Few-Shot Learning (FSL) is a challenging task, i.e., how to recognize novel classes with few examples? Pre-training based methods effectively tackle the problem by pre-training a feature extractor and then predict novel classes via a nearest neighbor classifier with mean-based prototypes. Nevertheless, due to the data scarcity, the mean-based prototypes are usually biased. In this paper, we diminish the bias by regarding it as a prototype optimization problem. Although the existing meta-optimizers can also be applied for the optimization, they all overlook a crucial gradient bias issue, i.e., the mean-based gradient estimation is also biased on scarce data. Consequently, we regard the gradient itself as meta-knowledge and then propose a novel prototype optimization-based meta-learning framework, called MetaNODE. Specifically, we first regard the mean-based prototypes as initial prototypes, and then model the process of prototype optimization as continuous-time dynamics specified by a Neural Ordinary Differential Equation (Neural ODE). A gradient flow inference network is carefully designed to learn to estimate the continuous gradients for prototype dynamics. Finally, the optimal prototypes can be obtained by solving the Neural ODE using the Runge-Kutta method. Extensive experiments demonstrate that our proposed method obtains superior performance over the previous state-of-the-art methods. Our code will be publicly available upon acceptance.
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