Further, we emphasize the significance of principled regularization of the network parameters and prediction.

Estimating causal quantities from observational data is crucial for understanding the safety and effectiveness of medical treatments. However, to make reliable inferences, medical practitioners require not only estimating averaged causal quantities, such as the conditional average treatment effect, but also understanding the randomness of the treatment effect as a random variable. This randomness is referred to as aleatoric uncertainty and is necessary for understanding the probability of benefit from treatment or quantiles of the treatment effect. Yet, the aleatoric uncertainty of the treatment effect has received surprisingly little attention in the causal machine learning community. To fill this gap, we aim to quantify the aleatoric uncertainty of the treatment effect at the covariate-conditional level, namely, the conditional distribution of the treatment effect (CDTE).

The rapid progress of diffusion models highlights the growing need for detecting generated images. Previous research demonstrates that incorporating diffusion-based measurements, such as reconstruction error, can enhance the gener-alizability of detectors. However, ignoring the differing impacts of aleatoric and epistemic uncertainty on reconstruction error can undermine detection performance. Aleatoric uncertainty, arising from inherent data noise, creates ambiguity that impedes accurate detection of generated images. As it reflects random variations within the data (e.g., noise in natural textures), it does not help distinguish generated images. In contrast, epistemic uncertainty, which represents the model's lack of knowledge about unfamiliar patterns, supports detection. In this paper, we propose a novel framework, Diffusion Epistemic Uncertainty with Asymmetric Learning (DEUA), for detecting diffusion-generated images. W e introduce Diffusion Epistemic Uncertainty (DEU) estimation via the Laplace approximation to assess the proximity of data to the manifold of diffusion-generated samples. Additionally, an asymmetric loss function is introduced to train a balanced classifier with larger margins, further enhancing generalizability.

Estimating and disentangling epistemic uncertainty, uncertainty that is reducible with more training data, and aleatoric uncertainty, uncertainty that is inherent to the task at hand, is critically important when applying machine learning to high-stakes applications such as medical imaging and weather forecasting. Conditional diffusion models' breakthrough ability to accurately and efficiently sample from the posterior distribution of a dataset now makes uncertainty estimation conceptually straightforward: One need only train and sample from a large ensemble of diffusion models. Unfortunately, training such an ensemble becomes computationally intractable as the complexity of the model architecture grows. In this work we introduce a new approach to ensembling, hyper-diffusion models (HyperDM), which allows one to accurately estimate both epistemic and aleatoric uncertainty with a single model. Unlike existing single-model uncertainty methods like Monte-Carlo dropout and Bayesian neural networks, HyperDM offers prediction accuracy on par with, and in some cases superior to, multi-model ensembles. Furthermore, our proposed approach scales to modern network architectures such as Attention U-Net and yields more accurate uncertainty estimates compared to existing methods.

In Bayesian regression, we often use a Gaussian observation model, where we control the level of aleatoric uncertainty with a noise variance parameter. By contrast, for Bayesian classification we use a categorical distribution with no mechanism to represent our beliefs about aleatoric uncertainty. Our work shows that explicitly accounting for aleatoric uncertainty significantly improves the performance of Bayesian neural networks. We note that many standard benchmarks, such as CIFAR-10, have essentially no aleatoric uncertainty. Moreover, we show that data augmentation in approximate inference softens the likelihood, leading to underconfidence and misrepresenting our beliefs about aleatoric uncertainty. Accordingly, we find that a cold posterior, tempered by a power greater than one, often more honestly reflects our beliefs about aleatoric uncertainty than no tempering --- providing an explicit link between data augmentation and cold posteriors. We further show that we can match or exceed the performance of posterior tempering by using a Dirichlet observation model, where we explicitly control the level of aleatoric uncertainty, without any need for tempering.

