May the Forgetting Be with You: Alternate Replay for Learning with Noisy Labels

Following the reviewers' suggestion we conduct additional analysis on the real-world noisy dataset, Food-101N, as done in [PuriDivER]. The results show that our method produces an increase of $4.52$% accuracy points w.r.t. our second-best PuriDivER.ME and of $5.40$% accuracy points when 'fine-tuning on the buffer' is enabled for both methods, with our method being only $5.28$% accuracy point under the upper-bound (Joint).

We also note that our work comprises an initial empirical evaluation of the behaviour of clean and noisy data in the continual learning scenario, out of which the method is then built. On this premise, and in line with the current literature [PudiDivER,SPR], instance-independent label noise allows us to carry out such analyses. Moreover, we want to stress that we closely follow the settings of the other CNL methods and therefore conduct experiments suitable for comparisons. For what concerns the other types of noise, we firstly want to remark that the asymmetric noise setting, also called class-dependent label noise, is indeed an approximation of real-world corruption patterns. Specifically, in the CIFAR-100 dataset, images are grouped based on their relative superclasses, thus each image comes with a "fine" label (specific class) and a "coarse" label (superclass). The asymmetric noise injection alters labels within the same superclass. This results in sample ambiguity occurring only between similar classes as it would in a realistic scenario. Secondly, instance-dependent noise has not yet been extensively investigated and only a few studies address it, owing to its complex modelling [ALNL].

We are unsure about what makes the reviewer refer to our results as unimpressive, whereas the other reviewers valued our work for the novelty, the comprehensive experiments (2XeP), the effectiveness (Jj1M) of the method and the thoroughness of the analysis (aFAe).

As for the question on the CIFAR-10 experiments missing: due to space constraints, we prioritize more complex and longer benchmarks.

[PuriDivER]: Bang, Jihwan, et al. "Online continual learning on a contaminated data stream with blurry task boundaries." In CVPR. 2022. 
[SPR]: Kim, Chris Dongjoo, et al. "Continual Learning on Noisy Data Streams via Self-Purified Replay." In ICCV. 2021.  
[ALNL]: Song H, Kim M, Park D, Shin Y, Lee JG. Learning from noisy labels with deep neural networks: A survey. IEEE Transactions

Weakness 1:
We struggle to understand the point raised by the reviewer; they recognize the novelty of Alternate Replay (the main contribution of our work) but still find the contribution not good enough.

As the vast majority of current LNL works, our work combines existing techniques to bring new ideas and methodologies (i.e. our AER and ABS). While we borrow and draw inspiration from well-established techniques in the literature about noisy labels, they do not constitute our primary contributions.

Indeed, as appreciated by reviewer 2XeP, our work rearranges experience replay to handle noisy label problems, introducing a novel bi-fold sampling strategy which favours the presence of clean data from both the past and current tasks. Such a strategy exploits the fact that mislabeled examples are forgotten faster than regular ones and introduces buffer forgetting to separate clean and noisy in-memory samples.

Notably, we are the first to address incremental learning under the noisy and offline setup, whereas the current existing works focus on the online setup. For example, PuriDivER cannot adequately fit complex distributions when only one epoch is allowed, as holds for FOOD-101N.

Weakness 2:

The methods suggested by the reviewer rely on meta-learning to learn a label correction mechanism. To do so, these approaches need a small clean validation set. We argue that such a requirement might clash with our setting, tailored for realistic scenarios. Indeed, several real-world noisy datasets do not come with annotations regarding which examples are "clean" and which are not. Hence, we believe that the direct application of [1],[2] is slightly out-of-scope for our work; we will modify our manuscript to include the suggested works in the related materials.

Regarding the simplicity of our sample selection technique, we have a different perspective and see it as a strength of our approach. We emphasise that our algorithm has a single hyper-parameter (the learning rate) and does not require any other tuning (we use the same threshold for each dataset).

Nonetheless, to assess the merits/validity of our choice, we conducted new experiments by fitting the more "complex" Gaussian Mixture Model (GMM) on per-sample loss values to divide training samples into labelled vs unlabeled sets. We equip our approach with this selection technique and report here a comparison with our original "simple" approach (we do so for both synthetic - CIFAR-100 - and real label noise - FOOD-101N - datasets). For the experiments with synthetic noise, since we have information regarding which targets are noisy or not, we can report the buffer cleanliness percentages at the end of training for both selection techniques.

