We leverage Large Language Models (LLMs) to predict interactions with the environment by conditioning the LLM prediction on rich contextual information about the scene. This information is given as a 3D Dynamic Scene Graph that encodes the geometry, semantics, and traversability of the environment into a hierarchical representation. We then ground these interaction sequences into multi-modal spatio-temporal distributions over human positions using a probabilistic approach based on continuous-time Markov Chains. To evaluate our approach, we introduce a new semi-synthetic dataset of long-term human trajectories in complex indoor environments, which also includes annotations of human-object interactions. We show in thorough experimental evaluations that our approach achieves a 54% lower average negative log-likelihood and a 26.5% lower Best-of-20 displacement error compared to the best non-privileged (i.e., evaluated in a zero-shot fashion on the dataset) baselines for a time horizon of 60s.

Landslide monitoring is essential for understanding geohazards and mitigating associated risks. However, existing point cloud-based methods typically rely on either geometric or radiometric information and often yield sparse or non-3D displacement estimates. In this paper, we propose a hierarchical partition-based coarse-to-fine approach that fuses 3D point clouds and co-registered RGB images to estimate dense 3D displacement vector fields. We construct patch-level matches using both 3D geometry and 2D image features. These matches are refined via geometric consistency checks, followed by rigid transformation estimation per match. Experimental results on two real-world landslide datasets demonstrate that our method produces 3D displacement estimates with high spatial coverage (79% and 97%) and high accuracy. Deviations in displacement magnitude with respect to external measurements (total station or GNSS observations) are 0.15 m and 0.25 m on the two datasets, respectively, and only 0.07 m and 0.20 m compared to manually derived references. These values are below the average scan resolutions (0.08 m and 0.30 m). Our method outperforms the state-of-the-art method F2S3 in spatial coverage while maintaining comparable accuracy. Our approach offers a practical and adaptable solution for TLS-based landslide monitoring and is extensible to other types of point clouds and monitoring tasks. Our example data and source code are publicly available at https://github.com/zhaoyiww/fusion4landslide.

Deep learning methods for unsupervised registration often rely on objectives that assume a uniform noise level across the spatial domain (e.g. mean-squared error loss), but noise distributions are often heteroscedastic and input-dependent in real-world medical images. Thus, this assumption often leads to degradation in registration performance, mainly due to the undesired influence of noise-induced outliers. To mitigate this, we propose a framework for heteroscedastic image uncertainty estimation that can adaptively reduce the influence of regions with high uncertainty during unsupervised registration. The framework consists of a collaborative training strategy for the displacement and variance estimators, and a novel image fidelity weighting scheme utilizing signal-to-noise ratios. Our approach prevents the model from being driven away by spurious gradients caused by the simplified homoscedastic assumption, leading to more accurate displacement estimation. To illustrate its versatility and effectiveness, we tested our framework on two representative registration architectures across three medical image datasets. Our method consistently outperforms baselines and produces sensible uncertainty estimates. The code is publicly available at https://voldemort108x.github.io/hetero_uncertainty/.

Neural surrogates and operator networks for solving partial differential equation (PDE) problems have attracted significant research interest in recent years. However, most existing approaches are limited in their ability to generalize solutions across varying non-parametric geometric domains. In this work, we address this challenge in the context of Polyethylene Terephthalate (PET) bottle buckling analysis, a representative packaging design problem conventionally solved using computationally expensive finite element analysis (FEA). We introduce a hybrid DeepONet-Transolver framework that simultaneously predicts nodal displacement fields and the time evolution of reaction forces during top load compression. Our methodology is evaluated on two families of bottle geometries parameterized by two and four design variables. Training data is generated using nonlinear FEA simulations in Abaqus for 254 unique designs per family. The proposed framework achieves mean relative L^{2} errors of 2.5-13% for displacement fields and approximately 2.4% for time-dependent reaction forces for the four-parameter bottle family. Point-wise error analyses further show absolute displacement errors on the order of 10^{-4}-10^{-3}, with the largest discrepancies confined to localized geometric regions. Importantly, the model accurately captures key physical phenomena, such as buckling behavior, across diverse bottle geometries. These results highlight the potential of our framework as a scalable and computationally efficient surrogate, particularly for multi-task predictions in computational mechanics and applications requiring rapid design evaluation.

We present an experimental analysis on the use of a camera-based approach for high-altitude navigation by associating mapped landmarks from a satellite image database to camera images, and by leveraging inertial sensors between camera frames. We evaluate performance of both a sideways-tilted and downward-facing camera on data collected from a World View Enterprises high-altitude balloon with data beginning at an altitude of 33 km and descending to near ground level (4.5 km) with 1.5 hours of flight time. We demonstrate less than 290 meters of average position error over a trajectory of more than 150 kilometers. In addition to showing performance across a range of altitudes, we also demonstrate the robustness of the Terrain Relative Navigation (TRN) method to rapid rotations of the balloon, in some cases exceeding 20 degrees per second, and to camera obstructions caused by both cloud coverage and cords swaying underneath the balloon. Additionally, we evaluate performance on data collected by two cameras inside the capsule of Blue Origin's New Shepard rocket on payload flight NS-23, traveling at speeds up to 880 km/hr, and demonstrate less than 55 meters of average position error.

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.

We discuss the numerical solution of initial value problems for varepsilon^2,varphi''+a(x),varphi=0 in the highly oscillatory regime, i.e., with a(x)>0 and 0<varepsilonll 1. We analyze and implement an approximate solution based on the well-known WKB-ansatz. The resulting approximation error is of magnitude O(varepsilon^{N}) where N refers to the truncation order of the underlying asymptotic series. When the optimal truncation order N_{opt} is chosen, the error behaves like O(varepsilon^{-2}exp(-cvarepsilon^{-1})) with some c>0.

Motion artefacts in magnetic resonance brain images can have a strong impact on diagnostic confidence. The assessment of MR image quality is fundamental before proceeding with the clinical diagnosis. Motion artefacts can alter the delineation of structures such as the brain, lesions or tumours and may require a repeat scan. Otherwise, an inaccurate (e.g. correct pathology but wrong severity) or incorrect diagnosis (e.g. wrong pathology) may occur. "Image quality assessment" as a fast, automated step right after scanning can assist in deciding if the acquired images are diagnostically sufficient. An automated image quality assessment based on the structural similarity index (SSIM) regression through a residual neural network is proposed in this work. Additionally, a classification into different groups - by subdividing with SSIM ranges - is evaluated. Importantly, this method predicts SSIM values of an input image in the absence of a reference ground truth image. The networks were able to detect motion artefacts, and the best performance for the regression and classification task has always been achieved with ResNet-18 with contrast augmentation. The mean and standard deviation of residuals' distribution were mu=-0.0009 and sigma=0.0139, respectively. Whilst for the classification task in 3, 5 and 10 classes, the best accuracies were 97, 95 and 89\%, respectively. The results show that the proposed method could be a tool for supporting neuro-radiologists and radiographers in evaluating image quality quickly.

In this paper, we revisit the rotation averaging problem applied in global Structure-from-Motion pipelines. We argue that the main problem of current methods is the minimized cost function that is only weakly connected with the input data via the estimated epipolar geometries.We propose to better model the underlying noise distributions by directly propagating the uncertainty from the point correspondences into the rotation averaging. Such uncertainties are obtained for free by considering the Jacobians of two-view refinements. Moreover, we explore integrating a variant of the MAGSAC loss into the rotation averaging problem, instead of using classical robust losses employed in current frameworks. The proposed method leads to results superior to baselines, in terms of accuracy, on large-scale public benchmarks. The code is public. https://github.com/zhangganlin/GlobalSfMpy

Effective rehabilitation assessment is essential for monitoring patient progress, particularly in home-based settings. Existing systems often face challenges such as data imbalance and difficulty detecting subtle movement errors. This paper introduces Error-Guided Pose Augmentation (EGPA), a method that generates synthetic skeleton data by simulating clinically relevant movement mistakes. Unlike standard augmentation techniques, EGPA targets biomechanical errors observed in rehabilitation. Combined with an attention-based graph convolutional network, EGPA improves performance across multiple evaluation metrics. Experiments demonstrate reductions in mean absolute error of up to 27.6 percent and gains in error classification accuracy of 45.8 percent. Attention visualizations show that the model learns to focus on clinically significant joints and movement phases, enhancing both accuracy and interpretability. EGPA offers a promising approach for improving automated movement quality assessment in both clinical and home-based rehabilitation contexts.

We estimate ([M/H], [alpha/M]) for 48 million giants and dwarfs in low-dust extinction regions from the Gaia DR3 XP spectra by using tree-based machine-learning models trained on APOGEE DR17 and metal-poor star sample from Li et al. The root mean square error of our estimation is 0.0890 dex for [M/H] and 0.0436 dex for [alpha/M], when we evaluate our models on the test data that are not used in training the models. Because the training data is dominated by giants, our estimation is most reliable for giants. The high-[alpha/M] stars and low-[alpha/M] stars selected by our ([M/H], [alpha/M]) show different kinematical properties for giants and low-temperature dwarfs. We further investigate how our machine-learning models extract information on ([M/H], [alpha/M]). Intriguingly, we find that our models seem to extract information on [alpha/M] from Na D lines (589 nm) and Mg I line (516 nm). This result is understandable given the observed correlation between Na and Mg abundances in the literature. The catalog of ([M/H], [alpha/M]) as well as their associated uncertainties are publicly available online.

This work presents the first quantitative study of alignment errors between small uncrewed aerial systems (sUAS) geospatial imagery and a priori building polygons and finds that alignment errors are non-uniform and irregular. The work also introduces a publicly available dataset of imagery, building polygons, and human-generated and curated adjustments that can be used to evaluate existing strategies for aligning building polygons with sUAS imagery. There are no efforts that have aligned pre-existing spatial data with sUAS imagery, and thus, there is no clear state of practice. However, this effort and analysis show that the translational alignment errors present in this type of data, averaging 82px and an intersection over the union of 0.65, which would induce further errors and biases in downstream machine learning systems unless addressed. This study identifies and analyzes the translational alignment errors of 21,619 building polygons in fifty-one orthomosaic images, covering 16787.2 Acres (26.23 square miles), constructed from sUAS raw imagery from nine wide-area disasters (Hurricane Ian, Hurricane Harvey, Hurricane Michael, Hurricane Ida, Hurricane Idalia, Hurricane Laura, the Mayfield Tornado, the Musset Bayou Fire, and the Kilauea Eruption). The analysis finds no uniformity among the angle and distance metrics of the building polygon alignments as they present an average degree variance of 0.4 and an average pixel distance variance of 0.45. This work alerts the sUAS community to the problem of spatial alignment and that a simple linear transform, often used to align satellite imagery, will not be sufficient to align spatial data in sUAS orthomosaic imagery.

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.

The software package Volna-OP2 is a robust and efficient code capable of simulating the complete life cycle of a tsunami whilst harnessing the latest High Performance Computing (HPC) architectures. In this paper, a comprehensive error analysis and scalability study of the GPU version of the code is presented. A novel decomposition of the numerical errors into the dispersion and dissipation components is explored. Most tsunami codes exhibit amplitude smearing and/or phase lagging/leading, so the decomposition shown here is a new approach and novel tool for explaining these occurrences. It is the first time that the errors of a tsunami code have been assessed in this manner. To date, Volna-OP2 has been widely used by the tsunami modelling community. In particular its computational efficiency has allowed various sensitivity analyses and uncertainty quantification studies. Due to the number of simulations required, there is always a trade-off between accuracy and runtime when carrying out these statistical studies. The analysis presented in this paper will guide the user towards an acceptable level of accuracy within a given runtime.

RTK-SLAM systems integrate simultaneous localization and mapping (SLAM) with real-time kinematic (RTK) GNSS positioning, promising both relative consistency and globally referenced coordinates for efficient georeferenced surveying. A critical and underappreciated issue is that the standard evaluation metric, Absolute Trajectory Error (ATE), first fits an optimal rigid-body transformation between the estimated trajectory and reference before computing errors. This so-called SE(3) alignment absorbs global drift and systematic errors, making trajectories appear more accurate than they are in practice, and is unsuitable for evaluating the global accuracy of RTK-SLAM. We present a geodetically referenced dataset and evaluation methodology that expose this gap. A key design principle is that the RTK receiver is used solely as a system input, while ground truth is established independently via a geodetic total station. This separation is absent from all existing datasets, where GNSS typically serves as (part of) the ground truth. The dataset is collected with a handheld RTK-SLAM device, comprising two scenes. We evaluate LiDAR-inertial, visual-inertial, and LiDAR-visual-inertial RTK-SLAM systems alongside standalone RTK, reporting direct global accuracy and SE(3)-aligned relative accuracy to make the gap explicit. Results show that SE(3) alignment can underestimate absolute positioning error by up to 76\%. RTK-SLAM achieves centimeter-level absolute accuracy in open-sky conditions and maintains decimeter-level global accuracy indoors, where standalone RTK degrades to tens of meters. The dataset, calibration files, and evaluation scripts are publicly available at https://rtk-slam-dataset.github.io/.

