Scalable Derivative Gaussian Processes via Exact Gradient Reduction

Researchers have introduced two new methods to improve Gaussian processes and Large Vision-Language Models (LVLMs): TERA, for scalable derivative Gaussian processes, and Semantic Gaussian Process Uncertainty (SGPU), for semantic uncertainty quantification.

TERA, introduced in a paper on arXiv^[1], improves the scalability of derivative Gaussian processes by using target-specific exact gradient reduction. This method reduces the computational bottleneck from O(n^3 d^3) to O(dm^2 + m^6) time and O(dm^2 + m^4) memory^[1]. TERA achieves state-of-the-art predictive accuracy while operating orders of magnitude faster than standard derivative GPs. Another paper on arXiv^[2] proposed SGPU, a Bayesian framework that quantifies semantic uncertainty in LVLMs by analyzing the geometric structure of answer embeddings. SGPU maps generated answers into a dense semantic space and computes the Gram matrix of their embeddings. The spectral representation of SGPU is then fed into a Gaussian Process Classifier that learns to map patterns of semantic consistency to predictive uncertainty. SGPU achieves state-of-the-art calibration and discriminative performance across six LLMs and LVLMs on eight datasets^[2]. Furthermore, SGPU transfers across models and modalities, indicating that its spectral representation captures general patterns of semantic uncertainty.