Catapults in SGD: spikes in the training loss and their impact on generalization through feature learning
It addresses the problem of understanding and improving generalization in neural network training for machine learning practitioners, but is incremental as it builds on prior work on catapults.
The paper explains that spikes in SGD training loss are 'catapults' linked to optimization in a low-dimensional subspace, and shows they improve generalization by enhancing feature learning through increased alignment with the Average Gradient Outer Product, with smaller batch sizes inducing more catapults and better test performance.
In this paper, we first present an explanation regarding the common occurrence of spikes in the training loss when neural networks are trained with stochastic gradient descent (SGD). We provide evidence that the spikes in the training loss of SGD are "catapults", an optimization phenomenon originally observed in GD with large learning rates in [Lewkowycz et al. 2020]. We empirically show that these catapults occur in a low-dimensional subspace spanned by the top eigenvectors of the tangent kernel, for both GD and SGD. Second, we posit an explanation for how catapults lead to better generalization by demonstrating that catapults promote feature learning by increasing alignment with the Average Gradient Outer Product (AGOP) of the true predictor. Furthermore, we demonstrate that a smaller batch size in SGD induces a larger number of catapults, thereby improving AGOP alignment and test performance.