Challenging Common Assumptions about Catastrophic Forgetting
Authors: Timothee LESORT
Oleksiy Ostapenko
Pau Rodriguez
Md Rifat Arefin
Diganta Misra
Laurent Charlin
Irina Rish
Venue: Submitted to ICLR 2023 (2023)
Keywords: Continual Learning
Knowledge Accumulation
Scaling

Abstract: Standard gradient descent algorithms applied to sequences of tasks are known to induce catastrophic forgetting in deep neural networks. When trained on a new task, the model's parameters are updated in a way that degrades performance on past tasks. 
This article explores continual learning (CL) on long sequences of tasks sampled from a finite environment.
\textbf{We show that in this setting, learning with stochastic gradient descent (SGD) results in knowledge retention and accumulation without specific memorization mechanisms.} This is in contrast to the current notion of forgetting from the CL literature, which shows that training on new tasks with such an approach results in forgetting previous tasks, especially in class-incremental settings.
To study this phenomenon, we propose an experimental framework, \Scole{} (Scaling Continual Learning), which allows to generate arbitrarily long task sequences. Our experiments show that the previous results obtained on relatively short task sequences may not reveal certain phenomena that emerge in longer ones.

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CHALLENGING COMMON CATASTROPHIC FORGETTING
ASSUMPTIONS
ABOUT
Anonymous authors Paper under double-hlind review
ABSTRACT
Standard gradient descent algorithms applied to sequences of tasks are known induce catastrophic forgetting in deep neural networks. When trained on a new task, the model's parameters are updated in a way that degrades performance on past tasks. This article explores continual learning (CL) on long sequences of tasks sampled from a finite environment. We show that in this setting, learning with stochastic gradient descent (SGD) results in knowledge retention and accumulation without specific memorization mechanisms. This contrast to the current notion of forgetting from the CL. literature, which shows that training on new task with such an approach results in forgetting previous tasks, especially in mlas-inncemmnnal settings. To study this phenomenon, we propose experi- mental framework, SCole (Scaling Continual Learning), which allows to generate arbitrarily long task sequences. Our experiments show that the previous results obtained on relatively short task sequences may not reveal certain phenomena that emerge in longer ones.
INTRODUCTION
Continual learning (CL) aims to design algorithms that learn from non-stationary sequences of tasks. Classically, the main challenge of CL is catastrophic forgetting (CF) - fast performance degradation on previous tasks when learning from new data. CF is usually evaluated on scenarios with sequences of disjoint tasks (Lesort et al., 2020; Lange et al., 2019; Belouadah et al., 2021; Hadsell et al., 2020). In these scenarios, fine-tuning model with plain empirical risk minimization objective and stochastic gradient descent (SGD) results in CF (Rebuffi et al., 2017; Lesort al., 2019 9a; Kang et al., 2022).
The main motivation for this work is to step back from classical continual learning and investigate if fine-tuning with gradient descents approaches only truly leads to catastrophic forgetting or if it can result in knowledge accumulation and decaying forget- ting. For example, Evron et al. (2022) theoretically showed that, for linear regression trained with SGD knowledge accumulation exists, leading to CF reducing uniformly when tasks reoccur randomly or eyclically. This indicates that CF might not be as
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Figure 1: With SGD, knowledge accumulation is not observable in standard CL benchmarks (inset top). However, when repeating the sequence of tasks (bottom), knowledge accumulation is appar- ent and accuracy rises (MNIST, 2 per task, averaged over and seeds, each task trained until con- vergence).
In this work, we empirically show that deep neural networks (DNNs) may consistently learn more than they forget when trained with SGD 1F. We investigate how DNNs trained continually for single-head classification on long sequences of task with data reocurrence forget and accumulate knowledge.
To this end we propose SCoLe (Scaling Continual Learning), an evaluation framework for CL algorithms that generates task sequences of arbitrary length. As visualized in Fig. 2, SCoLe creates each new task from randomly selected subset of all classes. A model is trained for some epochs data from these classes until the task switches. The SCole framework creates tasks online

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by sampling an existing source dataset such as CIFAR (Krizhevsky et al.). By modifying the sampling strategy of the source dataset, we can control data recurrence frequencies, the complexity of the scenario, and the type of shifts in distribution (random, long-term, cyclic, etc.).
