论文标题
部分可观测时空混沌系统的无模型预测
Rethinking the Number of Shots in Robust Model-Agnostic Meta-Learning
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
Robust Model-Agnostic Meta-Learning (MAML) is usually adopted to train a meta-model which may fast adapt to novel classes with only a few exemplars and meanwhile remain robust to adversarial attacks. The conventional solution for robust MAML is to introduce robustness-promoting regularization during meta-training stage. With such a regularization, previous robust MAML methods simply follow the typical MAML practice that the number of training shots should match with the number of test shots to achieve an optimal adaptation performance. However, although the robustness can be largely improved, previous methods sacrifice clean accuracy a lot. In this paper, we observe that introducing robustness-promoting regularization into MAML reduces the intrinsic dimension of clean sample features, which results in a lower capacity of clean representations. This may explain why the clean accuracy of previous robust MAML methods drops severely. Based on this observation, we propose a simple strategy, i.e., increasing the number of training shots, to mitigate the loss of intrinsic dimension caused by robustness-promoting regularization. Though simple, our method remarkably improves the clean accuracy of MAML without much loss of robustness, producing a robust yet accurate model. Extensive experiments demonstrate that our method outperforms prior arts in achieving a better trade-off between accuracy and robustness. Besides, we observe that our method is less sensitive to the number of fine-tuning steps during meta-training, which allows for a reduced number of fine-tuning steps to improve training efficiency.