We investigate large language model performance across five orders of magnitude of compute scaling in eleven recent model architectures. We show that average benchmark performance, aggregating over many individual tasks and evaluations as in the commonly-used BIG-Bench dataset, is decently predictable as a function of training compute scale. Specifically, when extrapolating BIG-Bench Hard performance across one order of magnitude in compute, we observe average absolute errors of 6 percentage points (pp). By contrast, extrapolation for individual BIG-Bench tasks across an order of magnitude in compute yields higher average errors of 18pp. Nonetheless, individual task performance remains significantly more predictable than chance. Overall, our work suggests compute scaling provides a promising basis to forecast AI capabilities in diverse benchmarks, though predicting performance in specific tasks poses challenges.

Kalman filter (KF) based methods for multi-object tracking (MOT) make an assumption that objects move linearly. While this assumption is acceptable for very short periods of occlusion, linear estimates of motion for prolonged time can be highly inaccurate. Moreover, when there is no measurement available to update Kalman filter parameters, the standard convention is to trust the priori state estimations for posteriori update. This leads to the accumulation of errors during a period of occlusion. The error causes significant motion direction variance in practice. In this work, we show that a basic Kalman filter can still obtain state-of-the-art tracking performance if proper care is taken to fix the noise accumulated during occlusion. Instead of relying only on the linear state estimate (i.e., estimation-centric approach), we use object observations (i.e., the measurements by object detector) to compute a virtual trajectory over the occlusion period to fix the error accumulation of filter parameters during the occlusion period. This allows more time steps to correct errors accumulated during occlusion. We name our method Observation-Centric SORT (OC-SORT). It remains Simple, Online, and Real-Time but improves robustness during occlusion and non-linear motion. Given off-the-shelf detections as input, OC-SORT runs at 700+ FPS on a single CPU. It achieves state-of-the-art on multiple datasets, including MOT17, MOT20, KITTI, head tracking, and especially DanceTrack where the object motion is highly non-linear. The code and models are available at https://github.com/noahcao/OC_SORT.

Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length n summation, the worst-case error of SR grows as n with high probability, unlike for standard modes, like round-to-nearest (RN), which grows as n. For this reason, the former is increasingly employed in large-scale, low-precision computations as an RN alternative. Additionally, SR alleviates stagnation, whereby relatively small summands are completely rounded off and do not contribute to the sum. We provide an update to [Croci et al., Roy. Soc. Open Sci. 9.3 (2022), pp. 1-25], a survey which discusses the development and use of SR between 1949 and 2022, citing over 100 references. Since then, there has been a surge of new research, and this update covers almost four years of further progress in applying, analysing, and implementing SR. Our main focus is limited-precision stochastic rounding, a new variant that fixes the precision of the random numbers used. We provide insights into industrial and numerical analysis activities surrounding SR, highlighting the next possible steps in making this rounding mode more widely available in hardware.

Models trained on different datasets can be merged by a weighted-averaging of their parameters, but why does it work and when can it fail? Here, we connect the inaccuracy of weighted-averaging to mismatches in the gradients and propose a new uncertainty-based scheme to improve the performance by reducing the mismatch. The connection also reveals implicit assumptions in other schemes such as averaging, task arithmetic, and Fisher-weighted averaging. Our new method gives consistent improvements for large language models and vision transformers, both in terms of performance and robustness to hyperparameters.

Exponential moving average (EMA) has recently gained significant popularity in training modern deep learning models, especially diffusion-based generative models. However, there have been few theoretical results explaining the effectiveness of EMA. In this paper, to better understand EMA, we establish the risk bound of online SGD with EMA for high-dimensional linear regression, one of the simplest overparameterized learning tasks that shares similarities with neural networks. Our results indicate that (i) the variance error of SGD with EMA is always smaller than that of SGD without averaging, and (ii) unlike SGD with iterate averaging from the beginning, the bias error of SGD with EMA decays exponentially in every eigen-subspace of the data covariance matrix. Additionally, we develop proof techniques applicable to the analysis of a broad class of averaging schemes.

We present an end-to-end pipeline for estimating stellar parameters from Sloan Digital Sky Survey Data Release 12 spectra using a fully connected multitask neural network with residual blocks, whose hyperparameters are tuned via Bayesian optimization. The preprocessing pipeline includes per-spectrum standardization, RobustScaler normalization of the target variables -- effective temperature T_{eff}, metallicity [Fe/H], and surface gravity log g -- and data augmentation via Gaussian noise injection. On a held-out test set, the model achieved Mean Absolute Errors (MAE) of 59.76~K for T_{eff}, 0.103~dex for [Fe/H], and 0.130~dex for log g. Normalized against the full-scale range of each parameter, these results represent range-normalized errors between 1% and 3%, achieved with a highly efficient model complexity of approximately 540,000 trainable parameters. These results demonstrate that a compact residual multitask architecture, combined with principled signal preprocessing, provides a parameter-efficient solution for nonlinear parameter estimation in large-scale spectral datasets. In particular, the proposed model achieves competitive performance with substantially lower complexity than deeper neural network baselines.

A content-moderation system can score well on every standard accuracy metric and still cause real harm, if its mistakes fall on the few users who connect otherwise separate communities. We show this in an agent-based model where N=240 learning agents on a community-structured network each post harmless, productive, or dangerous content, and a regulator removes or penalizes whatever a noisy classifier flags. Overall usefulness barely moves as the noise changes (one-way ANOVA, p=0.96): by aggregate measures, nothing looks wrong. The damage instead concentrates on these bridge users, whose useful posts are wrongly suppressed and whose dangerous posts are wrongly spared. A governance loss (L_gov) that prices these two mistakes separately from the cost of enforcement more than doubles under false-positive-heavy noise. Aggregate accuracy hides who is harmed, and the cheap quantity to audit is how many connections a user has (degree), a near-perfect proxy for the betweenness that defines a bridge (r=0.96).

This article presents an experiment in fine-tuning a pretrained causal language model (Meta's Llama 3.1 8B Instruct) for aiding in three fundamental tasks of philological research: chronological and geographic attribution as well as text restoration in ancient Greek inscriptions and documentary papyri. Using a prompt-based instruct approach, the fine-tuned models surpass the state of the art in key metrics. For inscriptions, the models achieve a lower average character error rate (CER) of 22.5% (vs. 26.3%), while closely matching top-1 accuracy (60.9% vs. 61.8%) and top-20 accuracy (77.5% vs. 78.3%) for sequences up to 10 characters. They also provide a practical advantage by ignoring spaces during reconstruction, aligning better with the scriptio continua typically used in ancient written artifacts. In geographic attribution, the model outperforms previous benchmarks with a top-1 accuracy of 75.0% (vs. 70.8%) and a top-3 accuracy of 83.7% (vs. 82.1%). For dating, it achieves an average deviation of 26.2 years (vs. 29.3) and a median deviation of 1 year (vs. 3) from the actual date range. The models also set new baselines for documentary papyri, with a CER of 16.3%, a top-1 accuracy of 71.3%, and top-20 of 85.0% in text reconstruction; a top-1 accuracy of 66.4% and top-3 of 79.9% in geographic attribution; and, in chronological attribution, a deviation of 21.7 years from the actual termini post/ante quem, with a median deviation of 0 years.

During the radiotherapy treatment of patients with lung cancer, the radiation delivered to healthy tissue around the tumor needs to be minimized, which is difficult because of respiratory motion and the latency of linear accelerator systems. In the proposed study, we first use the Lucas-Kanade pyramidal optical flow algorithm to perform deformable image registration of chest computed tomography scan images of four patients with lung cancer. We then track three internal points close to the lung tumor based on the previously computed deformation field and predict their position with a recurrent neural network (RNN) trained using real-time recurrent learning (RTRL) and gradient clipping. The breathing data is quite regular, sampled at approximately 2.5Hz, and includes artificial drift in the spine direction. The amplitude of the motion of the tracked points ranged from 12.0mm to 22.7mm. Finally, we propose a simple method for recovering and predicting 3D tumor images from the tracked points and the initial tumor image based on a linear correspondence model and Nadaraya-Watson non-linear regression. The root-mean-square error, maximum error, and jitter corresponding to the RNN prediction on the test set were smaller than the same performance measures obtained with linear prediction and least mean squares (LMS). In particular, the maximum prediction error associated with the RNN, equal to 1.51mm, is respectively 16.1% and 5.0% lower than the maximum error associated with linear prediction and LMS. The average prediction time per time step with RTRL is equal to 119ms, which is less than the 400ms marker position sampling time. The tumor position in the predicted images appears visually correct, which is confirmed by the high mean cross-correlation between the original and predicted images, equal to 0.955.

This study presents an explainable artificial intelligent (XAI) model for predicting pile driving vibrations in Bangkok's soft clay subsoil. A deep neural network was developed using a dataset of 1,018 real-world pile driving measurements, encompassing variations in pile dimensions, hammer characteristics, sensor locations, and vibration measurement axes. The model achieved a mean absolute error (MAE) of 0.276, outperforming traditional empirical methods and other machine learning approaches such as XGBoost and CatBoost. SHapley Additive exPlanations (SHAP) analysis was employed to interpret the model's predictions, revealing complex relationships between input features and peak particle velocity (PPV). Distance from the pile driving location emerged as the most influential factor, followed by hammer weight and pile size. Non-linear relationships and threshold effects were observed, providing new insights into vibration propagation in soft clay. A web-based application was developed to facilitate adoption by practicing engineers, bridging the gap between advanced machine learning techniques and practical engineering applications. This research contributes to the field of geotechnical engineering by offering a more accurate and nuanced approach to predicting pile driving vibrations, with implications for optimizing construction practices and mitigating environmental impacts in urban areas. The model and its source code are publicly available, promoting transparency and reproducibility in geotechnical research.

We propose an adaptive training scheme for unsupervised medical image registration. Existing methods rely on image reconstruction as the primary supervision signal. However, nuisance variables (e.g. noise and covisibility), violation of the Lambertian assumption in physical waves (e.g. ultrasound), and inconsistent image acquisition can all cause a loss of correspondence between medical images. As the unsupervised learning scheme relies on intensity constancy between images to establish correspondence for reconstruction, this introduces spurious error residuals that are not modeled by the typical training objective. To mitigate this, we propose an adaptive framework that re-weights the error residuals with a correspondence scoring map during training, preventing the parametric displacement estimator from drifting away due to noisy gradients, which leads to performance degradation. To illustrate the versatility and effectiveness of our method, we tested our framework on three representative registration architectures across three medical image datasets along with other baselines. Our adaptive framework consistently outperforms other methods both quantitatively and qualitatively. Paired t-tests show that our improvements are statistically significant. Code available at: https://voldemort108x.github.io/AdaCS/.

Noise plagues many numerical datasets, where the recorded values in the data may fail to match the true underlying values due to reasons including: erroneous sensors, data entry/processing mistakes, or imperfect human estimates. We consider general regression settings with covariates and a potentially corrupted response whose observed values may contain errors. By accounting for various uncertainties, we introduced veracity scores that distinguish between genuine errors and natural data fluctuations, conditioned on the available covariate information in the dataset. We propose a simple yet efficient filtering procedure for eliminating potential errors, and establish theoretical guarantees for our method. We also contribute a new error detection benchmark involving 5 regression datasets with real-world numerical errors (for which the true values are also known). In this benchmark and additional simulation studies, our method identifies incorrect values with better precision/recall than other approaches.

We introduce a few-shot learning framework for error detection. We show that data augmentation (a form of weak supervision) is key to training high-quality, ML-based error detection models that require minimal human involvement. Our framework consists of two parts: (1) an expressive model to learn rich representations that capture the inherent syntactic and semantic heterogeneity of errors; and (2) a data augmentation model that, given a small seed of clean records, uses dataset-specific transformations to automatically generate additional training data. Our key insight is to learn data augmentation policies from the noisy input dataset in a weakly supervised manner. We show that our framework detects errors with an average precision of ~94% and an average recall of ~93% across a diverse array of datasets that exhibit different types and amounts of errors. We compare our approach to a comprehensive collection of error detection methods, ranging from traditional rule-based methods to ensemble-based and active learning approaches. We show that data augmentation yields an average improvement of 20 F1 points while it requires access to 3x fewer labeled examples compared to other ML approaches.

