Deep Ensembles (DEs) demonstrate improved accuracy, calibration and robustness to perturbations over single neural networks partly due to their functional diversity. Particle-based variational inference (ParVI) methods enhance diversity by formalizing a repulsion term based on a network similarity kernel. However, weight-space repulsion is inefficient due to over-parameterization, while direct function-space repulsion has been found to produce little improvement over DEs. To sidestep these difficulties, we propose First-order Repulsive Deep Ensemble (FoRDE), an ensemble learning method based on ParVI, which performs repulsion in the space of first-order input gradients. As input gradients uniquely characterize a function up to translation and are much smaller in dimension than the weights, this method guarantees that ensemble members are functionally different. Intuitively, diversifying the input gradients encourages each network to learn different features, which is expected to improve the robustness of an ensemble. Experiments on image classification datasets and transfer learning tasks show that FoRDE significantly outperforms the gold-standard DEs and other ensemble methods in accuracy and calibration under covariate shift due to input perturbations.
Original languageEnglish
Title of host publicationThe Twelfth International Conference on Learning Representations
Publication statusAccepted/In press - 2024
MoE publication typeA4 Conference publication
EventInternational Conference on Learning Representations - Messe Wien Exhibition and Congress Center, Vienna, Austria
Duration: 7 May 202411 May 2024
Conference number: 12


ConferenceInternational Conference on Learning Representations
Abbreviated titleICLR
Internet address


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