Final Average Accuracy

Final percentage of clean samples in the buffer

With the results in the tables above, we show that the simple sample selection technique adopted proves more effective at separating clean samples. Nevertheless, sample selection via GMM remains a valuable option to avoid additional hyperparameters.

Weakness 3:
Despite the reviewer considering the offline setting unrealistic and negligibly important, we would like to clarify that our experimental setting aligns with many notable works [PASS, DER, LIP, ICARL, LUCIR, CO2L, LSIL, PODNET]. In this respect, we advocate for what has been said in [DER]: when only one epoch is allowed on the current task, even the SGD baseline fails at fitting it with adequate accuracy, especially with complex datasets such as CIFAR-100 and FOOD-101N. Therefore, the resulting performance - and in turn the comparisons among different approaches - can be difficult to read, as the effects of catastrophic forgetting and those linked to underfitting interleave here.

Since in our work Alternated Replay is activated/deactivated every other epoch, the method does not fit the online training scenario.

[PASS]: Zhu et al. Prototype augmentation and self-supervision for incremental learning. CVPR 21.
[DER]: Buzzega et al. Dark experience for general continual learning: a strong, simple baseline. aNeurIPS 20.
[LIP]: Bonicelli et al. On the Effectiveness of Lipschitz-Driven Rehearsal in Continual Learning. aNeurIPS 21.
[ICARL]: Rebuffi et al. icarl: Incremental classifier and representation learning. CVPR 17.
[LUCIR]: Hou et al. Learning a unified classifier incrementally via rebalancing. CVPR 19.
[CO2L]: Cha et al. Co2L: Cooperative continual learning for lifelong visual recognition. ICCV 21.
[LSIL]: Wu et al. Large Scale Incremental Learning CVPR 19.
[PODNET]: Douillard et al. 8: Pooled Outputs Distillation for Small-Tasks Incremental Learning ECCV 20.

Weakness 4:
We here report some comparative experiments on the contribution of our AER and ABS on the two methods cited by the reviewer (for both CIFAR-100 and NTU-60 datasets).

We observe from the following tables that for both DivideERMix and PuriDivER, the addition of AER and ABS has always a positive impact on performance. The increase is more noticeable in PuriDivER than in DividERmix, thus supporting our choice of having it as our main competitor.

I appreciate the authors for their response. I would like to keep my score unchanged. At least for now, I don't think it's necessary to consider noisy label settings in the current continual learning (CL), since CL itself remains many challenges such that its performance is quite poor compared to the offline learning manner. In my personal opinion, we should guide ones in this field to explore that truly improves continual learning rather than considering some very special settings.

We thank the reviewer for taking the time to respond. We remark that, contrarily to the reviewer's beliefs, the current advances in CL have shown performance approaching that of the offline (joint) counterpart [l2p, coda-prompt, attriclip, slca, first_session_adaptation] at least in image classification tasks. Moreover, we observe that plenty of "special settings" have contributed significantly to the performance of current CL methods (e.g., CL and unsupervised representation learning [lump (NeurIPS 2021)] or domain adaptation [ci-uda (ECCV 2022)], CL under limited supervision [ccic (PRL 2022), nnscl (CVPR 2023 - oral)], neuro symbolic CL [cool (ICML 2023)], continual predictive learning [cpl (CVPR 2022 - oral)], CL and reinforcement learning [csp (ICLR 2023 - oral)], ...). Learning in the presence of noisy labels considers the non-ideal but highly plausible case in which the dataset contains annotation errors. Notably, this is the case of most real-world datasets and most of the literature benchmarks e.g., the Imagenet dataset has a label error rate of 5-6% [label_errors_benchmarks].

Finally, we would expect and solicit the reviewer to give a technical comment about the soundness, applicability, and whether the rebuttal has answered the questions that determined the original score. Notably, we were surprised about the reviewers' motivations for being so firm in their decision. Indeed, we feel that their judge is highly biased and not truly dependent on the content of the article and its technical/scientific contributions.