The Inversion-Denoising Paradigm, which is based on diffusion models, excels in diverse image editing and restoration tasks. We revisit its mechanism and reveal a critical, overlooked factor in reconstruction degradation: the approximate noise error. This error stems from approximating the noise at step t with the prediction at step t-1, resulting in severe error accumulation throughout the inversion process. We introduce Projection-Orthogonal Least Squares for Robust and Adaptive Inversion (POLARIS), which reformulates inversion from an error-compensation problem into an error-origin problem. Rather than optimizing embeddings or latent codes to offset accumulated drift, POLARIS treats the guidance scale ω as a step-wise variable and derives a mathematically grounded formula to minimize inversion error at each step. Remarkably, POLARIS improves inversion latent quality with just one line of code. With negligible performance overhead, it substantially mitigates noise approximation errors and consistently improves the accuracy of downstream tasks.

Despite the popularity of guitar effects, there is very little existing research on classification and parameter estimation of specific plugins or effect units from guitar recordings. In this paper, convolutional neural networks were used for classification and parameter estimation for 13 overdrive, distortion and fuzz guitar effects. A novel dataset of processed electric guitar samples was assembled, with four sub-datasets consisting of monophonic or polyphonic samples and discrete or continuous settings values, for a total of about 250 hours of processed samples. Results were compared for networks trained and tested on the same or on a different sub-dataset. We found that discrete datasets could lead to equally high performance as continuous ones, whilst being easier to design, analyse and modify. Classification accuracy was above 80\%, with confusion matrices reflecting similarities in the effects timbre and circuits design. With parameter values between 0.0 and 1.0, the mean absolute error is in most cases below 0.05, while the root mean square error is below 0.1 in all cases but one.

In this article, we study the consistency of the template estimation with the Fr\'echet mean in quotient spaces. The Fr\'echet mean in quotient spaces is often used when the observations are deformed or transformed by a group action. We show that in most cases this estimator is actually inconsistent. We exhibit a sufficient condition for this inconsistency, which amounts to the folding of the distribution of the noisy template when it is projected to the quotient space. This condition appears to be fulfilled as soon as the support of the noise is large enough. To quantify this inconsistency we provide lower and upper bounds of the bias as a function of the variability (the noise level). This shows that the consistency bias cannot be neglected when the variability increases.

Modern deep neural networks can achieve high accuracy when the training distribution and test distribution are identically distributed, but this assumption is frequently violated in practice. When the train and test distributions are mismatched, accuracy can plummet. Currently there are few techniques that improve robustness to unforeseen data shifts encountered during deployment. In this work, we propose a technique to improve the robustness and uncertainty estimates of image classifiers. We propose AugMix, a data processing technique that is simple to implement, adds limited computational overhead, and helps models withstand unforeseen corruptions. AugMix significantly improves robustness and uncertainty measures on challenging image classification benchmarks, closing the gap between previous methods and the best possible performance in some cases by more than half.

The global warehousing industry is experiencing rapid growth, with the market size projected to grow at an annual rate of 8.1% from 2024 to 2030 [Grand View Research, 2021]. This expansion has led to a surge in demand for efficient pallet detection and localisation systems. While automation can significantly streamline warehouse operations, the development of such systems often requires extensive manual data annotation, with an average of 35 seconds per image, for a typical computer vision project. This paper presents a novel approach to enhance pallet detection and localisation using purely synthetic data and geometric features derived from their side faces. By implementing a domain randomisation engine in Unity, the need for time-consuming manual annotation is eliminated while achieving high-performance results. The proposed method demonstrates a pallet detection performance of 0.995 mAP50 for single pallets on a real-world dataset. Additionally, an average position accuracy of less than 4.2 cm and an average rotation accuracy of 8.2° were achieved for pallets within a 5-meter range, with the pallet positioned head-on.

Generating accurate 3D reconstructions from endoscopic video is a promising avenue for longitudinal radiation-free analysis of sinus anatomy and surgical outcomes. Several methods for monocular reconstruction have been proposed, yielding visually pleasant 3D anatomical structures by retrieving relative camera poses with structure-from-motion-type algorithms and fusion of monocular depth estimates. However, due to the complex properties of the underlying algorithms and endoscopic scenes, the reconstruction pipeline may perform poorly or fail unexpectedly. Further, acquiring medical data conveys additional challenges, presenting difficulties in quantitatively benchmarking these models, understanding failure cases, and identifying critical components that contribute to their precision. In this work, we perform a quantitative analysis of a self-supervised approach for sinus reconstruction using endoscopic sequences paired with optical tracking and high-resolution computed tomography acquired from nine ex-vivo specimens. Our results show that the generated reconstructions are in high agreement with the anatomy, yielding an average point-to-mesh error of 0.91 mm between reconstructions and CT segmentations. However, in a point-to-point matching scenario, relevant for endoscope tracking and navigation, we found average target registration errors of 6.58 mm. We identified that pose and depth estimation inaccuracies contribute equally to this error and that locally consistent sequences with shorter trajectories generate more accurate reconstructions. These results suggest that achieving global consistency between relative camera poses and estimated depths with the anatomy is essential. In doing so, we can ensure proper synergy between all components of the pipeline for improved reconstructions that will facilitate clinical application of this innovative technology.

Generating 2-by-2 unitary matrices in floating-precision arithmetic is a delicate task. One way to reduce the accumulation error is to use less floating-point operations to compute each of the entries in the 2-by-2 unitary matrix. This paper shows an algorithm that reduces the number of operations to compute the entries of a Givens rotation. Overall, the new algorithm has more operations in total when compared to algorithms in different releases of LAPACK, but less operations per entry. Numerical tests show that the new algorithm is more accurate on average.

Flow matching generates data by integrating a learned velocity field, where the number of integration steps (NFE) directly determines inference cost. We analyze which properties of the velocity field govern integration error by decomposing the velocity Jacobian into its symmetric part S (strain rate) and antisymmetric part Omega (vorticity). We prove that strain and vorticity play different roles: strain controls exponential error amplification through the logarithmic norm, while vorticity contributes only linearly to the local truncation error. We further show that the optimal transport velocity field is irrotational and has zero material derivative, implying second-order Euler accuracy; for exact displacement interpolation, the associated Lagrangian particle dynamics are integrated exactly by Euler. Motivated by this analysis, we study weighted Jacobian regularization with strain weight alpha and vorticity weight beta. Experiments on 2D synthetic data confirm the main theoretical predictions, showing up to 2.7x lower integration error at NFE=5. Preliminary CIFAR-10 experiments show consistent trends, with a lightweight fine-tuning procedure improving FID by 14 percent at NFE=10 while preserving high-NFE quality.

The reduced basis method is a model reduction technique yielding substantial savings of computational time when a solution to a parametrized equation has to be computed for many values of the parameter. Certification of the approximation is possible by means of an a posteriori error bound. Under appropriate assumptions, this error bound is computed with an algorithm of complexity independent of the size of the full problem. In practice, the evaluation of the error bound can become very sensitive to round-off errors. We propose herein an explanation of this fact. A first remedy has been proposed in [F. Casenave, Accurate a posteriori error evaluation in the reduced basis method. C. R. Math. Acad. Sci. Paris 350 (2012) 539--542.]. Herein, we improve this remedy by proposing a new approximation of the error bound using the Empirical Interpolation Method (EIM). This method achieves higher levels of accuracy and requires potentially less precomputations than the usual formula. A version of the EIM stabilized with respect to round-off errors is also derived. The method is illustrated on a simple one-dimensional diffusion problem and a three-dimensional acoustic scattering problem solved by a boundary element method.

We develop a data-driven deep neural operator framework to approximate multiple output states for a diesel engine and generate real-time predictions with reasonable accuracy. As emission norms become more stringent, the need for fast and accurate models that enable analysis of system behavior have become an essential requirement for system development. The fast transient processes involved in the operation of a combustion engine make it difficult to develop accurate physics-based models for such systems. As an alternative to physics based models, we develop an operator-based regression model (DeepONet) to learn the relevant output states for a mean-value gas flow engine model using the engine operating conditions as input variables. We have adopted a mean-value model as a benchmark for comparison, simulated using Simulink. The developed approach necessitates using the initial conditions of the output states to predict the accurate sequence over the temporal domain. To this end, a sequence-to-sequence approach is embedded into the proposed framework. The accuracy of the model is evaluated by comparing the prediction output to ground truth generated from Simulink model. The maximum mathcal L_2 relative error observed was approximately 6.5%. The sensitivity of the DeepONet model is evaluated under simulated noise conditions and the model shows relatively low sensitivity to noise. The uncertainty in model prediction is further assessed by using a mean ensemble approach. The worst-case error at the (mu + 2sigma) boundary was found to be 12%. The proposed framework provides the ability to predict output states in real-time and enables data-driven learning of complex input-output operator mapping. As a result, this model can be applied during initial development stages, where accurate models may not be available.

Diffusion models suffer from substantial computational overhead due to their inherently iterative inference process. While feature caching offers a promising acceleration strategy by reusing intermediate outputs across timesteps, naive reuse often incurs noticeable quality degradation. In this work, we formally analyze the cumulative error introduced by caching and decompose it into two principal components: feature shift error, caused by inaccuracies in cached outputs, and step amplification error, which arises from error propagation under fixed timestep schedules. To address these issues, we propose ERTACache, a principled caching framework that jointly rectifies both error types. Our method employs an offline residual profiling stage to identify reusable steps, dynamically adjusts integration intervals via a trajectory-aware correction coefficient, and analytically approximates cache-induced errors through a closed-form residual linearization model. Together, these components enable accurate and efficient sampling under aggressive cache reuse. Extensive experiments across standard image and video generation benchmarks show that ERTACache achieves up to 2x inference speedup while consistently preserving or even improving visual quality. Notably, on the state-of-the-art Wan2.1 video diffusion model, ERTACache delivers 2x acceleration with minimal VBench degradation, effectively maintaining baseline fidelity while significantly improving efficiency. The code is available at https://github.com/bytedance/ERTACache.

Tagged magnetic resonance imaging (tMRI) has been employed for decades to measure the motion of tissue undergoing deformation. However, registration-based motion estimation from tMRI is difficult due to the periodic patterns in these images, particularly when the motion is large. With a larger motion the registration approach gets trapped in a local optima, leading to motion estimation errors. We introduce a novel "momenta, shooting, and correction" framework for Lagrangian motion estimation in the presence of repetitive patterns and large motion. This framework, grounded in Lie algebra and Lie group principles, accumulates momenta in the tangent vector space and employs exponential mapping in the diffeomorphic space for rapid approximation towards true optima, circumventing local optima. A subsequent correction step ensures convergence to true optima. The results on a 2D synthetic dataset and a real 3D tMRI dataset demonstrate our method's efficiency in estimating accurate, dense, and diffeomorphic 2D/3D motion fields amidst large motion and repetitive patterns.

In this work, we study an optimizer, Grad-Avg to optimize error functions. We establish the convergence of the sequence of iterates of Grad-Avg mathematically to a minimizer (under boundedness assumption). We apply Grad-Avg along with some of the popular optimizers on regression as well as classification tasks. In regression tasks, it is observed that the behaviour of Grad-Avg is almost identical with Stochastic Gradient Descent (SGD). We present a mathematical justification of this fact. In case of classification tasks, it is observed that the performance of Grad-Avg can be enhanced by suitably scaling the parameters. Experimental results demonstrate that Grad-Avg converges faster than the other state-of-the-art optimizers for the classification task on two benchmark datasets.

Although diffusion models (DMs) have shown promising performances in a number of tasks (e.g., speech synthesis and image generation), they might suffer from error propagation because of their sequential structure. However, this is not certain because some sequential models, such as Conditional Random Field (CRF), are free from this problem. To address this issue, we develop a theoretical framework to mathematically formulate error propagation in the architecture of DMs, The framework contains three elements, including modular error, cumulative error, and propagation equation. The modular and cumulative errors are related by the equation, which interprets that DMs are indeed affected by error propagation. Our theoretical study also suggests that the cumulative error is closely related to the generation quality of DMs. Based on this finding, we apply the cumulative error as a regularization term to reduce error propagation. Because the term is computationally intractable, we derive its upper bound and design a bootstrap algorithm to efficiently estimate the bound for optimization. We have conducted extensive experiments on multiple image datasets, showing that our proposed regularization reduces error propagation, significantly improves vanilla DMs, and outperforms previous baselines.

Human shape estimation has become increasingly important both theoretically and practically, for instance, in 3D mesh estimation, distance garment production and computational forensics, to mention just a few examples. As a further specialization, Human Body Dimensions Estimation (HBDE) focuses on estimating human body measurements like shoulder width or chest circumference from images or 3D meshes usually using supervised learning approaches. The main obstacle in this context is the data scarcity problem, as collecting this ground truth requires expensive and difficult procedures. This obstacle can be overcome by obtaining realistic human measurements from 3D human meshes. However, a) there are no well established methods to calculate HBDs from 3D meshes and b) there are no benchmarks to fairly compare results on the HBDE task. Our contribution is twofold. On the one hand, we present a method to calculate right and left arm length, shoulder width, and inseam (crotch height) from 3D meshes with focus on potential medical, virtual try-on and distance tailoring applications. On the other hand, we use four additional body dimensions calculated using recently published methods to assemble a set of eight body dimensions which we use as a supervision signal to our Neural Anthropometer: a convolutional neural network capable of estimating these dimensions. To assess the estimation, we train the Neural Anthropometer with synthetic images of 3D meshes, from which we calculated the HBDs and observed that the network's overall mean estimate error is 20.89 mm (relative error of 2.84\%). The results we present are fully reproducible and establish a fair baseline for research on the task of HBDE, therefore enabling the community with a valuable method.

