The success of SGD in deep learning has been ascribed by prior works to the implicit bias induced by high learning rate or small batch size ("SGD noise"). While prior works that focused on offline learning (i.e., multiple-epoch training), we study the impact of SGD noise on online (i.e., single epoch) learning. Through an extensive empirical analysis of image and language data, we demonstrate that large learning rate and small batch size do not confer any implicit bias advantages in online learning. In contrast to offline learning, the benefits of SGD noise in online learning are strictly computational, facilitating larger or more cost-effective gradient steps. Our work suggests that SGD in the online regime can be construed as taking noisy steps along the "golden path" of the noiseless gradient flow algorithm. We provide evidence to support this hypothesis by conducting experiments that reduce SGD noise during training and by measuring the pointwise functional distance between models trained with varying SGD noise levels, but at equivalent loss values. Our findings challenge the prevailing understanding of SGD and offer novel insights into its role in online learning.

Our techniques generalize to a wide range of linear transformations that are used in data analysis such as the Discrete Cosine and Sine transforms, the Hadamard transform, and their high-dimensional analogs. We use our algorithm to successfully defend against well known L adversaries in the setting of image classification.

Our techniques generalize to a wide range of linear transformations that are used in data analysis such as the Discrete Cosine and Sine transforms, the Hadamard transform, and their high-dimensional analogs.

Our techniques generalize to a wide range of linear transformations that are used in data analysis such as the Discrete Cosine and Sine transforms, the Hadamard transform, and their high-dimensional analogs.