Wenyuan Zhao

Wenyuan Zhao, Rui Tuo, Chao Tian

Gaussian processes (GPs) provide a principled Bayesian framework for uncertainty estimation, but their computational complexity severely limits scalability to large datasets. We propose SIKA-GP, which accelerates GP inference using sparse inducing kernel approximations based on a dyadic ordered template basis, incurring only ${O}(\log M)$ complexity dependence on the number of inducing points. Our approach constructs compact and expressive kernel representations from sparsely activated bases, enabling efficient tensorized GPU computation and seamless integration with modern large-scale models. SIKA-GP can be naturally embedded into Bayesian neural networks (BNNs) with sparse activations, yielding significant speedups in both training and inference without sacrificing predictive performance. The method naturally extends to deep feature learning, addressing the scalability challenges introduced by deep architectures and high-dimensional feature representations. Empirical results on vision and transformer-based language benchmarks demonstrate that our approach consistently delivers fast and accurate GP models, providing a principled path toward scalable kernel learning.

Zihao Zhu, Wenyuan Zhao, Nuo Chen et al.

Geometric foundation models hold promise for unconstrained dense geometry prediction from uncalibrated images. However, in current feed-forward designs, their predicted confidence scores are heuristic, lack probabilistic interpretation, and often fail to indicate where and how much the predicted geometry can be trusted. To address this gap, we present Trust3R, a lightweight evidential uncertainty framework for feed-forward 3D reconstruction. Trust3R combines gated residual mean refinement with a Normal-Inverse-Wishart evidential head, yielding a closed-form multivariate Student-t distribution for per-point geometric uncertainty. This design provides probabilistically grounded pointmap uncertainty estimates while adding moderate inference overhead. We evaluate on diverse indoor and outdoor benchmarks and compare against MASt3R's built-in confidence map as well as common uncertainty-aware baselines spanning single-pass heteroscedastic regression and sampling-based methods such as MC dropout and deep ensembles. Experimental results show that Trust3R consistently improves risk-coverage and sparsification, and generally improves geometric accuracy. These gains are reflected in stronger uncertainty ranking across benchmarks, with 25% lower AURC and 41% lower AUSE on ScanNet++, providing a practical reliability signal for uncertainty-aware weighting in downstream geometry pipelines. The project page and code are available at https://trust3r-z.github.io/.

Wenyuan Zhao, Adithya Balachandran, Chao Tian et al.

The study of multimodality has garnered significant interest in fields where the analysis of interactions among multiple information sources can enhance predictive modeling, data fusion, and interpretability. Partial information decomposition (PID) has emerged as a useful information-theoretic framework to quantify the degree to which individual modalities independently, redundantly, or synergistically convey information about a target variable. However, existing PID methods depend on optimizing over a joint distribution constrained by estimated pairwise probability distributions, which are costly and inaccurate for continuous and high-dimensional modalities. Our first key insight is that the problem can be solved efficiently when the pairwise distributions are multivariate Gaussians, and we refer to this problem as Gaussian PID (GPID). We propose a new gradient-based algorithm that substantially improves the computational efficiency of GPID based on an alternative formulation of the underlying optimization problem. To generalize the applicability to non-Gaussian data, we learn information-preserving encoders to transform random variables of arbitrary input distributions into pairwise Gaussian random variables. Along the way, we resolved an open problem regarding the optimality of joint Gaussian solutions for GPID. Empirical validation in diverse synthetic examples demonstrates that our proposed method provides more accurate and efficient PID estimates than existing baselines. We further evaluate a series of large-scale multimodal benchmarks to show its utility in real-world applications of quantifying PID in multimodal datasets and selecting high-performing models.

Wenyuan Zhao, Haoyuan Chen, Tie Liu et al.

With the strengths of both deep learning and kernel methods like Gaussian Processes (GPs), Deep Kernel Learning (DKL) has gained considerable attention in recent years. From the computational perspective, however, DKL becomes challenging when the input dimension of the GP layer is high. To address this challenge, we propose the Deep Additive Kernel (DAK) model, which incorporates i) an additive structure for the last-layer GP; and ii) induced prior approximation for each GP unit. This naturally leads to a last-layer Bayesian neural network (BNN) architecture. The proposed method enjoys the interpretability of DKL as well as the computational advantages of BNN. Empirical results show that the proposed approach outperforms state-of-the-art DKL methods in both regression and classification tasks.