As in classical continual learning scenarios, SCoLe scenarios have regular distribution shifts that should lead to CF. However, in SCoLe, tasks and data sparsely reoccur. This reoccurrence makes it possible when training with naive SGD, to study knowledge can accumulate through time. The idea is: if the model does not forget catastrophically but progressively, some knowledge can be retained until the next occurrence of the data leading to potential knowledge accumulation. We study the impact of such reoceurrence in series of SCoLe experiments and confirm that DNNs trained with gradient descent only accumulate knowledge without any supplementary CL mechanism.
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Figure 2: Illustration of SCoLe scenario. With classes in total (one per color) and 2 classes per task. The data are selected randomly based on their label to build the scenario dynamically, into potential infinite sequence. The evaluation is performed on the test set containing all possible classes.
Our contributions are as follows: (1) We propose an experimentation framework "SCoLe" with a potentially infinitely long sequence of tasks. SCole scenarios are built study knowledge retention and accumulation in DNNs with non-stationnary training distributions. (2) We show that in such scenarios standard SGD retains and accumulates knowledge without any CL algorithm, i.c. without supplementary memorization mechanism. This result is counterintuitive given the well-known phenomenon of catastrophic forgetting in DNNs. (3) We study the capabilities and limitations of such training with scenario based on a variety of datasets (MNIST, Fashion- KMNIST, CIFARIO 10, CIFAR 100, minilmageNNt) and scenarios.
SCoLe:A FRAMEWORK FOR CL WITH LONG TASK SEQUENCES
General Idea. We propose framework that allows the creation of an arbitrarily long sequence of tasks. The setting is based on the finite-world assumption (Mundt et al., 2020), which hypothesizes that the world has finite set of states, and in a finite period of time, the agent will see all of them. Later data will, therefore, necessarily be a repetition of previous ones. As in classical CL, in SCoLe each task is comprised of subset of world's data, whereby the evaluation is done the whole world. In such a world, a learning system must accumulate knowledge about the world by experiencing parts of it in isolation. The difference to the classical CL scenarios that data sparsely reoccurs. An agent can succeed in this setup only by accumulating knowledge faster than forgetting it. SCoLe can reveal learning dynamics of DNNs under distribution shift that are not observable on short sequences of non-overlapping tasks, as we show next. Measuring the performance on whole world allows us to estimate whether. overall, the agent accumulates knowledge faster than forgets.
Framework.
We instantiate this idea in a classification setting (Fig. 2). At each task, subset of classes is randomly selected from the total of N available classes (N is dataset dependent). The agent is a DNN that learns to classify on this subset only and is tested on the full test set with all classes. The framework considers scenarios with varying numbers of tasks T and classes per task C.
Formally, the training set D, for task & consists of (æ,, y) pairs sampled from the distribution p(X, Y (S:) = (X Here S, = [- is the set of classes in task t. In the default SCoLe scenario, the elements of S, are sampled from the uniform distribution over all N classes G ~ U00 N - 1) without replacement. We also consider cases where p(S;; C') is non-uniform (Sec. 4.2) or evolves over time (Sec. 5). Label y is sampled uniformly over S, and x is obtained as x ~ p(X) Y = v). The test set Diest contains all classes in the scenario. Following the data generation process, it is generated with C N.
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Figure Initial experiments with default prrem-parameters on MNIST. Masking gradient and removing momentum, increase knowledge accumulation leading reduction of forgetting.
