Revisiting Mode Connectivity in Neural Networks with Bezier Surface

Understanding the loss landscapes of neural networks (NNs) is critical for optimizing model performance. Previous research has identified the phenomenon of mode connectivity on curves, where two well-trained NNs can be connected by a continuous path in parameter space where the path maintains nearly constant loss. In this work, we extend the concept of mode connectivity to explore connectivity on surfaces, significantly broadening its applicability and unlocking new opportunities. While initial attempts to connect models via linear surfaces in parameter space were unsuccessful, we propose a novel optimization technique that consistently discovers Bézier surfaces with low-loss and highaccuracy connecting multiple NNs in a nonlinear manner. We further demonstrate that even without optimization, mode connectivity exists in certain cases of Bézier surfaces, where the models are carefully selected and combined linearly. This approach provides a deeper and more comprehensive understanding of the loss landscape and offers a novel way to identify models with enhanced performance for model averaging and output ensembling. We demonstrate the effectiveness of our method on CIFAR-10, CIFAR-100, and Tiny-ImageNet datasets using VGG16, ResNet18, and ViT architectures. The codes are available at https://github.com/TIML-Group/MCSurface .