[label_errors_benchmarks]: Curtis Northcutt, et al. "Pervasive Label Errors in Test Sets Destabilize Machine Learning Benchmarks." NeurIPS 2021.
[l2p]: Wang, Zifeng, et al. "Learning to prompt for continual learning." CVPR 2022.
[coda-prompt]: Smith, James Seale, et al. "CODA-Prompt: COntinual Decomposed Attention-based Prompting for Rehearsal-Free Continual Learning." CVPR 2023.
[attriclip]: Wang, Runqi, et al. "AttriCLIP: A Non-Incremental Learner for Incremental Knowledge Learning." CVPR 2023.
[slca]: Zhang, G., Wang, L., Kang, G., Chen, L., & Wei, Y. (2023). SLCA: Slow Learner with Classifier Alignment for Continual Learning on a Pre-trained Model. ICCV 2023.
[first_session_adaptation]: Panos, Aristeidis, et al. "First Session Adaptation: A Strong Replay-Free Baseline for Class-Incremental Learning." ICCV 2023.
[nnscl]: Kang, Zhiqi, et al. "A soft nearest-neighbor framework for continual semi-supervised learning." CVPR 2023.
[ccic]: Boschini, Matteo, et al. "Continual semi-supervised learning through contrastive interpolation consistency." PRL 2022.
[lump]: Madaan, Divyam, et al. "Representational continuity for unsupervised continual learning." ICLR 2022.
[cool]: Marconato, Emanuele, et al. "Neuro symbolic continual learning: Knowledge, reasoning shortcuts and concept rehearsal." ICML 2023.
[ci-uda]: Lin, Hongbin, et al. "Prototype-guided continual adaptation for class-incremental unsupervised domain adaptation." ECCV 2022.
[cpl]: Chen, Geng, et al. "Continual predictive learning from videos." CVPR 2022.
[csp]: Gaya, Jean-Baptiste, et al. "Building a subspace of policies for scalable continual learning." ICLR 2023.

• The settings in the paper are far away from pretrain-based continual learning (CL) models. Additionally, the authors haven't discuss these methods in the paper, and there is no theoretical or experimental support for their work to be applicable to pretrain-based CL models.
• I would like to maintain my score just according to the authors' response, rather than what I previously stated regarding "At least for now, ..., we should guide ones in this field to explore that truly improves continual learning rather than considering some very special settings." I apologize to the author for any confusion caused.

We kindly thank the reviewer for their suggestions and the strengths highlighted. We encourage the reviewer to have a further discussion to help us improve the paper and the rating.

Question (a): We ground our technique on the findings in both [SSF] and [toneva2018ans], which demonstrate that both noisy and complex samples exhibit a stronger tendency to be forgotten and can be distinguished based on their loss, as well as empirical findings of most of the works on Leaning with Noisy Labels (LNL). Indeed, in most cases, LNL methods successfully rely on the small-loss criterion as a technique for separating clean data [Dividemix, CoTeaching, PuriDivER]. Additionally, we conducted empirical evaluations to ensure the same behaviour occurs in a continual learning scenario, as demonstrated in the loss separation depicted in Fig. 1(a). While we cannot completely guarantee the absence of noise in the buffer, the effectiveness of our method in preserving non-noisy data within the buffer demonstrates its improved robustness, as well as subsequent evaluations on the cleanliness of buffer data shown in Fig. 6 of the main paper.
Question (b): Regarding the question about how the size of the buffer impacts the performances, we argue that in a scenario where it is crucial to maintain a clean buffer for accurate memory of past tasks, having a very large buffer, as is common in cases aimed at mitigating forgetting, might have a small impact on performance due to the poisoning effect of noise in the data stored. Instead, in such a scenario it is far more effective to extract a smaller amount of clean samples. To demonstrate this, we conduct a small evaluation of the hardest scenarios of the main table to investigate the effect of different buffer sizes. Such an evaluation shows that the second-best methods we evaluated (i.e., our ad-hoc version of PuriDivER, PuriDivER.ME), cannot effectively take advantage of the increased buffer, whereas our proposal can, and remains competitive across the board. The Final Average Accuracy results to assess the just-mentioned evaluations are reported in the following table.

Question (c): Following the reviewer's suggestion, in the following table, we present the accuracy averaged over 3 runs with 3 different random shuffles. The results are on par with those originally reported, exhibiting a relatively modest standard deviation. This sustains the finding that, regardless of the method used, the choice of class order has a negligible impact on performances.

Question (d):Most rehearsal methods rely on the $reservoir$ mechanism, which is designed to yield an i.i.d. representation of the original distribution. This, combined with our selection strategy, which guarantees the data is both clean and class-balanced, leads to strong performances of the method even as the number of tasks increases.

