A Appendix

By Assumption 4.1 and 4.2, we have E By Assumption 4.1, an important consequence is that for all {θ,θ Assumption 4.2, we have (see [1, p. 183]) V By Assumption 4.1, 4.2 and 4.3, we have lim inf The first condition in Assumption 4.3 ensures that Under assumptions 4.1, 4.2 and 4.3, we further assume that the risk function Figure 3: Our re-implementation results of Re-balance and ICaRL are very close to those reported in [2]. Mean Standard Deviation Base classes 7.97 0.63 New classes 7.48 0.71 A.3 Additional Experiment Results We re-implement FSLL because the code is not provided. Rebalance are very close to those reported in [2]. To verify the correctness of our implementation of FSLL [3], we compare the results of our implementation and those reported in [3] in Table 8. In our experiments, we observe that after training on base classes with balanced data, the norms of the class prototypes of base classes tend to be similar.