Abstract
Meta-learning algorithms such as MAML, Reptile, and FOMAML have led to improved performance of several neural models. The primary difference between standard gradient descent and these meta-learning approaches is that they contain as a small component the gradient for maximizing dot-product between gradients of batches, leading to improved generalization. Previous work has shown that aligned gradients are related to generalization, and have also used the Reptile algorithm in a single-task setting to improve generalization. Inspired by these approaches for a single task setting, this paper proposes to use the finite differences first-order algorithm to calculate this gradient from dot-product of gradients, allowing explicit control on the weightage of this component relative to standard gradients. We use this gradient as a regularization technique, leading to more aligned gradients between different batches. By using the finite differences approximation, our approach does not suffer from O(nˆ2) memory usage of naively calculating the Hessian and can be easily applied to large models with large batch sizes. Our approach achieves state-of-the-art performance on the Gigaword dataset, and shows performance improvements on several datasets such as SQuAD-v2.0, Quasar-T, NewsQA and all the SuperGLUE datasets, with a range of models such as BERT, RoBERTa and ELECTRA. Our method also outperforms previous approaches of Reptile and FOMAML when used as a regularization technique, in both single and multi-task settings. Our method is model agnostic, and introduces no extra trainable weights.