2024/10/21 by Marcin Sendera, Sendera, Marcin, Amin Sorkhei +3 · 1 citation
Computer Science · #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications
paper · pdf · doi:10.48550/arxiv.2410.15777
openalex publication_date 2024/10/21 · openalex created_date 2024/11/06 · openalex updated_date 2026/07/30
Gaussian Processes (GPs) provide a convenient framework for specifying function-space priors, making them a natural choice for modeling uncertainty. In contrast, Bayesian Neural Networks (BNNs) offer greater scalability and extendability but lack the advantageous properties of GPs. This motivates the development of BNNs capable of replicating GP-like behavior. However, existing solutions are either limited to specific GP kernels or rely on heuristics. We demonstrate that trainable activations are crucial for effective mapping of GP priors to wide BNNs. Specifically, we leverage the closed-form 2-Wasserstein distance for efficient gradient-based optimization of reparameterized priors and activations. Beyond learned activations, we also introduce trainable periodic activations that ensure global stationarity by design, and functional priors conditioned on GP hyperparameters to allow efficient model selection. Empirically, our method consistently outperforms existing approaches or matches performance of the heuristic methods, while offering stronger theoretical foundations.