Sharpness-diversity tradeoff: improving flat ensembles with SharpBalance

Haiquan Lu, Xiaotian Liu, Yefan Zhou, Qunli Li, Kurt Keutzer, Michael W. Mahoney, Yujun Yan, Huanrui Yang, Yaoqing Yang

Keywords: Diversity, loss landscape, deep ensemble

TL;DR: This paper reveals a trade-off between sharpness and diversity in deep ensembles, both empirically and theoretically, and proposes SharpBalance, a novel ensemble algorithm that achieves an optimal balance between these two crucial metrics.

Abstract: Recent studies on deep ensembles have identified the sharpness of the local minima of individual learners and the diversity of the ensemble members as key factors in improving test-time performance. Building on this, our study investigates the interplay between sharpness and diversity within deep ensembles, illustrating their crucial role in robust generalization to both in-distribution (ID) and out-of-distribution (OOD) data. We discover a trade-off between sharpness and diversity: minimizing the sharpness in the loss landscape tends to diminish the diversity of individual members within the ensemble, adversely affecting the ensemble's improvement. The trade-off is justified through our rigorous theoretical analysis and verified empirically through extensive experiments. To address the issue of reduced diversity, we introduce SharpBalance, a novel training approach that balances sharpness and diversity within ensembles. Theoretically, we show that our training strategy achieves a better sharpness-diversity trade-off. Empirically, we conducted comprehensive evaluations in various data sets (CIFAR-10, CIFAR-100, TinyImageNet) and showed that SharpBalance not only effectively improves the sharpness-diversity trade-off but also significantly improves ensemble performance in ID and OOD scenarios.

Primary Area: Optimization for deep networks

Submission Number: 8107