Respiratory motion complicates accurate irradiation of thoraco-abdominal tumors during radiotherapy, as treatment-system latency entails target-location uncertainties. This work addresses frame forecasting in chest and liver cine MRI to compensate for such delays. We investigate RNNs trained with online learning algorithms, enabling adaptation to changing respiratory patterns via on-the-fly parameter updates, and transformers, increasingly common in time-series forecasting for their ability to capture long-term dependencies. Experiments used 12 sagittal thoracic and upper-abdominal cine-MRI sequences from ETH Zürich and OvGU; the OvGU data exhibited higher motion variability, noise, and lower contrast. PCA decomposes the Lucas-Kanade optical-flow field into static deformation modes and low-dimensional, time-dependent weights. We compare various methods for forecasting these weights: linear filters, population and sequence-specific transformer encoders, and RNNs trained with real-time recurrent learning (RTRL), unbiased online recurrent optimization, decoupled neural interfaces, and sparse one-step approximation (SnAp-1). Predicted displacements were used to warp the reference frame and generate future images. Prediction accuracy decreased with the horizon h. Linear regression performed best at short horizons (1.3mm geometrical error at h=0.32s, ETH Zürich dataset), while RTRL and SnAp-1 outperformed the other algorithms at medium-to-long horizons, with geometrical errors below 1.4mm and 2.8mm on the sequences from ETH Zürich and OvGU, respectively. The sequence-specific transformer was competitive for low-to-medium horizons, but transformers remained overall limited by data scarcity and domain shift between datasets. Predicted frames visually resembled the ground truth, with notable errors occurring near the diaphragm at end-inspiration and regions affected by out-of-plane motion.

Intra-fraction motion in radiotherapy is commonly modeled using deformable image registration (DIR). However, existing methods often struggle to balance speed and accuracy, limiting their applicability in clinical scenarios. This study introduces a novel approach that harnesses Neural Graphics Primitives (NGP) to optimize the displacement vector field (DVF). Our method leverages learned primitives, processed as splats, and interpolates within space using a shallow neural network. Uniquely, it enables self-supervised optimization at an ultra-fast speed, negating the need for pre-training on extensive datasets and allowing seamless adaptation to new cases. We validated this approach on the 4D-CT lung dataset DIR-lab, achieving a target registration error (TRE) of 1.15\pm1.15 mm within a remarkable time of 1.77 seconds. Notably, our method also addresses the sliding boundary problem, a common challenge in conventional DIR methods.

High-resolution images offer more information about scenes that can improve model accuracy. However, the dominant model architecture in computer vision, the vision transformer (ViT), cannot effectively leverage larger images without finetuning -- ViTs poorly extrapolate to more patches at test time, although transformers offer sequence length flexibility. We attribute this shortcoming to the current patch position encoding methods, which create a distribution shift when extrapolating. We propose a drop-in replacement for the position encoding of plain ViTs that restricts attention heads to fixed fields of view, pointed in different directions, using 2D attention masks. Our novel method, called LookHere, provides translation-equivariance, ensures attention head diversity, and limits the distribution shift that attention heads face when extrapolating. We demonstrate that LookHere improves performance on classification (avg. 1.6%), against adversarial attack (avg. 5.4%), and decreases calibration error (avg. 1.5%) -- on ImageNet without extrapolation. With extrapolation, LookHere outperforms the current SoTA position encoding method, 2D-RoPE, by 21.7% on ImageNet when trained at 224^2 px and tested at 1024^2 px. Additionally, we release a high-resolution test set to improve the evaluation of high-resolution image classifiers, called ImageNet-HR.

We consider in this work quantities that can be obtained as limits of powers of parametrized matrices, for instance the inverse matrix or the logarithm of the determinant. Under the assumption of affine dependence in the parameters, we use the Empirical Interpolation Method (EIM) to derive an approximation for powers of these matrices, from which we derive a nonintrusive approximation for the aforementioned limits. We derive upper bounds of the error made by the obtained formula. Finally, numerical comparisons with classical intrusive and nonintrusive approximation techniques are provided: in the considered test-cases, our algorithm performs well compared to the nonintrusive ones.

Existing optimization-based methods for non-rigid registration typically minimize an alignment error metric based on the point-to-point or point-to-plane distance between corresponding point pairs on the source surface and target surface. However, these metrics can result in slow convergence or a loss of detail. In this paper, we propose SPARE, a novel formulation that utilizes a symmetrized point-to-plane distance for robust non-rigid registration. The symmetrized point-to-plane distance relies on both the positions and normals of the corresponding points, resulting in a more accurate approximation of the underlying geometry and can achieve higher accuracy than existing methods. To solve this optimization problem efficiently, we introduce an as-rigid-as-possible regulation term to estimate the deformed normals and propose an alternating minimization solver using a majorization-minimization strategy. Moreover, for effective initialization of the solver, we incorporate a deformation graph-based coarse alignment that improves registration quality and efficiency. Extensive experiments show that the proposed method greatly improves the accuracy of non-rigid registration problems and maintains relatively high solution efficiency. The code is publicly available at https://github.com/yaoyx689/spare.

In this work we propose an analytical model that reproduces the core-bounds phase of gravitational waves (GW) of Rapidly Rotating (RR) from Core Collapse Supernovae (CCSNe), as a function of three parameters, the arrival time tau, the ratio of the kinetic and potential energy beta and a phenomenological parameter alpha related to rotation and equation of state (EOS). To validate the model we use 126 waveforms from the Richers catalog Richers_2017 selected with the criteria of exploring a range of rotation profiles, and involving EOS. To quantify the degree of accuracy of the proposed model, with a particular focus on the rotation parameter beta, we show that the average Fitting Factor (FF) between the simulated waveforms with the templates is 94.4\%. In order to estimate the parameters we propose a frequentist matched filtering approach in real interferometric noise which does not require assigning any priors. We use the Matched Filter (MF) technique, where we inject a bank of templates considering simulated colored Gaussian noise and the real noise of O3L1. For example for A300w6.00\_BHBLP at 10Kpc we obtain a standar deviation of sigma = 3.34times 10^{-3} for simulated colored Gaussian noise and sigma= 1.46times 10^{-2} for real noise. On the other hand, from the asymptotic expansion of the variance we obtain the theoretical minimum error for beta at 10 kpc and optimal orientation. The estimation error in this case is from 10^{-2} to 10^{-3} as beta increases. We show that the results of the estimation error of beta for the 3-parameter space (3D) is consistent with the single-parameter space (1D), which allows us to conclude that beta is decoupled from the others two parameters.

In location estimation, we are given n samples from a known distribution f shifted by an unknown translation lambda, and want to estimate lambda as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error mathcal N(0, 1{nmathcal I}), where mathcal I is the Fisher information of f. However, the n required for convergence depends on f, and may be arbitrarily large. We build on the theory using smoothed estimators to bound the error for finite n in terms of mathcal I_r, the Fisher information of the r-smoothed distribution. As n to infty, r to 0 at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional f to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

We identify label errors in the test sets of 10 of the most commonly-used computer vision, natural language, and audio datasets, and subsequently study the potential for these label errors to affect benchmark results. Errors in test sets are numerous and widespread: we estimate an average of at least 3.3% errors across the 10 datasets, where for example label errors comprise at least 6% of the ImageNet validation set. Putative label errors are identified using confident learning algorithms and then human-validated via crowdsourcing (51% of the algorithmically-flagged candidates are indeed erroneously labeled, on average across the datasets). Traditionally, machine learning practitioners choose which model to deploy based on test accuracy - our findings advise caution here, proposing that judging models over correctly labeled test sets may be more useful, especially for noisy real-world datasets. Surprisingly, we find that lower capacity models may be practically more useful than higher capacity models in real-world datasets with high proportions of erroneously labeled data. For example, on ImageNet with corrected labels: ResNet-18 outperforms ResNet-50 if the prevalence of originally mislabeled test examples increases by just 6%. On CIFAR-10 with corrected labels: VGG-11 outperforms VGG-19 if the prevalence of originally mislabeled test examples increases by just 5%. Test set errors across the 10 datasets can be viewed at https://labelerrors.com and all label errors can be reproduced by https://github.com/cleanlab/label-errors.

Optimal transport (OT) theory focuses, among all maps T:R^drightarrow R^d that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost c(x, T(x)) between x and its image T(x) be as small as possible. Many computational approaches have been proposed to estimate such Monge maps when c is the ell_2^2 distance, e.g., using entropic maps [Pooladian'22], or neural networks [Makkuva'20, Korotin'20]. We propose a new model for transport maps, built on a family of translation invariant costs c(x, y):=h(x-y), where h:=1{2}|cdot|_2^2+tau and tau is a regularizer. We propose a generalization of the entropic map suitable for h, and highlight a surprising link tying it with the Bregman centroids of the divergence D_h generated by h, and the proximal operator of tau. We show that choosing a sparsity-inducing norm for tau results in maps that apply Occam's razor to transport, in the sense that the displacement vectors Delta(x):= T(x)-x they induce are sparse, with a sparsity pattern that varies depending on x. We showcase the ability of our method to estimate meaningful OT maps for high-dimensional single-cell transcription data, in the 34000-d space of gene counts for cells, without using dimensionality reduction, thus retaining the ability to interpret all displacements at the gene level.

Evaluating ASR systems for Indian languages is challenging due to spelling variations, suffix splitting flexibility, and non-standard spellings in code-mixed words. Traditional Word Error Rate (WER) often presents a bleaker picture of system performance than what human users perceive. Better aligning evaluation with real-world performance requires capturing permissible orthographic variations, which is extremely challenging for under-resourced Indian languages. Leveraging recent advances in LLMs, we propose a framework for creating benchmarks that capture permissible variations. Through extensive experiments, we demonstrate that OIWER, by accounting for orthographic variations, reduces pessimistic error rates (an average improvement of 6.3 points), narrows inflated model gaps (e.g., Gemini-Canary performance difference drops from 18.1 to 11.5 points), and aligns more closely with human perception than prior methods like WER-SN by 4.9 points.

We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., ell^1 or ell^2, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.

In natural language processing, a recently popular line of work explores how to best report the experimental results of neural networks. One exemplar publication, titled "Show Your Work: Improved Reporting of Experimental Results," advocates for reporting the expected validation effectiveness of the best-tuned model, with respect to the computational budget. In the present work, we critically examine this paper. As far as statistical generalizability is concerned, we find unspoken pitfalls and caveats with this approach. We analytically show that their estimator is biased and uses error-prone assumptions. We find that the estimator favors negative errors and yields poor bootstrapped confidence intervals. We derive an unbiased alternative and bolster our claims with empirical evidence from statistical simulation. Our codebase is at http://github.com/castorini/meanmax.

The commitment to single-precision floating-point arithmetic is widespread in the deep learning community. To evaluate whether this commitment is justified, the influence of computing precision (single and double precision) on the optimization performance of the Conjugate Gradient (CG) method (a second-order optimization algorithm) and RMSprop (a first-order algorithm) has been investigated. Tests of neural networks with one to five fully connected hidden layers and moderate or strong nonlinearity with up to 4 million network parameters have been optimized for Mean Square Error (MSE). The training tasks have been set up so that their MSE minimum was known to be zero. Computing experiments have disclosed that single-precision can keep up (with superlinear convergence) with double-precision as long as line search finds an improvement. First-order methods such as RMSprop do not benefit from double precision. However, for moderately nonlinear tasks, CG is clearly superior. For strongly nonlinear tasks, both algorithm classes find only solutions fairly poor in terms of mean square error as related to the output variance. CG with double floating-point precision is superior whenever the solutions have the potential to be useful for the application goal.

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.

Text-guided diffusion models have significantly advanced image editing, enabling high-quality and diverse modifications driven by text prompts. However, effective editing requires inverting the source image into a latent space, a process often hindered by prediction errors inherent in DDIM inversion. These errors accumulate during the diffusion process, resulting in inferior content preservation and edit fidelity, especially with conditional inputs. We address these challenges by investigating the primary contributors to error accumulation in DDIM inversion and identify the singularity problem in traditional noise schedules as a key issue. To resolve this, we introduce the Logistic Schedule, a novel noise schedule designed to eliminate singularities, improve inversion stability, and provide a better noise space for image editing. This schedule reduces noise prediction errors, enabling more faithful editing that preserves the original content of the source image. Our approach requires no additional retraining and is compatible with various existing editing methods. Experiments across eight editing tasks demonstrate the Logistic Schedule's superior performance in content preservation and edit fidelity compared to traditional noise schedules, highlighting its adaptability and effectiveness.

