It depends: Incorporating correlations for joint aleatoric and epistemic uncertainties of high-dimensional output spaces

Uncertainty Quantification (UQ) plays a vital role in enhancing the reliability of deep learning model predictions, especially in scenarios with high-dimensional output spaces. This paper addresses the dual nature of uncertainty -- aleatoric and epistemic -- focusing on their joint integration in high-dimensional regression tasks. For example, in applications like medical image segmentation or restoration, aleatoric uncertainty captures inherent data noise, while epistemic uncertainty quantifies the model's confidence in unfamiliar conditions. Modeling both jointly enables more reliable predictions by reflecting both unavoidable variability and knowledge gaps, whereas modeling only one limits transparency and robustness. We propose a novel approach that approximates the resulting joint uncertainty using a low-rank plus diagonal covariance structure, capturing essential output correlations while avoiding the computational burdens of full covariance matrices. Unlike prior work, our method explicitly combines aleatoric and epistemic uncertainties into a unified second-order distribution that supports robust downstream analyses like sampling and log-likelihood evaluation. We further introduce stabilization strategies for efficient training and inference, achieving superior UQ in the tasks of image inpainting, colorization, optical flow, and depth estimation.

The Effects of Synthetic Data and Label Distribution on Canola Branch Counting

Collecting annotated plant images for automated phenotyping is often slow and expensive. Plant models simulating growth and development can generate unlimited synthetic images with exact labels. However, previous work has established that whether incorporating synthetic data improves performance depends on the ratio of synthetic to real images and the label distribution of the synthetic dataset. To systematically quantify both factors, we train ResNet-18 models on a canola branch-counting task using a calibrated L-system plant model. We vary each factor independently. Synthetic-to-real ratios of 1:5 to 1:22 broadly improve performance; the best ratio (1:7) reduces mean absolute difference by 7.6% over real-only training. For label distribution, a uniform synthetic distribution is strongly suboptimal (abs. diff. of approximately 1.70); interpolating 90% toward the real distribution yields abs. diff. 0.927, whereas Gaussian smoothing of the real label distribution yields the best overall result (abs. diff. 0.912, a 14.7% improvement over real-only). A minimum of 10 synthetic images per label offers a simpler alternative with modest gains, while 100 per label over-corrects and hurts performance.

Jacobi-Anger Method for Deterministic Initialization in Implicit Neural Representation

Existing implicit neural representation (INR) approaches suffer from stochastic initialization that does not guarantee consistent or high-quality performance across runs, with variations reaching more than 2.5 dB (~78%) in image regression. This variation is problematic for scientific computing and simulation, where result reproducibility is crucial. To address this problem, we present Jacobi-Anger Sinusoidal Representation Network (JA-SIREN), a deterministic initialization scheme for sinusoidal networks grounded in classical spectral analysis. By computing the Discrete Sine Transform (DST) of the target signal and leveraging the Jacobi-Anger expansion, we derive closed-form weights for a two-layer sinusoidal MLP that analytically match the network's initial spectral response to the target signal, requiring no random seed or additional hyperparameter tuning. On the Kodak dataset, JA-SIREN achieves a mean PSNR of 67.18 dB, a 21.30 dB improvement over the best baseline. This is achieved with zero run-to-run variance, confirming that spectrally-informed initialization is a more effective and reproducible alternative to stochastic initialization for sinusoidal INRs.