Weakness 1: In our paper, $D_t$ was the set of data belonging to the specific $t^{th}$ task, containing $(X_t , Y_t)$ tuples of image and label. Consequently, in Eq. (4), $D_t \cap M$ is the intersection between current task data and buffer data, so $(x_t,y_t) \sim D_t \cap M$ stands for data belonging to both sets. We acknowledge that the $*problem setting*$ is crucial for method comprehension, and we understand the importance of providing detailed information for those who have no knowledge about the continual learning setting. Following the reviewer's suggestion, we therefore rearranged Sec. 3.1 to enhance comprehensibility and now treat $D_t$ as a distribution. Specifically, the new version of the sentence is now "We formalize the problem of Continual Learning under Noisy labels (CLN) as learning from a sequence of $T$ tasks. During each task $t \in \{0, 1, \dots, T\}$, input samples $\mathbf{X_t}$ and their corresponding annotations $\mathbf{Y_t}$ are drawn from an i.i.d. distribution $\mathcal{D}_t$."

Weakness 2: We have opted for the most commonly used forgetting metric in the Continual Learning field (see Eq.(1) of the submitted supplementary material), applying this measure to each conducted experiment. As mentioned in Sec. 4.1 of the main paper, we kindly invite the readers to examine the supplementary materials provided alongside the main paper, as the evaluations they consider lacking are documented there. Moreover, as reported in Tab. D of the supplementary material, our method outperforms the others in terms of Final Forgetting metrics.

[SSF]: Maini, Pratyush, et al. "Characterizing datapoints via second409 split forgetting." In aNeurIPS, 2022.
[toneva2018an]: Toneva, Mariya, et al. "An empirical study of example forgetting during deep neural network learning." In ICLR Workshop, 2019.
[DivideMix]: Li, Junnan, et al. "Dividemix: Learning with noisy labels as semi-supervised learning." In ICLR Workshop, 2020. [CoTeaching]: Han, Bo, et al. "Co-teaching: Robust training of deep neural networks with extremely noisy labels." In aNeuIPS. 2018.
[PuriDivER]: Bang, Jihwan, et al. "Online continual learning on a contaminated data stream with blurry task boundaries." In CVPR. 2022.

We appreciate the reviewer's suggestion and comments about both strenghts and weaknesses, inviting further discussion to enhance the paper and its evaluation.
Weakness 1:

• Similarly to the approaches in Continual Learning under Noisy Labels (CLN) studies [PuriDivER, SPR], we opt for selecting classes from the WebVision dataset by choosing the ones containing the largest number of images each. This decision is motivated by observations from the PuriDivER experiments on the WebVision and Food-101 datasets presented in the original paper, where the method noticeably underfits. Our emphasis is on addressing forgetting rather than the underfitting resulting from having numerous classes with varying cardinalities, given the continual learning scenario we are tackling. Following this and other comments from the reviewers, we have incorporated an experiment with Food-101N, and now we evaluate two datasets with real-world noise We would like to include these additional results in the main paper should the reviewers reconsider their ratings. | Benchmark | Food-101N | |---------------------|-----------| | Joint | $39.91$ | | PuriDivER.ME | $25.34$ | | w. buffer fit. | $29.23$ | | OURs | $29.86$ | | w. buffer fit. | 34.63 |
  • [SPR]: Kim, Chris Dongjoo, et al. "Continual Learning on Noisy Data Streams via Self-Purified Replay." In ICCV. 2021.
    [PuriDivER]: Bang, Jihwan, et al. "Online continual learning on a contaminated data stream with blurry task boundaries." In CVPR. 2022.
• It is important to highlight that PuriDivER inherently includes the buffer fitting stage as a vital aspect of the method, while our AER+ABS does not. Consequently, a fair comparison should be drawn between our method, incorporating the buffer fitting stage, and theirs. It is noteworthy that we have meticulously tailored Puridiver.ME to our offline setting, with consistently superior results compared to PuriDivER. Additionally, we decided to also include the performance of PuriDivER.ME with the buffer fitting stage disabled. Results are reported in the following table and we argue these provide a fair comparison between our method and PuriDivER.ME. Furthermore, the results on the newly introduced real-world noisy dataset (Food-101N) validate the efficacy of our method even in the absence of buffer fitting.

• As for the evaluations they consider lacking, these are precisely documented in the supplementary materials provided alongside the main paper. As evident from the results in Tab. E (reported again here), the introduction of each additional feature contributes to a performance improvement, particularly noteworthy when incorporating AER and ABS individually, as well as in combination.