Prior work has shown that fine-tuning models on a narrow domain with misaligned data can lead to broad misalignment - a phenomenon termed "emergent misalignment" (Betley et al. 2025). While all tested models were susceptible to emergent misalignment, some models showed more resistance than others. Specifically the Qwen-2.5 family proved to be relatively resistant, while GPT-4o exhibited the strongest misalignment. In this paper we evaluate if current-generation open-weights models exhibit similar resistance to the Qwen-2.5 family and measure misalignment robustness over a range of model architectures and scales. We replicate the effect across nine modern open-weights models (Gemma 3 and Qwen 3 families, 1B-32B parameters). Models fine-tuned on insecure code generation show a 0.68% misalignment rate (compared to 0.07% for base models), matching the lower end of prior open-model results but dramatically lower than GPT-4o's 20%. We identify a critical format-dependent vulnerability: requiring JSON output doubles misalignment rates compared to natural language prompts (0.96% vs 0.42%). This suggests that structural constraints may bypass safety training by reducing the model's 'degrees of freedom' to refuse. These findings confirm emergent misalignment as a reproducible phenomenon in modern open-weights models, with rates substantially lower than observed in proprietary systems.

Modern distributed training relies heavily on communication compression to reduce the communication overhead. In this work, we study algorithms employing a popular class of contractive compressors in order to reduce communication overhead. However, the naive implementation often leads to unstable convergence or even exponential divergence due to the compression bias. Error Compensation (EC) is an extremely popular mechanism to mitigate the aforementioned issues during the training of models enhanced by contractive compression operators. Compared to the effectiveness of EC in the data homogeneous regime, the understanding of the practicality and theoretical foundations of EC in the data heterogeneous regime is limited. Existing convergence analyses typically rely on strong assumptions such as bounded gradients, bounded data heterogeneity, or large batch accesses, which are often infeasible in modern machine learning applications. We resolve the majority of current issues by proposing EControl, a novel mechanism that can regulate error compensation by controlling the strength of the feedback signal. We prove fast convergence for EControl in standard strongly convex, general convex, and nonconvex settings without any additional assumptions on the problem or data heterogeneity. We conduct extensive numerical evaluations to illustrate the efficacy of our method and support our theoretical findings.

Instruction tuned reasoning models are increasingly deployed with safety classifiers trained on frozen embeddings, assuming representation stability across model updates. We systematically investigate this assumption and find it fails: normalized perturbations of magnitude σ=0.02 (corresponding to approx 1^circ angular drift on the embedding sphere) reduce classifier performance from 85% to 50% ROC-AUC. Critically, mean confidence only drops 14%, producing dangerous silent failures where 72% of misclassifications occur with high confidence, defeating standard monitoring. We further show that instruction-tuned models exhibit 20% worse class separability than base models, making aligned systems paradoxically harder to safeguard. Our findings expose a fundamental fragility in production AI safety architectures and challenge the assumption that safety mechanisms transfer across model versions.

Respiratory motion and the associated deformations of abdominal organs and tumors are essential information in clinical applications. However, inter- and intra-patient multi-organ deformations are complex and have not been statistically formulated, whereas single organ deformations have been widely studied. In this paper, we introduce a multi-organ deformation library and its application to deformation reconstruction based on the shape features of multiple abdominal organs. Statistical multi-organ motion/deformation models of the stomach, liver, left and right kidneys, and duodenum were generated by shape matching their region labels defined on four-dimensional computed tomography images. A total of 250 volumes were measured from 25 pancreatic cancer patients. This paper also proposes a per-region-based deformation learning using the reproducing kernel to predict the displacement of pancreatic cancer for adaptive radiotherapy. The experimental results show that the proposed concept estimates deformations better than general per-patient-based learning models and achieves a clinically acceptable estimation error with a mean distance of 1.2 pm 0.7 mm and a Hausdorff distance of 4.2 pm 2.3 mm throughout the respiratory motion.

Correctness of instance segmentation constitutes counting the number of objects, correctly localizing all predictions and classifying each localized prediction. Average Precision is the de-facto metric used to measure all these constituents of segmentation. However, this metric does not penalize duplicate predictions in the high-recall range, and cannot distinguish instances that are localized correctly but categorized incorrectly. This weakness has inadvertently led to network designs that achieve significant gains in AP but also introduce a large number of false positives. We therefore cannot rely on AP to choose a model that provides an optimal tradeoff between false positives and high recall. To resolve this dilemma, we review alternative metrics in the literature and propose two new measures to explicitly measure the amount of both spatial and categorical duplicate predictions. We also propose a Semantic Sorting and NMS module to remove these duplicates based on a pixel occupancy matching scheme. Experiments show that modern segmentation networks have significant gains in AP, but also contain a considerable amount of duplicates. Our Semantic Sorting and NMS can be added as a plug-and-play module to mitigate hedged predictions and preserve AP.

We revisit the theoretical properties of Hamiltonian stochastic differential equations (SDES) for Bayesian posterior sampling, and we study the two types of errors that arise from numerical SDE simulation: the discretization error and the error due to noisy gradient estimates in the context of data subsampling. Our main result is a novel analysis for the effect of mini-batches through the lens of differential operator splitting, revising previous literature results. The stochastic component of a Hamiltonian SDE is decoupled from the gradient noise, for which we make no normality assumptions. This leads to the identification of a convergence bottleneck: when considering mini-batches, the best achievable error rate is O(eta^2), with eta being the integrator step size. Our theoretical results are supported by an empirical study on a variety of regression and classification tasks for Bayesian neural networks.

Equivariance theory predicts that an architectural symmetry prior reduces sample complexity by a factor of |G|; this is widely cited but rarely measured as a scaling law with controls that separate the prior from its confounds. On a controlled C_n-symmetric task, we report three findings. First, a wrong-group control with identical orbit size and matched compute is worse than no constraint (joint pairwise CI [+0.79, +3.26] excludes zero, robust across estimators); misaligned constraint is actively harmful, not merely unhelpful. Second, an augmentation baseline equipped with test-time orbit averaging matches the equivariant model exactly -- bit-identical per-epoch validation curves across matched cells -- so the architecture-vs-augmentation gap is conditional on asymmetric test-time computation, not unconditional. Third, the relative exchange rate beta_diff = 1.28 is consistent in sign and order of magnitude with the theoretical 1.0 (single-level CI [+0.92, +2.05]); the more conservative two-level bootstrap (seeds x group sizes) widens this to [-0.63, +1.72], including zero, and a finer-N replication on a sqrt(2)-spaced grid is inconclusive (point estimate -0.82). The methodological contributions -- the relative-rate estimator that cancels the shared-difficulty confound, the wrong-group control, and a pre-specified failure taxonomy -- transfer to any inductive bias whose strength can be parameterised. Honest scoping: the primary estimator beta_diff was adopted post-hoc after the initial analysis revealed a positive-slope identifiability problem; the design was never externally pre-registered; and the headline number rests on an OLS slope over seven group sizes on a coarse N grid. This is an exploratory study, not a confirmatory measurement; the wrong-group result is the cleanest finding and the one we report with the most confidence. A registered replication on fresh seeds is future work.

Automatic age estimation is widely used for age verification, where input images often vary considerably in resolution. This study evaluates the effect of image resolution on age estimation accuracy using DeepFace and InsightFace. A total of 1000 images from the IMDB-Clean dataset were processed in seven resolutions, resulting in 7000 test samples. Performance was evaluated using Mean Absolute Error (MAE), Standard Deviation (SD), and Median Absolute Error (MedAE). Based on this study, we conclude that input image resolution has a clear and consistent impact on the accuracy of age estimation in both DeepFace and InsightFace. Both frameworks achieve optimal performance at 224x224 pixels, with an MAE of 10.83 years (DeepFace) and 7.46 years (InsightFace). At low resolutions, MAE increases substantially, while very high resolutions also degrade accuracy. InsightFace is consistently faster than DeepFace across all resolutions.

Large language models frequently fail to produce correct code on their first attempt, yet most benchmarks evaluate them in a single-shot setting. We investigate iterative self-repair (feeding execution errors back to the model for correction) across seven models spanning three families and both open-weight and proprietary providers: Llama 3.1 8B, Llama 3.3 70B, Llama 4 Scout (MoE, 16 experts), Llama 4 Maverick (MoE, 128 experts), Qwen3 32B, Gemini 2.5 Flash, and Gemini 2.5 Pro. On HumanEval (164 problems) and MBPP Sanitized (257 problems) with up to five attempts, self-repair universally improves pass rates: +4.9 to +17.1 pp on HumanEval and +16.0 to +30.0 pp on MBPP. Gemini 2.5 Flash achieves the highest final pass rates (96.3% HumanEval, 93.8% MBPP). Most gains concentrate in the first two rounds.Error-type analysis shows assertion errors (logical mistakes) are the hardest to repair at ~45%, while syntax and name errors are repaired at substantially higher rates, connecting to broader findings on the limits of LLM self-correction. Prior work found that weaker models fail at self-repair or require fine-tuning; we show that modern instruction-tuned models succeed with prompting alone, even at 8B scale. We also provide the first comparison of dense and MoE architectures for self-repair, and extend the repair-vs-resampling tradeoff analysis to modern models. A prompt ablation reveals chain-of-thought repair yields up to +5.5 pp additional self-repair gain (measured as improvement in repair delta) over minimal prompting for capable models.

Real-world machine learning deployments are characterized by mismatches between the source (training) and target (test) distributions that may cause performance drops. In this work, we investigate methods for predicting the target domain accuracy using only labeled source data and unlabeled target data. We propose Average Thresholded Confidence (ATC), a practical method that learns a threshold on the model's confidence, predicting accuracy as the fraction of unlabeled examples for which model confidence exceeds that threshold. ATC outperforms previous methods across several model architectures, types of distribution shifts (e.g., due to synthetic corruptions, dataset reproduction, or novel subpopulations), and datasets (Wilds, ImageNet, Breeds, CIFAR, and MNIST). In our experiments, ATC estimates target performance 2-4times more accurately than prior methods. We also explore the theoretical foundations of the problem, proving that, in general, identifying the accuracy is just as hard as identifying the optimal predictor and thus, the efficacy of any method rests upon (perhaps unstated) assumptions on the nature of the shift. Finally, analyzing our method on some toy distributions, we provide insights concerning when it works. Code is available at https://github.com/saurabhgarg1996/ATC_code/.

Tissue tracking in echocardiography is challenging due to the complex cardiac motion and the inherent nature of ultrasound acquisitions. Although optical flow methods are considered state-of-the-art (SOTA), they struggle with long-range tracking, noise occlusions, and drift throughout the cardiac cycle. Recently, novel learning-based point tracking techniques have been introduced to tackle some of these issues. In this paper, we build upon these techniques and introduce EchoTracker, a two-fold coarse-to-fine model that facilitates the tracking of queried points on a tissue surface across ultrasound image sequences. The architecture contains a preliminary coarse initialization of the trajectories, followed by reinforcement iterations based on fine-grained appearance changes. It is efficient, light, and can run on mid-range GPUs. Experiments demonstrate that the model outperforms SOTA methods, with an average position accuracy of 67% and a median trajectory error of 2.86 pixels. Furthermore, we show a relative improvement of 25% when using our model to calculate the global longitudinal strain (GLS) in a clinical test-retest dataset compared to other methods. This implies that learning-based point tracking can potentially improve performance and yield a higher diagnostic and prognostic value for clinical measurements than current techniques. Our source code is available at: https://github.com/riponazad/echotracker/.

The growing body of research shows how to replace classical partial differential equation (PDE) integrators with neural networks. The popular strategy is to generate the input-output pairs with a PDE solver, train the neural network in the regression setting, and use the trained model as a cheap surrogate for the solver. The bottleneck in this scheme is the number of expensive queries of a PDE solver needed to generate the dataset. To alleviate the problem, we propose a computationally cheap augmentation strategy based on general covariance and simple random coordinate transformations. Our approach relies on the fact that physical laws are independent of the coordinate choice, so the change in the coordinate system preserves the type of a parametric PDE and only changes PDE's data (e.g., initial conditions, diffusion coefficient). For tried neural networks and partial differential equations, proposed augmentation improves test error by 23% on average. The worst observed result is a 17% increase in test error for multilayer perceptron, and the best case is a 80% decrease for dilated residual network.

