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.

AI/ML problems, and in each such case σ is assumed to be known .

Density Functional Theory (DFT) is a widely used computational method for estimating the energy and behavior of molecules. Machine Learning Interatomic Potentials (MLIPs) are models trained to approximate DFT-level energies and forces at dramatically lower computational cost. Many modern MLIPs rely on a scalar regression formulation; given information about a molecule, they predict a single energy value and corresponding forces while minimizing absolute error with DFT's calculations. In this work, we explore a multi-class classification formulation that predicts a categorical distribution over energy/force values, providing richer supervision through multiple targets. Most importantly, this approach offers a principled way to quantify model uncertainty. In particular, our method predicts a histogram of the energy/force distribution, converts scalar targets into histograms, and trains the model using cross-entropy loss. Our results demonstrate that this categorical formulation can achieve absolute error performance comparable to regression baselines. Furthermore, this representation enables the quantification of epistemic uncertainty through the entropy of the predicted distribution, offering a measure of model confidence absent in scalar regression approaches.

While promising, graph reasoners based on Large Language Models (LLMs) lack built-in invariance to symmetries in graph representations. Operating on sequential graph serializations, LLMs can produce different outputs under node reindexing, edge reordering, or formatting changes, raising robustness concerns. We systematically analyze these effects, studying how fine-tuning impacts encoding sensitivity as well generalization on unseen tasks. We propose a principled decomposition of graph serializations into node labeling, edge encoding, and syntax, and evaluate LLM robustness to variations of each of these factors on a comprehensive benchmarking suite. We also contribute a novel set of spectral tasks to further assess generalization abilities of fine-tuned reasoners. Results show that larger (non-fine-tuned) models are more robust. Fine-tuning reduces sensitivity to node relabeling but may increase it to variations in structure and format, while it does not consistently improve performance on unseen tasks.

Accurate multivariate time-series prediction of vital signs and laboratory results is crucial for early intervention and precision medicine in intensive care units (ICUs). However, vital signs are often noisy and exhibit rapid fluctuations, while laboratory tests suffer from missing values, measurement lags, and device-specific bias, making integrative forecasting highly challenging. To address these issues, we propose OmniTFT, a deep learning framework that jointly learns and forecasts high-frequency vital signs and sparsely sampled laboratory results based on the Temporal Fusion Transformer (TFT). Specifically, OmniTFT implements four novel strategies to enhance performance: sliding window equalized sampling to balance physiological states, frequency-aware embedding shrinkage to stabilize rare-class representations, hierarchical variable selection to guide model attention toward informative feature clusters, and influence-aligned attention calibration to enhance robustness during abrupt physiological changes. By reducing the reliance on target-specific architectures and extensive feature engineering, OmniTFT enables unified modeling of multiple heterogeneous clinical targets while preserving cross-institutional generalizability. Across forecasting tasks, OmniTFT achieves substantial performance improvement for both vital signs and laboratory results on the MIMIC-III, MIMIC-IV, and eICU datasets. Its attention patterns are interpretable and consistent with known pathophysiology, underscoring its potential utility for quantitative decision support in clinical care.

Estimating quantum entropies and divergences is an important problem in quantum physics, information theory, and machine learning. Quantum neural estimators (QNEs), which utilize a hybrid classical-quantum architecture, have recently emerged as an appealing computational framework for estimating these measures. Such estimators combine classical neural networks with parametrized quantum circuits, and their deployment typically entails tedious tuning of hyperparameters controlling the sample size, network architecture, and circuit topology. This work initiates the study of formal guarantees for QNEs of measured (Rényi) relative entropies in the form of non-asymptotic error risk bounds. We further establish exponential tail bounds showing that the error is sub-Gaussian, and thus sharply concentrates about the ground truth value. For an appropriate sub-class of density operator pairs on a space of dimension $d$ with bounded Thompson metric, our theory establishes a copy complexity of $O(|Θ(\mathcal{U})|d/ε^2)$ for QNE with a quantum circuit parameter set $Θ(\mathcal{U})$, which has minimax optimal dependence on the accuracy $ε$. Additionally, if the density operator pairs are permutation invariant, we improve the dimension dependence above to $O(|Θ(\mathcal{U})|\mathrm{polylog}(d)/ε^2)$. Our theory aims to facilitate principled implementation of QNEs for measured relative entropies and guide hyperparameter tuning in practice.

Early approaches to multiple-output Gaussian processes (MOGPs) relied on linear combinations of independent, latent, single-output Gaussian processes (GPs).

Neural Information Processing Systems http://nips.cc/

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.

Various developed countries have experienced a continuous rise in obesity [1]. This can be burdensome on healthcare and has thus prompted governments to introduce laws and regulations to restaurants and food chains in an attempt to promote healthier eating [1]. One patent rule is the mandatory display of calories in menus, which has not come without an added cost to businesses. For example, Section 4205 of the Affordable Care Act (ACA) in the USA required certain food chains to display caloric information on menu items which was estimated to cost $315 million to comply [2]. These costs were primarily due to nutritional analysis - if one could drastically diminish this overhead, it would greatly lower business spending [2].