#01Oct 16, 2026
stat.ML
Learning without relearning physical symmetry: an SO(3)-equivariant convolutional network (CNN) on the sphere
Joshua Williamson, Niall Jeffrey, Lorne Whiteway
Many of the most important datasets in the physical sciences live natively on the sphere, and these data often carry no preferred position or orientation. Using methods that do not reflect this symmetry leads to far higher simulation requirements, which can be catastrophic for scientific analyses (forcing reliance on cheap, imperfect models that bias results). We present a novel spherical implementation of a gauge equivariant mesh architecture that is specifically designed for the Hierarchical Equal Area isoLatitude Pixelization (\healpix{}) of the sphere. The $\mathrm{SO}(3)$-equivariant convolution is built from steerable filters, parallel transport and spin-weighted features. The architecture supplies the exact symmetry, so the network does not spend training data learning it. The convolution operations are constructed to give provably exact equivariance, given a band-limit. Our full CNNs can achieve SO(3)-invariance error at per-cent-level and lower, which is controlled through well-understood hyperparameters. On benchmarks, our technique gives the most accurate dense gradient regression and competitive cosmic microwave background foreground removal and denoising. The improved simulation efficiency matters most in simulation-based inference (SBI), where high-fidelity simulations are expensive and neural compressors require large training sets, so a fixed budget forces analyses with less accurate simulators. In cosmology lensing SBI, our technique yields the tightest posteriors at matched simulation count. This approach is a novel method that will enable new convolutional neural network analyses, including generative and inference tasks, for processes and data on the sphere.
#02Oct 16, 2026
stat.ML
ENFR: Evidence Networks with Flow-Matched References for Amortized Simulation-Based Model Inference
Kai Lehman, Jameson Dong, Carolina Cuesta-Lazaro and 5 more
The evidence, $\mathcal{Z} = p(x | \mathcal{M})$, of a data-generating model $\mathcal{M}$ is a powerful tool in Bayesian frameworks: it enables model inference, model misspecification tests, and goodness-of-fit assessment as an alternative to standard discrepancy statistics, e.g. $χ^2$. While versatile, the evidence is notoriously difficult to compute, even when the likelihood is available. In both likelihood-based and simulation-based inference, estimating $\mathcal{Z}$ provides an immediate solution to high-dimensional goodness-of-fit or model misspecification tests: using $\mathcal{Z}(x)$ as the test statistic induces a minimum-volume level-$α$ test. Such tests are essential to assess model fidelity, which is necessary to trust simulation-based parameter inference. Existing learned approaches largely target Bayes factors, which only measure evidence ratios. Instead, we provide accurate, fast, and amortized estimates of the absolute evidence. We present ENFR: Evidence Networks with Flow-matched References. Building on the Evidence Network framework of Jeffrey & Wandelt (2024), the proposed method first learns Bayes factors with respect to a flow-matched reference, from which the absolute evidence is recovered. We show improvement in estimation of $\mathcal{Z}$ over the flow-based baseline in all applications considered and the best performance of all density estimation methods considered in our benchmarks. We furthermore introduce and provide the proof for an architecture that jointly learns the individual evidences of a set of models $\{\mathcal{M}_i\}$. We demonstrate the performance and scaling behavior of these approaches on data from a variety of scientific applications.
#03Oct 16, 2026
cs.CV
Rethinking the design space of Vanilla Pixel Diffusion Transformers
Soumik Mukhopadhyay, Long Mai, Abhinav Shrivastava and 1 more
Pixel-space diffusion models have recently re-emerged as a compelling alternative to latent diffusion, avoiding the lossy latent bottleneck and separately trained autoencoder. JiT shows that a vanilla diffusion transformer can generate directly in pixel space by replacing the commonly used velocity prediction ($\boldsymbol{u}$-prediction) with clean image prediction ($\boldsymbol{x_0}$-prediction). In this work, we revisit this choice and introduce MFlow, an adaptive parameterization that learns to interpolate between $\boldsymbol{x_0}$- and $\boldsymbol{u}$-prediction across principal directions of the data, learned end-to-end with diffusion training. We find that the preferred parameterization varies systematically with the data representation and model capacity -- notably, increasing model capacity shifts preference toward velocity prediction. We evaluate MFlow across ImageNet, UCF-101 video, and large-scale text-to-image generation, demonstrating competitive or improved generative performance across diverse settings. In addition, we find that vanilla pixel diffusion transformers, irrespective of parameterization, retain a persistent high-frequency deficit relative to real images. To address this, we introduce ConvRefiner, a lightweight convolutional module trained post-hoc with an adversarial loss while keeping the diffusion backbone frozen. With only a small amount of additional training, ConvRefiner restores the high-frequency statistics of generated images while preserving FID. Project webpage: https://soumik-kanad.github.io/mflow-diffusion/.
#04Oct 16, 2026
cs.LG
Waiting Buys Exactly Two Moments: Endogenous Identification in Prediction-Driven Allocation
Rama AlHamidi, Rasul Khanbayov, Erchin Serpedin and 1 more
A planner with a fixed budget of preventive help must decide whom to help and when. Waiting reveals risk but removes intervention opportunities as higher-risk individuals leave first. We characterize this tradeoff under repeated noisy signals and risk-dependent attrition: in the canonical model, a length-$τ$ observation prefix identifies exactly the latent risk moments $m_j=\mathbb E[p^j]$ for $j=0,\ldots,2τ-1$, buying two new moments per additional period. These identify average next-period attrition among survivors but need not identify allocation welfare or attrition among those prioritized for treatment. Our observationally equivalent constructions establish unavoidable timing regret at any sample size for a fixed observation length, while exact certificates determine whether all compatible populations share a unique optimal date. Matched experiments separate the effects of estimation, bootstrap averaging, and regret weighting. Longer observation often resolves timing ambiguity, but the optimal date may already have passed. In our experiments, bootstrap averaging and early stopping improve decisions, while regret weighting adds no improvement in pooled mean squared regret: better statistical fit need not yield better allocation welfare. The code and artifacts are available at https://github.com/KurbanIntelligenceLab/waiting-buys-two-moments.
#05Oct 16, 2026
cs.LG
Explainable Machine Learning Analysis of Temperature Effects on Mechanical Strength of Fiber-Reinforced High-Performance Concrete
Jagaran Chakma, Zhiguang Zhou, Badhan Chakma and 1 more
Predicting the compressive strength of fiber-reinforced high-performance concrete subjected to temperature exposure is challenging because to the intricate interdependencies of mixture composition, fiber properties, curing conditions, and temperature. A data-driven framework to predict compressive strength utilizing 1,204 experimental records containing a diverse array of material designs and exposure situations. This study evaluates eight machine-learning models and demonstrate that ensemble approaches routinely surpass individual learners. Both gradient boosting and extreme gradient boosting exhibit superior performance on unseen data, each attaining a R^2 of 0.903. Gradient boosting produces the minimal root mean square error (6.67 MPa), whereas extreme gradient boosting achieves the lowest mean absolute error (3.97 MPa) and mean absolute percentage error (10.60%). The models are further interpreted utilizing Shapley additive explanations and partial dependence analysis, which reveal temperature as the primary factor influencing compressive strength, succeeded by fine aggregate, superplasticizer, cement content, water-to-binder ratio, and water content. Strength diminishes significantly with rising temperature, albeit the extent of deterioration is contingent upon the specific combination design. The best performing models are subsequently implemented in a Python-based graphical user interface for expedited prediction. Our findings offer a precise and comprehensible methodology for evaluating temperature-dependent compressive strength and facilitate the practical, data-driven design of fiber-reinforced high-performance concrete.