Surface normal estimation from a single image is an important task in 3D scene understanding. In this paper, we address two limitations shared by the existing methods: the inability to estimate the aleatoric uncertainty and lack of detail in the prediction. The proposed network estimates the per-pixel surface normal probability distribution. We introduce a new parameterization for the distribution, such that its negative log-likelihood is the angular loss with learned attenuation. The expected value of the angular error is then used as a measure of the aleatoric uncertainty. We also present a novel decoder framework where pixel-wise multi-layer perceptrons are trained on a subset of pixels sampled based on the estimated uncertainty. The proposed uncertainty-guided sampling prevents the bias in training towards large planar surfaces and improves the quality of prediction, especially near object boundaries and on small structures. Experimental results show that the proposed method outperforms the state-of-the-art in ScanNet and NYUv2, and that the estimated uncertainty correlates well with the prediction error. Code is available at https://github.com/baegwangbin/surface_normal_uncertainty.

We introduce a novel method for measuring properties of periodic phenomena with an event camera, a device asynchronously reporting brightness changes at independently operating pixels. The approach assumes that for fast periodic phenomena, in any spatial window where it occurs, a very similar set of events is generated at the time difference corresponding to the frequency of the motion. To estimate the frequency, we compute correlations of spatio-temporal windows in the event space. The period is calculated from the time differences between the peaks of the correlation responses. The method is contactless, eliminating the need for markers, and does not need distinguishable landmarks. We evaluate the proposed method on three instances of periodic phenomena: (i) light flashes, (ii) vibration, and (iii) rotational speed. In all experiments, our method achieves a relative error lower than 0.04%, which is within the error margin of ground truth measurements.

This paper measures hour-of-day effects, filter precision, fragility, and realised yield in a 15-day paper-traded deployment of an autonomous memecoin trading system on Solana decentralised exchanges. The 190-trade sample (March 29 to April 12, 2026) shows a 40.5 percent win rate, mean per-trade return of +0.62 percent, cumulative +117.7 percent (net SOL +0.039), skewness -1.21, excess kurtosis 6.61. A Mann-Whitney U test of three poorest-performing UTC hours (2, 13, 23) against the others yields U = 1,274, p = 0.22; directional but not significant at n = 190. The three hours were selected in-sample, so the comparison is exploratory, not confirmatory. A parallel counterfactual rejection-tracking system collected 4,874 forward-sample observations across 184 distinct rejection events. Of those events, 17.9 percent reached a 50 percent drawdown from reference within 24 hours; 26.0 percent of forward samples recorded the rejected token below half-reference. The filter stack avoided these realised drawdowns: evidence that the rejection criteria are net-positive against forward-market outcomes. Fragility is the principal caveat. Removing the top three trades (1.6 percent of sample) flips cumulative return unprofitable. Profitability rests on a small number of large winners and is structurally fragile. The dataset and audit script are deposited under CC-BY-4.0 (Zenodo DOI 10.5281/zenodo.20043302).

In this paper, we describe a feedforward artificial neural network trained on the ImageNet 2012 contest dataset [7] with the new method of [5] to an accuracy rate of 98.3% with a 99.69 Top-1 rate, and an average of 285.9 labels that are perfectly classified over the 10 batch partitions of the dataset. The best performing model uses 322,430,160 parameters, with 4 decimal places precision. We conjecture that the reason our model does not achieve a 100% accuracy rate is due to a double-labeling problem, by which there are duplicate images in the dataset with different labels.

Automatic speech recognition replaces typing only when correction costs less than manual entry, a threshold determined by error types, not counts: fixing a misrecognized domain term costs far more than inserting a comma. Word error rate (WER) fails on two fronts: it collapses distinct error categories into a single scalar, and it structurally penalizes agglutinative languages where valid sandhi merges inflate scores. We introduce SCRIBE, a diagnostic framework that provides categorical error decomposition into lexical, punctuation, numeral, and domain-entity rates through sandhi-tolerant alignment with domain vocabulary injection. Human validation confirms SCRIBE aligns with expert judgment where WER does not. We release SCRIBE, an LLM curation pipeline, benchmarks, and open-weight rich transcription models for Hindi, Malayalam, and Kannada.

Chinchilla Approach 2 is among the most widely used methods for fitting neural scaling laws. Its parabolic approximation introduces systematic biases in compute-optimal allocation estimates, even on noise-free synthetic data. Applied to published Llama 3 IsoFLOP data at open frontier compute scales, these biases imply a parameter underallocation corresponding to 6.5% of the 3.8times10^{25} FLOP training budget and \1.4M (90% CI: 412K-\2.9M) in unnecessary compute at 50% H100 MFU. Simulated multimodal model misallocations show even greater opportunity costs due to higher loss surface asymmetry. Three sources of this error are examined: IsoFLOP sampling grid width (Taylor approximation accuracy), uncentered IsoFLOP sampling, and loss surface asymmetry (α\neq β$). Chinchilla Approach 3 largely eliminates these biases but is often regarded as less data-efficient, numerically unstable, prone to local minima, and harder to implement. Each concern is shown to be unfounded or addressable, especially when the partially linear structure of the objective is exploited via Variable Projection, enabling unbiased inference on all five loss surface parameters through a two-dimensional optimization that is well-conditioned, analytically differentiable, and amenable to dense, or even exhaustive, grid search. It may serve as a more convenient replacement for Approach 2 or a more scalable alternative for adaptations of Approach 3 to richer scaling law formulations.

We introduce four new real-world distribution shift datasets consisting of changes in image style, image blurriness, geographic location, camera operation, and more. With our new datasets, we take stock of previously proposed methods for improving out-of-distribution robustness and put them to the test. We find that using larger models and artificial data augmentations can improve robustness on real-world distribution shifts, contrary to claims in prior work. We find improvements in artificial robustness benchmarks can transfer to real-world distribution shifts, contrary to claims in prior work. Motivated by our observation that data augmentations can help with real-world distribution shifts, we also introduce a new data augmentation method which advances the state-of-the-art and outperforms models pretrained with 1000 times more labeled data. Overall we find that some methods consistently help with distribution shifts in texture and local image statistics, but these methods do not help with some other distribution shifts like geographic changes. Our results show that future research must study multiple distribution shifts simultaneously, as we demonstrate that no evaluated method consistently improves robustness.

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.

Vision-language models (VLMs) achieve strong performance on standard, high-quality datasets, but we still do not fully understand how they perform under real-world image distortions. We present VLM-RobustBench, a benchmark spanning 49 augmentation types across noise, blur, weather, digital, and geometric perturbations, evaluated under graded severities (low/mid/high) and binary transforms, yielding 133 corrupted settings. We evaluate VLMs from four families (Qwen, InternVL, Molmo, Gemma) on two complementary benchmarks: MMBench (visually grounded) and MMMU-Pro (reasoning-oriented). Our results reveal that visual severity is a weak predictor of difficulty: low-severity spatial perturbations often degrade performance more than visually severe photometric corruptions. In particular, low-severity glass_blur reduces MMBench accuracy by about 8 pp on average across models, while the largest drops arise from resampling and geometric distortions (e.g., upsample, elastic_transform), reaching up to 34 pp. Overall, our findings suggest current VLMs are semantically strong but spatially fragile, motivating the definition of novel robustness evaluation protocols and training regimes that emphasize resampling and geometric invariances.

Optimal transport (OT) aims to find a map T that transports mass from one probability measure to another while minimizing a cost function. Recently, neural OT solvers have gained popularity in high dimensional biological applications such as drug perturbation, due to their superior computational and memory efficiency compared to traditional exact Sinkhorn solvers. However, the overly complex high dimensional maps learned by neural OT solvers often suffer from poor interpretability. Prior work addressed this issue in the context of exact OT solvers by introducing displacement-sparse maps via designed elastic cost, but such method failed to be applied to neural OT settings. In this work, we propose an intuitive and theoretically grounded approach to learning displacement-sparse maps within neural OT solvers. Building on our new formulation, we introduce a novel smoothed ell_0 regularizer that outperforms the ell_1 based alternative from prior work. Leveraging Input Convex Neural Network's flexibility, we further develop a heuristic framework for adaptively controlling sparsity intensity, an approach uniquely enabled by the neural OT paradigm. We demonstrate the necessity of this adaptive framework in large-scale, high-dimensional training, showing not only improved accuracy but also practical ease of use for downstream applications.

Optical Character Recognition (OCR) of eighteenth-century printed texts remains challenging due to degraded print quality, archaic glyphs, and non-standardized orthography. Although transformer-based OCR systems and Vision-Language Models (VLMs) achieve strong aggregate accuracy, metrics such as Character Error Rate (CER) and Word Error Rate (WER) provide limited insight into their reliability for scholarly use. We compare a dedicated OCR transformer (TrOCR) and a general-purpose Vision-Language Model (Qwen) on line-level historical English texts using length-weighted accuracy metrics and hypothesis driven error analysis. While Qwen achieves lower CER/WER and greater robustness to degraded input, it exhibits selective linguistic regularization and orthographic normalization that may silently alter historically meaningful forms. TrOCR preserves orthographic fidelity more consistently but is more prone to cascading error propagation. Our findings show that architectural inductive biases shape OCR error structure in systematic ways. Models with similar aggregate accuracy can differ substantially in error locality, detectability, and downstream scholarly risk, underscoring the need for architecture-aware evaluation in historical digitization workflows.

Can a diffusion model produce its own "mental average" of a concept-one that is as sharp and realistic as a typical sample? We introduce Diffusion Mental Averages (DMA), a model-centric answer to this question. While prior methods aim to average image collections, they produce blurry results when applied to diffusion samples from the same prompt. These data-centric techniques operate outside the model, ignoring the generative process. In contrast, DMA averages within the diffusion model's semantic space, as discovered by recent studies. Since this space evolves across timesteps and lacks a direct decoder, we cast averaging as trajectory alignment: optimize multiple noise latents so their denoising trajectories progressively converge toward shared coarse-to-fine semantics, yielding a single sharp prototype. We extend our approach to multimodal concepts (e.g., dogs with many breeds) by clustering samples in semantically-rich spaces such as CLIP and applying Textual Inversion or LoRA to bridge CLIP clusters into diffusion space. This is, to our knowledge, the first approach that delivers consistent, realistic averages, even for abstract concepts, serving as a concrete visual summary and a lens into model biases and concept representation.

Hoffmann et al. (2022) propose three methods for estimating a compute-optimal scaling law. We attempt to replicate their third estimation procedure, which involves fitting a parametric loss function to a reconstruction of data from their plots. We find that the reported estimates are inconsistent with their first two estimation methods, fail at fitting the extracted data, and report implausibly narrow confidence intervals--intervals this narrow would require over 600,000 experiments, while they likely only ran fewer than 500. In contrast, our rederivation of the scaling law using the third approach yields results that are compatible with the findings from the first two estimation procedures described by Hoffmann et al.

Functional magnetic resonance imaging techniques benefit from echo-planar imaging's fast image acquisition but are susceptible to inhomogeneities in the main magnetic field, resulting in geometric distortion and signal loss artifacts in the images. Traditional methods leverage a field map or voxel displacement map for distortion correction. However, voxel displacement map estimation requires additional sequence acquisitions, and the accuracy of the estimation influences correction performance. This work implements a novel approach called GDCNet, which estimates a geometric distortion map by non-linear registration to T1-weighted anatomical images and applies it for distortion correction. GDCNet demonstrated fast distortion correction of functional images in retrospectively and prospectively acquired datasets. Among the compared models, the 2D self-supervised configuration resulted in a statistically significant improvement to normalized mutual information between distortion-corrected functional and T1-weighted images compared to the benchmark methods FUGUE and TOPUP. Furthermore, GDCNet models achieved processing speeds 14 times faster than TOPUP in the prospective dataset.

We expect the generalization error to improve with more samples from a similar task, and to deteriorate with more samples from an out-of-distribution (OOD) task. In this work, we show a counter-intuitive phenomenon: the generalization error of a task can be a non-monotonic function of the number of OOD samples. As the number of OOD samples increases, the generalization error on the target task improves before deteriorating beyond a threshold. In other words, there is value in training on small amounts of OOD data. We use Fisher's Linear Discriminant on synthetic datasets and deep networks on computer vision benchmarks such as MNIST, CIFAR-10, CINIC-10, PACS and DomainNet to demonstrate and analyze this phenomenon. In the idealistic setting where we know which samples are OOD, we show that these non-monotonic trends can be exploited using an appropriately weighted objective of the target and OOD empirical risk. While its practical utility is limited, this does suggest that if we can detect OOD samples, then there may be ways to benefit from them. When we do not know which samples are OOD, we show how a number of go-to strategies such as data-augmentation, hyper-parameter optimization, and pre-training are not enough to ensure that the target generalization error does not deteriorate with the number of OOD samples in the dataset.

We propose a principled and effective framework for one-step generative modeling. We introduce the notion of average velocity to characterize flow fields, in contrast to instantaneous velocity modeled by Flow Matching methods. A well-defined identity between average and instantaneous velocities is derived and used to guide neural network training. Our method, termed the MeanFlow model, is self-contained and requires no pre-training, distillation, or curriculum learning. MeanFlow demonstrates strong empirical performance: it achieves an FID of 3.43 with a single function evaluation (1-NFE) on ImageNet 256x256 trained from scratch, significantly outperforming previous state-of-the-art one-step diffusion/flow models. Our study substantially narrows the gap between one-step diffusion/flow models and their multi-step predecessors, and we hope it will motivate future research to revisit the foundations of these powerful models.

