Non-Exemplar Online Class-incremental Continual Learning via
Dual-prototype Self-augment and Refinement
——Appendix——

The appendix presents more experimental settings, results, and analyses as follows:

Appendix A More implementation details

Appendix B More results on different dataset partitions.

Appendix C Results and analysis on different base session training strategies.

Appendix D Hyper parameter analysis

Appendix E Computation overhead analysis

Appendix A: More Implementation Details

Dataset Overview. We conduct experiments on three widely used datasets, including CORE-50 (Lomonaco and Maltoni 2017), CIFAR 100 (Krizhevsky and Hinton 2009), and Mini-ImageNet (Vinyals et al. 2016). Here we give brief introductions. CORE-50 (Lomonaco and Maltoni 2017) is a benchmark designed for class incremental learning with 50 classes. Each class has around 2,398 training images and 900 testing images, with the size of $3\times 128\times 128$. CIFAR 100 (Krizhevsky and Hinton 2009) contains 60000 images of $32\times 32$ size from 100 classes, and each class includes 500 training images and 100 test images. Mini-ImageNet (Vinyals et al. 2016) contains 100 classes and is divided into 10 sub-datasets for 10 disjoint tasks, and each task contains 10 classes. Each task comprises 5,000 training images and 1,000 testing images, all with the size of $3\times 84\times 84$.

Appendix B: Results on Different Dataset Partitions

Due to space constraints in the main paper, in this subsection, we report the additional results of different dataset partitions. Concretely, as shown in Tables 1 and 2, we conduct experiments on the configuration of $40\%+6\%\times 10$ and $80\%+2\%\times 10$, where $40\%$ and $60\%$ classes are selected as the base classes, and the rest classes are continually fed to the network in 10 sessions. Moreover, more incremental sessions (i.e., 20 sessions) with the configuration of $60\%+2\%\times 20$ are also compared in Table 3. The five representative state-of-the-art methods are compared with the same training and inference protocols as Non-exemplar Online Class-incremental continual Learning (NO-CL), including Online Class-incremental continual Learning (OCL) methods (i.e., SCR (Mai et al. 2021), OCM (Guo, Liu, and Zhao 2022), and DVC(Gu et al. 2022)), Non-Exemplar Class-incremental continual Learning (NE-CL) method (i.e., PASS (Zhu et al. 2021b)), and Few-Shot Class-incremental Learning (FS-CL) method (i.e., ALICE (Peng et al. 2022)). As we can see from Tables 1 and 2, fewer base classes result in poor performance, both in base and novel classes, because the network lacks enough pre-trained information to generalize to novel classes. Meanwhile, as our method depends on the inner-prototype computed by the pre-trained backbone, the well-trained backbone benefits us much for the prototype refinement. Notably, even with $40\%$ base classes, our method also achieves the best performance in Acc and HM metrics, which validates the robustness of prototype refinement strategies. Moreover, as for more incremental sessions in Table 3, the performance only drops slightly. Overall, experiments on different dataset partitions validate the effectiveness and robustness of our method.

Appendix C: Results and Analysis on Different the Base Session Training Strategies

The stability and plasticity dilemma is a thorny problem in the area of continual learning. To deal with this dilemma, previous NE-CL (Zhu et al. 2021b, a) and FS-CL (Peng et al. 2022; Kalla and Biswas 2022) methods employ self-supervised learning (Jing and Tian 2021) and class and data augmentation to learn task-agnostic and transferable representations. For the problem of NO-CL, the base session training strategies also matter for the stability and plasticity dilemma. For fair comparisons, similar to (Mai et al. 2021; Gu et al. 2022; Guo, Liu, and Zhao 2022), we also employ supervised contrastive (SC) learning. Here, we provide two training strategies. Concretely, we add the extra self-supervised learning loss (Lee, Hwang, and Shin 2020) (+SSL) like (Zhu et al. 2021b; Kalla and Biswas 2022) and use the data augmentation strategy (+DA) proposed by (Zhu et al. 2021a; Peng et al. 2022). The results in Table 4 show that the elaborately designed pre-training strategies improve the accuracy both in the base and novel classes. Therefore, developing a more robust pre-training strategies is a promising way for the proposed NO-CL problem.

Appendix D: Hyper Parameter Analysis

Here, we analyse hyperparameters including feature transform coefficient $\lambda$, online iteration $T$, and the number of sampled prototypes $K$. We provide quantitative results on the Mini-ImageNet dataset in Figures 1, 2, and 3. Also, the experiments of the varying dimension of hyperdimensional embedding are conducted in Table 5.

In Figure 1, we can see that $\lambda>1$ leads to degraded performance as the feature distribution is more concentrated close to 0. Meanwhile, decreasing too much $\lambda$ makes the distribution scattered and less aligned to the calibrated Gaussian distribution. Therefore, we set $\lambda$ as 0.5 in our experiment.

In Figure 2, we vary online iteration $T$. Less $T$ iterations harm the network to accommodate online novel classes by refining hyperdimensional prototypes and aligning the projection module. Meanwhile, more online iterations only lead to slight degradation, which validates the plasticity of our method. Therefore, we set $T$ to 20 to achieve the stability-plasticity trade-off.

In Figure 3, we vary the number of sampled prototypes $K$. Concretely, we vary the number of sampled prototypes of base classes $K_{base}$, novel classes $K_{novel}$, and all classes $K$. We can see that the imbalance sampling of classes leads to performance degradation, which is similar to the class imbalance problem (Hou et al. 2019; Wu et al. 2019). Also, increasing $K$ does not bring many gains while inducing computation overheads. Therefore, we set $K=20$.

From Table 5, we can learn that increasing the dimension of hyperdimensional embedding benefits the proposed method while too large dimension brings little gain. Therefore, we set the dimension of hyperdimensional embedding as 2048 in our experiments.

Appendix E: Computation Overhead Analysis

For computation overheads during online learning, which is usually considered in OCL scenarios (Fini et al. 2020), we provide more quantitative comparisons to OCL, NE-CL, and FS-CL methods in Table 6. The batchsize of example-based methods is set as 10. As we only align prototypes by finetuning the projection module, which is much more efficient compared with training the whole network. Therefore, our method has clear advantages on computation overheads for online continual learning. Meanwhile, the bi-level optimization quickly converges as shown in Figure 4.