Training Convolutional Networks at Temporarily Reduced Internal Resolution

Continuation methods train neural networks on a sequence of modified problems before recovering the original objective. We investigate spatial continuation for image classification with convolutional networks: the internal spatial resolution of feature maps is temporarily reduced, then progressively restored during training. This simple intervention improves mean test accuracy in all twenty no-augmentation settings, by 0.38 to 6.28 points, and most of this gain comes from the temporary reduction itself rather than from the progression. The settings span datasets, dataset sizes, architectures, activations, normalizations, optimizers and training budgets. The intervention is absent from the final network, so inference cost is unchanged. Its measured training time is comparable to standard training in the short reference setting and lower in a controlled long-SGD timing study. In matched comparisons with a prior smoothing curriculum, resolution reduction has higher mean accuracy in the no-augmentation recipes, while the augmented SGD comparison depends on BatchNorm calibration. The gains are more consistent with simple optimizers than with adaptive optimizers, where they remain present but vary more. Their magnitude, however, depends on the training recipe, and stronger data augmentation can substantially reduce it. Comparisons with Gaussian filtering of the feature maps, used here as a control, indicate that the gains cannot be attributed to smoothing alone. Geometric diagnostics show lower curvature in the reference setting, but comparisons across methods and training recipes do not support lower curvature as a general explanation of the gains. Overall, these results support temporary internal resolution reduction as a simple and useful intervention in unaugmented training, while showing that its advantage narrows under stronger recipes.