• We would like to clarify that the consolidation phase of the Puridiver method is not part of our approach. A single experiment was presented in the supplementary material for the purpose of comparison, validating the robustness of our consolidation. Nonetheless, we use this term to denote the technique employed by both PuriDivER and PuriDivER.ME to distinguish between clean and noisy data, subsequently applying pseudo-labeling in a DivideMix fashion.

• We concur with the reviewer's observation that "The single or multiple training iterations are decided by the offline/online setting, and not something that an algorithm could choose." The references to offline or online settings in the main paper are made to highlight that some competitors were tailored for online Continual Learning (CL), whereas our method is explicitly designed for offline CL. We will enhance the clarity on this aspect throughout the entire paper, with the hope that the reviewer will reconsider their evaluation.

• Following the suggestion of the reviewer, we compare experiments already reported in the main paper of AER and ABS applied to DER++ with PuriDivER relying on DER++, which we name PuriDivDER++. Results are reported in the following table

Thank you kindly for your response.

1. We apologize for the confusion regarding our statement on underfitting. Indeed, our choice of benchmark already includes classification with more than 10 classes (i.e., CIFAR-100, NTU-60, and Food 101-N). Instead, we referred to "underfitting" as the phenomenon linked to the restricted amount of epochs allowed in the online noisy CL setting, which, in our opinion, limits the applicability of current methods in real-world scenarios.

As for Food-101N, we kindly refer the reviewer to check carefully Sec. 4.1 (pag. 6) of the revised manuscript, as well as the results in Tab. 3 (pag. 7).

2. We avoided adopting PuriDivER as a starting point for our method as our intention is not to extend existing noisy online CL methods in the multi-epoch scenario, but rather to adapt current multi-epoch CL for a noisy scenario.

For what concerns the consolidation stage, we posit that its omission constitutes a strength of our method. Specifically, current online CL methods require a consolidation stage to avoid completely underfitting the current task. However, their effectiveness remains limited as this stage relies on finetuning only on data from the buffer at the end of each CL task. Instead, our method surpasses almost all consolidation-based methods without the need for any consolidation, with a notable gain in training time (on CIFAR-10 with 40% noise, our method takes about 1h30m to complete, while PuriDivER and PuriDivER.ME take 5h15m and 2h50m respectively).

For what concerns the weakness raised regarding the presentation of PuriDivER's consolidation, we agree with the reviewer and will include a brief description in the revised manuscript.

3. Yes, as stated in the introduction: "We depict the loss trend for both the clean and noisy samples in a memory buffer produced by a rehearsal baseline ..." Following the reviewer's comment, we will update the caption to include such detail to avoid future confusion.

4. To answer the reviewer's first part of the question, since $z$ is the same for both sides of the dis-equation, the imbalance would still persist, although it would favour the opposite case with samples from the past being selected for removal disproportionally. We argue that this motivates our choice of designing ABS. As for the second part, we would like to point out that $p(\mathbf{x})$ defines the distribution from which to sample the example from the buffer to replace. To do this while avoiding the aforementioned problem of balancing the buffer between samples from the present and the past, we rely on a two-stage algorithm. Specifically, we initially first sample from the binomial distribution $\phi$ (with probability $q$ = $\frac{M_{curr}}{M}$ if we wish to select a sample from the present (i.e., $p_{curr}$) or the past (i.e., $p_{past}$). The latter scores are defined as:
   $p_{curr}(x) = \frac{L(x)}{z_{curr}}$, with $z_{curr}=\sum_{x\in M_{curr}}$
   $p_{past}(x) = \frac{L(x)}{z_{past}}$, with $z_{past}=\sum_{x\in M_{past}}$
   Thus, following the reviewer's question, if we choose to replace a sample from the past, we will sample $x\sim p_{past}$. In the original manuscript, for brevity, we summarized the above solution as sampling from $p(x) = \phi p_{curr}(x) + (1-\phi) p_{past}(x)$, with $\phi$ being used as a binary selector. However, we agree with the reviewer that such a form might be confusing, thus we will extend the explanation of ABS in the revised manuscript.

We deeply value the reviewer's feedback on our paper. We've addressed every concern they raised, and earnestly request them to engage in a discussion with us. If they find our revisions satisfactory, we hope for a revised score reflecting the improvements, as such a gesture could encourage other inactive reviewers to engage in the discussion.

We have submitted a revised version of the manuscript incorporating improvements based on the suggestions provided by the reviewers. We look forward to the reviewers having the opportunity to check the updated manuscript along with our responses to their comments and questions.