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.

We study uncertainty quantification for partial differential equations subject to domain uncertainty. We parameterize the random domain using the model recently considered by Chernov and Le (2024) as well as Harbrecht, Schmidlin, and Schwab (2024) in which the input random field is assumed to belong to a Gevrey smoothness class. This approach has the advantage of being substantially more general than models which assume a particular parametric representation of the input random field such as a Karhunen-Loeve series expansion. We consider both the Poisson equation as well as the heat equation and design randomly shifted lattice quasi-Monte Carlo (QMC) cubature rules for the computation of the expected solution under domain uncertainty. We show that these QMC rules exhibit dimension-independent, essentially linear cubature convergence rates in this framework. In addition, we complete the error analysis by taking into account the approximation errors incurred by dimension truncation of the random input field and finite element discretization. Numerical experiments are presented to confirm the theoretical rates.

The asymptotically precise estimation of the generalization of kernel methods has recently received attention due to the parallels between neural networks and their associated kernels. However, prior works derive such estimates for training by kernel ridge regression (KRR), whereas neural networks are typically trained with gradient descent (GD). In the present work, we consider the training of kernels with a family of spectral algorithms specified by profile h(lambda), and including KRR and GD as special cases. Then, we derive the generalization error as a functional of learning profile h(lambda) for two data models: high-dimensional Gaussian and low-dimensional translation-invariant model. Under power-law assumptions on the spectrum of the kernel and target, we use our framework to (i) give full loss asymptotics for both noisy and noiseless observations (ii) show that the loss localizes on certain spectral scales, giving a new perspective on the KRR saturation phenomenon (iii) conjecture, and demonstrate for the considered data models, the universality of the loss w.r.t. non-spectral details of the problem, but only in case of noisy observation.

The rapid advancement of diffusion models has significantly improved high-quality image generation, making generated content increasingly challenging to distinguish from real images and raising concerns about potential misuse. In this paper, we observe that diffusion models struggle to accurately reconstruct mid-band frequency information in real images, suggesting the limitation could serve as a cue for detecting diffusion model generated images. Motivated by this observation, we propose a novel method called Frequency-guided Reconstruction Error (FIRE), which, to the best of our knowledge, is the first to investigate the influence of frequency decomposition on reconstruction error. FIRE assesses the variation in reconstruction error before and after the frequency decomposition, offering a robust method for identifying diffusion model generated images. Extensive experiments show that FIRE generalizes effectively to unseen diffusion models and maintains robustness against diverse perturbations.

We present a hardware-oriented description of GoldenFloat (GF), a static-split floating-point family generated by a single closed rule, and three concrete artefacts: (i) an open multi-width RTL generator covering GF4-GF256 with a continuous-integration differential sweep against a correctly-rounded reference; (ii) an integer-backed Lucas-exact accumulator path verified at 500-digit precision for n = 1, ..., 256; and (iii) a GF16 FPGA codec passing a 35-of-35 testbench at 323 MHz on Artix-7 (Xilinx XC7A35T). For each total width N >= 4, the exponent width is e = round((N-1)/phi^2) with fraction f = N-1-e and phi = (1+sqrt(5))/2. The rule reproduces the realised exponent widths of nine formats (9/9) and extends consistently to GF128, GF512, GF1024. The rule is positioned alongside posit, takum, OCP-MX, and the IEEE P3109 multi-width float draft. We make no per-rung accuracy or superiority claim against any of them. The breadth/toolchain-coherence framing is recorded as an open conjecture with a pre-registered falsification path. A falsification ledger (FL-002) records open questions and the experiments that would settle them. An RTL-correctness erratum dated 2026-05-31 is reported; the fabricated TTSKY26b dies carry the defective multiplier portfolio, and the corrected generator is the regeneration baseline.

In phase-shifting profilometry (PSP), any motion during the acquisition of fringe patterns can introduce errors because it assumes both the object and measurement system are stationary. Therefore, we propose a method to pixel-wise reduce the errors when the measurement system is in motion due to a motorized linear stage. The proposed method introduces motion-induced error reduction algorithm, which leverages the motor's encoder and pinhole model of the camera and projector. 3D shape measurement is possible with only three fringe patterns by applying geometric constraints of the digital fringe projection system. We address the mismatch problem due to the motion-induced camera pixel disparities and reduce phase-shift errors. These processes are easy to implement and require low computational cost. Experimental results demonstrate that the presented method effectively reduces the errors even in non-uniform motion.

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

Asphalt concrete's (AC) durability and maintenance demands are strongly influenced by its fatigue life. Traditional methods for determining this characteristic are both resource-intensive and time-consuming. This study employs artificial neural networks (ANNs) to predict AC fatigue life, focusing on the impact of strain level, binder content, and air-void content. Leveraging a substantial dataset, we tailored our models to effectively handle the wide range of fatigue life data, typically represented on a logarithmic scale. The mean square logarithmic error was utilized as the loss function to enhance prediction accuracy across all levels of fatigue life. Through comparative analysis of various hyperparameters, we developed a machine-learning model that captures the complex relationships within the data. Our findings demonstrate that higher binder content significantly enhances fatigue life, while the influence of air-void content is more variable, depending on binder levels. Most importantly, this study provides insights into the intricacies of using ANNs for modeling, showcasing their potential utility with larger datasets. The codes developed and the data used in this study are provided as open source on a GitHub repository, with a link included in the paper for full access.

Automatic evaluation metrics are central to the development of machine translation systems, yet their robustness under domain shift remains unclear. Most metrics are developed on the Workshop on Machine Translation (WMT) benchmarks, raising concerns about their robustness to unseen domains. Prior studies that analyze unseen domains vary translation systems, annotators, or evaluation conditions, confounding domain effects with human annotation noise. To address these biases, we introduce a systematic multi-annotator Cross-Domain Error-Span-Annotation dataset (CD-ESA), comprising 18.8k human error span annotations across three language pairs, where we fix annotators within each language pair and evaluate translations of the same six translation systems across one seen news domain and two unseen technical domains. Using this dataset, we first find that automatic metrics appear surprisingly robust to domain-shifts at the segment level (up to 0.69 agreement), but this robustness largely disappears once we account for human label variation. Averaging annotations increases inter-annotator agreement by up to +0.11. Metrics struggle on the unseen chemical domain compared to humans (inter-annotator agreement of 0.78-0.83 vs. 0.96). We recommend comparing metric-human agreement against inter-annotator agreement, rather than comparing raw metric-human agreement alone, when evaluating across different domains.

By design, average precision (AP) for object detection aims to treat all classes independently: AP is computed independently per category and averaged. On one hand, this is desirable as it treats all classes equally. On the other hand, it ignores cross-category confidence calibration, a key property in real-world use cases. Unfortunately, under important conditions (i.e., large vocabulary, high instance counts) the default implementation of AP is neither category independent, nor does it directly reward properly calibrated detectors. In fact, we show that on LVIS the default implementation produces a gameable metric, where a simple, un-intuitive re-ranking policy can improve AP by a large margin. To address these limitations, we introduce two complementary metrics. First, we present a simple fix to the default AP implementation, ensuring that it is independent across categories as originally intended. We benchmark recent LVIS detection advances and find that many reported gains do not translate to improvements under our new evaluation, suggesting recent improvements may arise from difficult to interpret changes to cross-category rankings. Given the importance of reliably benchmarking cross-category rankings, we consider a pooled version of AP (AP-Pool) that rewards properly calibrated detectors by directly comparing cross-category rankings. Finally, we revisit classical approaches for calibration and find that explicitly calibrating detectors improves state-of-the-art on AP-Pool by 1.7 points

In the reduced basis method, the evaluation of the a posteriori estimator can become very sensitive to round-off errors. In this note, the origin of the loss of accuracy is revealed, and a solution to this problem is proposed and illustrated on a simple example.

In this paper, we focus on quantifying model stability as a function of random seed by investigating the effects of the induced randomness on model performance and the robustness of the model in general. We specifically perform a controlled study on the effect of random seeds on the behaviour of attention, gradient-based and surrogate model based (LIME) interpretations. Our analysis suggests that random seeds can adversely affect the consistency of models resulting in counterfactual interpretations. We propose a technique called Aggressive Stochastic Weight Averaging (ASWA)and an extension called Norm-filtered Aggressive Stochastic Weight Averaging (NASWA) which improves the stability of models over random seeds. With our ASWA and NASWA based optimization, we are able to improve the robustness of the original model, on average reducing the standard deviation of the model's performance by 72%.

We provide a new theoretical framework for the variable-step deferred correction (DC) methods based on the well-known BDF2 formula. By using the discrete orthogonal convolution kernels, some high-order BDF2-DC methods are proven to be stable on arbitrary time grids according to the recent definition of stability (SINUM, 60: 2253-2272). It significantly relaxes the existing step-ratio restrictions for the BDF2-DC methods (BIT, 62: 1789-1822). The associated sharp error estimates are established by taking the numerical effects of the starting approximations into account, and they suggest that the BDF2-DC methods have no aftereffect, that is, the lower-order starting scheme for the BDF2 scheme will not cause a loss in the accuracy of the high-order BDF2-DC methods. Extensive tests on the graded and random time meshes are presented to support the new theory.

Reduced numerical precision is a common technique to reduce computational cost in many Deep Neural Networks (DNNs). While it has been observed that DNNs are resilient to small errors and noise, no general result exists that is capable of predicting a given DNN system architecture's sensitivity to reduced precision. In this project, we emulate arbitrary bit-width using a specified floating-point representation with a truncation method, which is applied to the neural network after each batch. We explore the impact of several model parameters on the network's training accuracy and show results on the MNIST dataset. We then present a preliminary theoretical investigation of the error scaling in both forward and backward propagations. We end with a discussion of the implications of these results as well as the potential for generalization to other network architectures.

We study the problem of optimizing a function under a budgeted number of evaluations. We only assume that the function is locally smooth around one of its global optima. The difficulty of optimization is measured in terms of 1) the amount of noise b of the function evaluation and 2) the local smoothness, d, of the function. A smaller d results in smaller optimization error. We come with a new, simple, and parameter-free approach. First, for all values of b and d, this approach recovers at least the state-of-the-art regret guarantees. Second, our approach additionally obtains these results while being agnostic to the values of both b and d. This leads to the first algorithm that naturally adapts to an unknown range of noise b and leads to significant improvements in a moderate and low-noise regime. Third, our approach also obtains a remarkable improvement over the state-of-the-art SOO algorithm when the noise is very low which includes the case of optimization under deterministic feedback (b=0). There, under our minimal local smoothness assumption, this improvement is of exponential magnitude and holds for a class of functions that covers the vast majority of functions that practitioners optimize (d=0). We show that our algorithmic improvement is borne out in experiments as we empirically show faster convergence on common benchmarks.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Particle gradient descent, which uses particles to represent a probability measure and performs gradient descent on particles in parallel, is widely used to optimize functions of probability measures. This paper considers particle gradient descent with a finite number of particles and establishes its theoretical guarantees to optimize functions that are displacement convex in measures. Concretely, for Lipschitz displacement convex functions defined on probability over R^d, we prove that O(1/epsilon^2) particles and O(d/epsilon^4) computations are sufficient to find the epsilon-optimal solutions. We further provide improved complexity bounds for optimizing smooth displacement convex functions. We demonstrate the application of our results for function approximation with specific neural architectures with two-dimensional inputs.

