
Figure 3: visualization of mode connectivity for ResNet-20 with no skip connections on CIFAR-10 dataset. The visualization is created in collaboration with Javier Ideami (https://losslandscape.com/). For more details, see this blogpost.
We expect solutions that are centered in the flat region of the loss to generalize better than those near the boundary. Indeed, train and test error surfaces are not perfectly aligned in the weight space. Solutions that are centered in the flat region are not as susceptible to the shifts between train and test error surfaces as those near the boundary. In Figure 4 below, we show the train loss and test error surfaces along the direction connecting the SWA and SGD solutions. As you can see, while the SWA solution has a higher train loss compared to the SGD solution, it is centered in a region of low loss and has a substantially better test error.
