Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation, treating the spectral density as a probability distribution for Monte Carlo approximation. Although this probabilistic interpretation works for stationary processes, it is overly restrictive for the nonstationary case, where spectral densities are generally not probability measures. We propose regular Fourier features for harmonizable processes that avoid this limitation. Our method discretizes the spectral representation directly, preserving the correlation structure among spectral weights without requiring probability assumptions. Under a finite spectral support assumption, this yields an efficient low-rank approximation that is positive semi-definite by construction. When the spectral density is unknown, the framework extends naturally to kernel learning from data. We demonstrate the method on locally stationary kernels and on harmonizable mixture kernels with complex-valued spectral densities.

This paper introduces a distillation framework for an ensemble of entropy-optimal Sparse Probabilistic Approximation (eSPA) models, trained exclusively on satellite-era observational and reanalysis data to predict ENSO phase up to 24 months in advance. While eSPA ensembles yield state-of-the-art forecast skill, they are harder to interpret than individual eSPA models. We show how to compress the ensemble into a compact set of "distilled" models by aggregating the structure of only those ensemble members that make correct predictions. This process yields a single, diagnostically tractable model for each forecast lead time that preserves forecast performance while also enabling diagnostics that are impractical to implement on the full ensemble. An analysis of the regime persistence of the distilled model "superclusters", as well as cross-lead clustering consistency, shows that the discretised system accurately captures the spatiotemporal dynamics of ENSO. By considering the effective dimension of the feature importance vectors, the complexity of the input space required for correct ENSO phase prediction is shown to peak when forecasts must cross the boreal spring predictability barrier. Spatial importance maps derived from the feature importance vectors are introduced to identify where predictive information resides in each field and are shown to include known physical precursors at certain lead times. Case studies of key events are also presented, showing how fields reconstructed from distilled model centroids trace the evolution from extratropical and inter-basin precursors to the mature ENSO state. Overall, the distillation framework enables a rigorous investigation of long-range ENSO predictability that complements real-time data-driven operational forecasts.

The "black-box" nature of representations, combined with the known susceptibility of networks to learn spurious correlations [

T o this end, we propose a simple yet powerful paradigm for seamlessly unifying different human pose and shape-related tasks and datasets. Our formulation is centered on the ability - both at training and test time - to query any arbitrary point of the human volume, and obtain its estimated location in 3D. We achieve this by learning a continuous neural field of body point localizer functions, each of which is a differently parameterized 3D heatmap-based convolutional point localizer (detector).

We propose a novel loss function called Energy Discrepancy (ED) which does not rely on the computation of scores or expensive Markov chain Monte Carlo.

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