Weusedtheentireimagesthatthe CUBdataset has (train, val, andtest). For example, onthe CUBdataset, theperformancegain (fork =5) is 0.249, 1.035, and 2.276for miniImageNet, tieredImageNet, and ImageNet, respectively.

The concept of "incidental correlations" is derived from the notion of incidental endogeneity [

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We thank all the reviewers for their insightful and encouraging comments. Per your suggestion, we will update the appendix by adding more explanations about the proof ideas. Similarly, we can extend convergence results in Theorem 4 in Appendix from FS to IFS. We expect that the approach developed in this paper will fuel this future investigation. We will update this into the revision.

In this supplementary, we provide additional details, results and visualizations.

While agood feature extractor may help cluster unseen data, thetask distribution shift between training andtesting [25] still makes it hard to estimate novel class distribution using a small number of samples from the support set. Thus, the performance is strongly correlated with the sample quality of the support data.