Measuring divergence IID. SCoLe enables studying knowledge accumulation function of divergence to IID of the training distribution. We formalize the closeness of SCoLe scenarios to the identically and independently distribution (IID) training regime using the expected (over tasks) KL-divergence. When p(Y) is uniform over N classes, the KL-divergence between p(X, Y|S) and the IID joint (X, (X, Y' is [DxL ( Y Ss) |1 PH,, of classes and C' the number classes per task. (for derivation cf. App. B). Hence, in SCoLe scenarios using an N/C ratio closer to 1 generates training tasks closer to IID. It also reduces the expected number of tasks between two occurrences of the same task Ttask (or of class Telass). Finally, it increases the probability Po that classes of consecutive tasks overlap (cf. App. A for details). For example with C = 2, Telass = 45 and Trask 5 for CIFARIO, while Telass = 4095 and Trask 50 for CIFAR100 100. Thus, revisiting exactly the same task in CIFAR100 for C = 2 is very rare (every 4,095 tasks). Note that standard CL Frask and Tcioss are inf while Po is
= log N Ø with N the total number
In this paper, we propose three sets of experiments. We first present how to observe knowledge accumulation (Sec. 3). Secondly, we experiment with various levels of non-stationarirty of the scenarios understand better the robustness of knowledge accumulation with gradient descent (Sec. 4), finally we observe knowledge accumulation with long term distribution shifts (Sec. 5).
OBSERVING KNOWLEDGE ACCUMULATION IN SCoLe
In this section show how, in SCole,, learn sequence of tasks without a continual learning algorithm such as replay, regularization, or a dynamic architecture.
3.1 INITIAL EXPERIMENT
In this experiments, we estimate knowledge accumulation with popular optimizers.
Setting: We study several standard approaches for training DNNs. We the two most popular optimizers in CL and ML in general: SGD with momentum (Qian, 1999), and Adam (Kingma & Ba, 2014). For SGD, we set the momentum 0.9, since is the default value in PyTorch (Paszke et al., 2019). We start to experiment with a scenario with only 20 tasks on the MNIST dataset with 2 classes per task and small convolutional neural network (c.f. Appendix
At task t, the objective is to find 0; that minimizes the (global) test set Drest loss. This is done through the proxy of training loss minimization (cross-entropy) ((x,)) (f(z; 0), where f(= 0) is function realized by neural network parameterized with 6. Training is done using batched training procedure with b denoting the batch size and e denoting the number of epochs per task. We
define u, to be the number of gradient updates per task, which in general case is u4
[D.]
The results in Fig. 3a show no progress in the test accuracy, even with a decrease in performance over time. This result is in accordance the common CF phenomenon (French, 1999).
Results:
Next we are going to show that knowledge can actually accumulate as seen in Figure and how to facilitate such accumulation with minimal modifications to the learning algorithm.
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3.2 IMPROVING KNOWLEDGE ACCUMULATION
Setting: We propose to use two small improvements for gradient descent (1) removing the momentum for SGD, (2) masking gradient for classes not currently in the task in the output layer: "gradient masking". Accumulation can be observed without those improvements those improvements becomes easier and more consistent. We test those improvements on the 20 tasks scenarios and 500 tasks scenarios (2 classes per task).
seen in Fig. 1 but with
Intuitively, in the presence of data distribution drifts, momentum (also present in Adam) produces a mixture between the gradient of the previous task and the gradient of the current task. This can create interference in the training process.
Recent papers show that masking the gradient in the last layer helps classifiers to learn continu- ally (Caccia et al., 2022; Zeno et al., 2018) even without any supplementary memorization pro- cess (Lesort et al., 2021a). Therefore, we tested whether "group masking" from Lesort et al. (2021a) could also be useful in training a model end-to-end in a SCoLe scenario. The idea is that, when learning on subsets of classes (without replay). the gradient is only backpropageted through the outputs corresponding to the classes in the current batch. The inference is realized in the same way as single head approaches but the loss computed by only taking into account outputs of classes currently in the mini-batch. On the other hand, Ramasesh et al. (2021) shows that CF happens the most on the higher layers and gradient masking is the most wrrwght-forward way to reduce forgetting in the output layer for free. We hypothesize that apparent reduction of forgetting through such masking can be partially attributed to its regularizing effect for preventing overfitting and not forgetting (even though in this case both are evidenced in the reduced performance): if no masking is applied the layer can quickly achieve low training error by reducing biases and norms classes not observed in the current batch hence Hou al. (2019); Lesort et al. (2021a).