Introduction: Mechanical thrombectomy can cause vessel deformation and procedure-related injury. Benchtop models are widely used for device testing, but time-resolved, full-field 3D vessel-motion measurements remain limited. Methods: We developed a nine-camera, low-cost multi-view workflow for benchtop thrombectomy in silicone middle cerebral artery phantoms (2160p, 20 fps). Multi-view videos were calibrated, segmented, and reconstructed with 4D Gaussian Splatting. Reconstructed point clouds were converted to fixed-connectivity edge graphs for region-of-interest (ROI) displacement tracking and a relative surface-based stress proxy. Stress-proxy values were derived from edge stretch using a Neo-Hookean mapping and reported as comparative surface metrics. A synthetic Blender pipeline with known deformation provided geometric and temporal validation. Results: In synthetic bulk translation, the stress proxy remained near zero for most edges (median approx 0 MPa; 90th percentile 0.028 MPa), with sparse outliers. In synthetic pulling (1-5 mm), reconstruction showed close geometric and temporal agreement with ground truth, with symmetric Chamfer distance of 1.714-1.815 mm and precision of 0.964-0.972 at τ= 1 mm. In preliminary benchtop comparative trials (one trial per condition), cervical aspiration catheter placement showed higher max-median ROI displacement and stress-proxy values than internal carotid artery terminus placement. Conclusion: The proposed protocol provides standardized, time-resolved surface kinematics and comparative relative displacement and stress proxy measurements for thrombectomy benchtop studies. The framework supports condition-to-condition comparisons and methods validation, while remaining distinct from absolute wall-stress estimation. Implementation code and example data are available at https://ethanuser.github.io/vessel4D

Video generators are increasingly evaluated as potential world models, which requires them to encode and understand physical laws. We investigate their representation of a fundamental law: gravity. Out-of-the-box video generators consistently generate objects falling at an effectively slower acceleration. However, these physical tests are often confounded by ambiguous metric scale. We first investigate if observed physical errors are artifacts of these ambiguities (e.g., incorrect frame rate assumptions). We find that even temporal rescaling cannot correct the high-variance gravity artifacts. To rigorously isolate the underlying physical representation from these confounds, we introduce a unit-free, two-object protocol that tests the timing ratio t_1^2/t_2^2 = h_1/h_2, a relationship independent of g, focal length, and scale. This relative test reveals violations of Galileo's equivalence principle. We then demonstrate that this physical gap can be partially mitigated with targeted specialization. A lightweight low-rank adaptor fine-tuned on only 100 single-ball clips raises g_{eff} from 1.81,m/s^2 to 6.43,m/s^2 (reaching 65% of terrestrial gravity). This specialist adaptor also generalizes zero-shot to two-ball drops and inclined planes, offering initial evidence that specific physical laws can be corrected with minimal data.

3D anomaly detection plays a crucial role in monitoring parts for localized inherent defects in precision manufacturing. Embedding-based and reconstruction-based approaches are among the most popular and successful methods. However, there are two major challenges to the practical application of the current approaches: 1) the embedded models suffer the prohibitive computational and storage due to the memory bank structure; 2) the reconstructive models based on the MAE mechanism fail to detect anomalies in the unmasked regions. In this paper, we propose R3D-AD, reconstructing anomalous point clouds by diffusion model for precise 3D anomaly detection. Our approach capitalizes on the data distribution conversion of the diffusion process to entirely obscure the input's anomalous geometry. It step-wisely learns a strict point-level displacement behavior, which methodically corrects the aberrant points. To increase the generalization of the model, we further present a novel 3D anomaly simulation strategy named Patch-Gen to generate realistic and diverse defect shapes, which narrows the domain gap between training and testing. Our R3D-AD ensures a uniform spatial transformation, which allows straightforwardly generating anomaly results by distance comparison. Extensive experiments show that our R3D-AD outperforms previous state-of-the-art methods, achieving 73.4% Image-level AUROC on the Real3D-AD dataset and 74.9% Image-level AUROC on the Anomaly-ShapeNet dataset with an exceptional efficiency.

Current language model evaluations measure what models know under ideal conditions but not how robustly they know it under realistic stress. Static benchmarks like MMLU and TruthfulQA cannot distinguish a model that lacks knowledge from one whose verification mechanisms collapse when information degrades or adversaries probe for weaknesses. We introduce the Drill-Down and Fabricate Test (DDFT), a protocol that measures epistemic robustness: a model's ability to maintain factual accuracy under progressive semantic compression and adversarial fabrication. We propose a two-system cognitive model comprising a Semantic System that generates fluent text and an Epistemic Verifier that validates factual accuracy. Our findings, based on evaluating 9 frontier models across 8 knowledge domains at 5 compression levels (1,800 turn-level evaluations), reveal that epistemic robustness is orthogonal to conventional design paradigms. Neither parameter count (r=0.083, p=0.832) nor architectural type (r=0.153, p=0.695) significantly predicts robustness, suggesting it emerges from training methodology and verification mechanisms distinct from current approaches. Error detection capability strongly predicts overall robustness (rho=-0.817, p=0.007), indicating this is the critical bottleneck. We find that flagship models exhibit brittleness despite their scale, while smaller models can achieve robust performance, challenging assumptions about the relationship between model size and reliability. The DDFT framework provides both theoretical foundation and practical tools for assessing epistemic robustness before deployment in critical applications.

Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less useful. We argue that low-precision floating points can perform well provided the error is properly compensated at the critical locations in the training process. We propose Collage which utilizes multi-component float representation in low-precision to accurately perform operations with numerical errors accounted. To understand the impact of imprecision to training, we propose a simple and novel metric which tracks the lost information during training as well as differentiates various precision strategies. Our method works with commonly used low-precision such as half-precision (16-bit floating points) and can be naturally extended to work with even lower precision such as 8-bit. Experimental results show that pre-training using Collage removes the requirement of using 32-bit floating-point copies of the model and attains similar/better training performance compared to (16, 32)-bit mixed-precision strategy, with up to 3.7times speedup and sim 15% to 23% less memory usage in practice.

This paper studies the error metric selection for long-term memory learning in sequence modelling. We examine the bias towards short-term memory in commonly used errors, including mean absolute/squared error. Our findings show that all temporally positive-weighted errors are biased towards short-term memory in learning linear functionals. To reduce this bias and improve long-term memory learning, we propose the use of a temporally rescaled error. In addition to reducing the bias towards short-term memory, this approach can also alleviate the vanishing gradient issue. We conduct numerical experiments on different long-memory tasks and sequence models to validate our claims. Numerical results confirm the importance of appropriate temporally rescaled error for effective long-term memory learning. To the best of our knowledge, this is the first work that quantitatively analyzes different errors' memory bias towards short-term memory in sequence modelling.

We revisit the well-studied problem of approximating a matrix product, A^TB, based on small space sketches S(A) and S(B) of A in R^{n times d} and Bin R^{n times m}. We are interested in the setting where the sketches must be computed independently of each other, except for the use of a shared random seed. We prove that, when A and B are sparse, methods based on coordinated random sampling can outperform classical linear sketching approaches, like Johnson-Lindenstrauss Projection or CountSketch. For example, to obtain Frobenius norm error epsilon|A|_F|B|_F, coordinated sampling requires sketches of size O(s/epsilon^2) when A and B have at most s leq d,m non-zeros per row. In contrast, linear sketching leads to sketches of size O(d/epsilon^2) and O(m/epsilon^2) for A and B. We empirically evaluate our approach on two applications: 1) distributed linear regression in databases, a problem motivated by tasks like dataset discovery and augmentation, and 2) approximating attention matrices in transformer-based language models. In both cases, our sampling algorithms yield an order of magnitude improvement over linear sketching.

With the increasing volume of high-frequency data in the information age, both challenges and opportunities arise in the prediction of stock volatility. On one hand, the outcome of prediction using tradition method combining stock technical and macroeconomic indicators still leaves room for improvement; on the other hand, macroeconomic indicators and peoples' search record on those search engines affecting their interested topics will intuitively have an impact on the stock volatility. For the convenience of assessment of the influence of these indicators, macroeconomic indicators and stock technical indicators are then grouped into objective factors, while Baidu search indices implying people's interested topics are defined as subjective factors. To align different frequency data, we introduce GARCH-MIDAS model. After mixing all the above data, we then feed them into Transformer model as part of the training data. Our experiments show that this model outperforms the baselines in terms of mean square error. The adaption of both types of data under Transformer model significantly reduces the mean square error from 1.00 to 0.86.

Pose estimation has promised to impact healthcare by enabling more practical methods to quantify nuances of human movement and biomechanics. However, despite the inherent connection between pose estimation and biomechanics, these disciplines have largely remained disparate. For example, most current pose estimation benchmarks use metrics such as Mean Per Joint Position Error, Percentage of Correct Keypoints, or mean Average Precision to assess performance, without quantifying kinematic and physiological correctness - key aspects for biomechanics. To alleviate this challenge, we develop OpenCapBench to offer an easy-to-use unified benchmark to assess common tasks in human pose estimation, evaluated under physiological constraints. OpenCapBench computes consistent kinematic metrics through joints angles provided by an open-source musculoskeletal modeling software (OpenSim). Through OpenCapBench, we demonstrate that current pose estimation models use keypoints that are too sparse for accurate biomechanics analysis. To mitigate this challenge, we introduce SynthPose, a new approach that enables finetuning of pre-trained 2D human pose models to predict an arbitrarily denser set of keypoints for accurate kinematic analysis through the use of synthetic data. Incorporating such finetuning on synthetic data of prior models leads to twofold reduced joint angle errors. Moreover, OpenCapBench allows users to benchmark their own developed models on our clinically relevant cohort. Overall, OpenCapBench bridges the computer vision and biomechanics communities, aiming to drive simultaneous advances in both areas.

Despite the remarkable success of diffusion models in image generation, slow sampling remains a persistent issue. To accelerate the sampling process, prior studies have reformulated diffusion sampling as an ODE/SDE and introduced higher-order numerical methods. However, these methods often produce divergence artifacts, especially with a low number of sampling steps, which limits the achievable acceleration. In this paper, we investigate the potential causes of these artifacts and suggest that the small stability regions of these methods could be the principal cause. To address this issue, we propose two novel techniques. The first technique involves the incorporation of Heavy Ball (HB) momentum, a well-known technique for improving optimization, into existing diffusion numerical methods to expand their stability regions. We also prove that the resulting methods have first-order convergence. The second technique, called Generalized Heavy Ball (GHVB), constructs a new high-order method that offers a variable trade-off between accuracy and artifact suppression. Experimental results show that our techniques are highly effective in reducing artifacts and improving image quality, surpassing state-of-the-art diffusion solvers on both pixel-based and latent-based diffusion models for low-step sampling. Our research provides novel insights into the design of numerical methods for future diffusion work.

The industrial application motivating this work is the fatigue computation of aircraft engines' high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the temperature. For this application, the temperature loading is not accurately known and can reach values relatively close to the creep temperature: important nonlinear effects occur and the solution strongly depends on the used thermal loading. We consider a nonlinear reduced order model able to compute, in the exploitation phase, the behavior of the blade for a new temperature field loading. The sensitivity of the solution to the temperature makes {the classical unenriched proper orthogonal decomposition method} fail. In this work, we propose a new error indicator, quantifying the error made by the reduced order model in computational complexity independent of the size of the high-fidelity reference model. In our framework, when the {error indicator} becomes larger than a given tolerance, the reduced order model is updated using one time step solution of the high-fidelity reference model. The approach is illustrated on a series of academic test cases and applied on a setting of industrial complexity involving 5 million degrees of freedom, where the whole procedure is computed in parallel with distributed memory.

Error Feedback (EF) is a highly popular and immensely effective mechanism for fixing convergence issues which arise in distributed training methods (such as distributed GD or SGD) when these are enhanced with greedy communication compression techniques such as TopK. While EF was proposed almost a decade ago (Seide et al., 2014), and despite concentrated effort by the community to advance the theoretical understanding of this mechanism, there is still a lot to explore. In this work we study a modern form of error feedback called EF21 (Richtarik et al., 2021) which offers the currently best-known theoretical guarantees, under the weakest assumptions, and also works well in practice. In particular, while the theoretical communication complexity of EF21 depends on the quadratic mean of certain smoothness parameters, we improve this dependence to their arithmetic mean, which is always smaller, and can be substantially smaller, especially in heterogeneous data regimes. We take the reader on a journey of our discovery process. Starting with the idea of applying EF21 to an equivalent reformulation of the underlying problem which (unfortunately) requires (often impractical) machine cloning, we continue to the discovery of a new weighted version of EF21 which can (fortunately) be executed without any cloning, and finally circle back to an improved analysis of the original EF21 method. While this development applies to the simplest form of EF21, our approach naturally extends to more elaborate variants involving stochastic gradients and partial participation. Further, our technique improves the best-known theory of EF21 in the rare features regime (Richtarik et al., 2023). Finally, we validate our theoretical findings with suitable experiments.

Benchmarks measure whether a model is correct. They do not measure whether a model is reliable. This distinction is largely academic for single-shot inference, but becomes critical for agentic AI systems, where a single rephrased prompt can trigger cascading failures in multi-step execution. Yet this form of instability is not captured by existing evaluations. Hallucinations live in variance: they arise when semantically equivalent prompts activate inconsistent internal pathways, producing divergent outputs. Consistent but incorrect outputs reflect bias or missing knowledge; confident guessing reflects calibration failure. Neither constitutes hallucination under this definition. When error is variance-dominated, reducing redundant pathways improves reliability without adding knowledge. We formalize this through Semantic Stability (SS), measured via Paraphrase Consistency (PC@k): generate k paraphrases, greedy decode each, compute mode agreement. SS is a diagnostic for variance-driven unreliability, not a method for improving correctness. We show that a dense Qwen3-0.6B agrees with itself only 23.8% of the time; at 32% sparsity, agreement jumps to 55.9%. A phase diagram reveals the sweet spot where variance reduction outpaces bias accumulation, and regimes where stability collapses onto wrong answers.