<ul data-eligibleForWebStory="true"><li>Gaussian Processes (GPs) are useful for modeling uncertainty with function-space priors, while Bayesian Neural Networks (BNNs) are more scalable but lack some GP advantages.</li><li>Efforts have been made to make BNNs behave like GPs, but previous solutions have limitations.</li><li>A study shows that using trainable activations is essential to map GP priors effectively to wide BNNs.</li><li>The closed-form 2-Wasserstein distance is used for efficient optimization of reparameterized priors and activations.</li><li>The method introduces trainable periodic activations for global stationarity and functional priors conditioned on GP hyperparameters for efficient model selection.</li><li>Empirical results demonstrate that the proposed method outperforms existing approaches and matches heuristic methods with stronger theoretical foundations.</li></ul>

Revisiting the Equivalence of Bayesian Neural Networks and Gaussian Processes: On the Importance of Learning Activations

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