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We study the problem of few-shot open-set recognition (FSOR), which learns a recognition system capable of both fast adaptation to new classes with limited labeled examples and rejection of unknown negative samples. Traditional large-scale open-set methods have been shown ineffective for FSOR problem due to data limitation. Current FSOR methods typically calibrate few-shot closed-set classifiers to be sensitive to negative samples so that they can be rejected via thresholding. However, threshold tuning is a challenging process as different FSOR tasks may require different rejection powers. In this paper, we instead propose task-adaptive negative class envision for FSOR to integrate threshold tuning into the learning process. Specifically, we augment the few-shot closed-set classifier with additional negative prototypes generated from few-shot examples. By incorporating few-shot class correlations in the negative generation process, we are able to learn dynamic rejection boundaries for FSOR tasks. Besides, we extend our method to generalized few-shot open-set recognition (GFSOR), which requires classification on both many-shot and few-shot classes as well as rejection of negative samples. Extensive experiments on public benchmarks validate our methods on both problems.