Large language models (LLMs) are rapidly being integrated into computational social science research, yet their blackboxed training and designed stochastic elements in inference pose unique challenges for scientific inquiry. This article argues that applying LLMs to social scientific tasks requires explicit assessment of uncertainty-an expectation long established in both quantitative methodology in the social sciences and machine learning. We introduce a unified framework for evaluating LLM uncertainty along two dimensions: the task type (T), which distinguishes between classification, short-form, and long-form generation, and the validation type (V), which captures the availability of reference data or evaluative criteria. Drawing from both computer science and social science literature, we map existing uncertainty quantification (UQ) methods to this T-V typology and offer practical recommendations for researchers. Our framework provides both a methodological safeguard and a practical guide for integrating LLMs into rigorous social science research.

Reliable real-time analysis of sensor data is essential for structural health monitoring (SHM) of high-value assets, yet a major challenge is to obtain spatially resolved full-field aleatoric and epistemic uncertainties for trustworthy decision-making. We present an integrated SHM framework that combines principal component analysis (PCA), a Bayesian neural network (BNN), and Hamiltonian Monte Carlo (HMC) inference, mapping sparse strain gauge measurements onto leading PCA modes to reconstruct full-field strain distributions with uncertainty quantification. The framework was validated through cyclic four-point bending tests on carbon fiber reinforced polymer (CFRP) specimens with varying crack lengths, achieving accurate strain field reconstruction (R squared value > 0.9) while simultaneously producing real-time uncertainty fields. A key contribution is that the BNN yields robust full-field strain reconstructions from noisy experimental data with crack-induced strain singularities, while also providing explicit representations of two complementary uncertainty fields. Considered jointly in full-field form, the aleatoric and epistemic uncertainty fields make it possible to diagnose at a local level, whether low-confidence regions are driven by data-inherent issues or by model-related limitations, thereby supporting reliable decision-making. Collectively, the results demonstrate that the proposed framework advances SHM toward trustworthy digital twin deployment and risk-aware structural diagnostics.

The intrinsic alignments (IA) of galaxies, a key contaminant in weak lensing analyses, arise from correlations in galaxy shapes driven by tidal interactions and galaxy formation processes. Accurate IA modeling is essential for robust cosmological inference, but current approaches rely on perturbative methods that break down on nonlinear scales or on expensive simulations. We introduce IAEmu, a neural network-based emulator that predicts the galaxy position-position ($ξ$), position-orientation ($ω$), and orientation-orientation ($η$) correlation functions and their uncertainties using mock catalogs based on the halo occupation distribution (HOD) framework. Compared to simulations, IAEmu achieves ~3% average error for $ξ$ and ~5% for $ω$, while capturing the stochasticity of $η$ without overfitting. The emulator provides both aleatoric and epistemic uncertainties, helping identify regions where predictions may be less reliable. We also demonstrate generalization to non-HOD alignment signals by fitting to IllustrisTNG hydrodynamical simulation data. As a fully differentiable neural network, IAEmu enables $\sim$10,000$\times$ speed-ups in mapping HOD parameters to correlation functions on GPUs, compared to CPU-based simulations. This acceleration facilitates inverse modeling via gradient-based sampling, making IAEmu a powerful surrogate model for galaxy bias and IA studies with direct applications to Stage IV weak lensing surveys.

Artificial intelligence (AI) systems increasingly influence safety-critical aspects of society, from medical diagnosis to autonomous mobility, making uncertainty awareness a central requirement for trustworthy AI. We present a photonic Bayesian machine that leverages the inherent randomness of chaotic light sources to enable uncertainty reasoning within the framework of Bayesian Neural Networks. The analog processor features a 1.28 Tbit/s digital interface compatible with PyTorch, enabling probabilistic convolutions processing within 37.5 ps per convolution. We use the system for simultaneous classification and out-of-domain detection of blood cell microscope images and demonstrate reasoning between aleatoric and epistemic uncertainties. The photonic Bayesian machine removes the bottleneck of pseudo random number generation in digital systems, minimizes the cost of sampling for probabilistic models, and thus enables high-speed trustworthy AI systems.