Fig. 3b shows that these two small improvements result in an increase in performance even after a few tasks. In Fig. 3c, we scale the number of tasks to see at which point the accuracy stops improving. Thereby, the accuracy of the model can reach close to IID accuracy.
Results:
Those slight improvements help see that gradient descent algorithms may not forget catastrophically even without using memorization mechanisms (beyond masking in the last layer).
3.3 HPS SEARCH.
To find the best setup to run our further experiments, we run a small hyperparameter search on the same scenario, but with 500 tasks on MNIST, Fashion-MNIST, and KMNIST. Fig. 4a shows the average performance on the three datasets with various learning rates.
Setting:
Results: In Fig, 4b we show that SGD without momentum and with masking is stable baseline, as it leads to knowledge accumulation consistently on all datasets. We also find that, with a small learning rate, Adam and SGD with momentum can achieve knowledge accumulation and improve their accuracy on the test set when scaling the number of tasks, even without masking.
Our results show that knowledge accumulation might happen with any gradient descent optimizer. SGD with masking (without momentum) is overall more stable. Hence, We will experiment this baseline in further experiments.
3.4 ROBUSTNESS OF KNOWLEDGE ACCUMULATION
We investigate if knowledge accumulation happens consistently among datasets and architectures.
Setting: We create scenarios on MNIST, Fashion-MNIST and KMNIST with 500 tasks, CIFAR10 100 CIFAR100 and minilmageNet with 1,000 tasks (3 seeds). We experiments the baseline SGD+Mask on all of them. For CIFAR 100 and minilmageNet, we set = 5, while for the other datasets C' 1. In addition, we train several architectures (Resnet18, Inception, vit b 16 and VGG) from the torch library and compare them in a default SCoLe scenario on CIFAR 10 with 2 classes per task.
Fig. 4b shows the learning curve the various datasets. We normalize accuracies by the IID accuracy to make curves comparable. The IID test accuracies are: MNIST 99%, Fashion MÑIST 89%, KMNIST 94%, CIFAR10 79%, CIFAR100 100 40%, and minilmageNet 20%. The accuracies
Results:
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Figure 4: Test with 7 scaled up to 1,000) tasks averaged over MNIST, Fashion-MNIST, KMNIST with 3 seeds. --- line is the best IID performance. SGD+Mask w/tMomentum is the most stable baseline that works with various datasets and architectures.
were obtained with the same models and Adam training with default parameters and without data augmentation. This figure shows that knowledge accumulation occurs consistently in all these datasets. Fig. 4c shows that on CIFAR1O the knowledge accumulation consistently happens with various type of architectures.
Conclusion. In this section, we showed that SGD without momentum and with gradient masking accumulates knowledge over time. After high number of tasks, it can even converge solution that is close to the IID training accuracy. This shows the limited effect of CF and the ability of models retain and accumulate knowledge.
A possible explanation for this behavior is that, while learning new tasks, DNNs do not forget catastrophically. Beyond the catastrophic drop in performance on previous tasks, some knowledge stays and is forgotten only progressively. If data reoccurs, as in SCoLe, before being completely forgotten, knowledge accumulation happens and leads to progressive diminution of forgetting. Hence, the model learns more than it forgets, and the accumulation of knowledge overcomes the forgetting. In CL without masking, forgetting occurs more strongly because the last layer determinant for prediction and more sensitive to forgetting (Wu et al., 2019; Hou et al., 2019; Zhao et al., 2020; Ramasesh et al., 2021; Bell & Lawrence, 2021; Lesort et al., 2021a). Masking stabilizes the last-layer weights, and when scale the number of tasks with reoccurring data, knowledge retention and accumulation is amplified and becomes visible.
EFFECT OF NON-STATIONARITY ON CONTINUAL LEARNING WITH SGD
In this section, turn attention various levels of non-stationarity in SCoLe scenarios. Specifi- cally, we study three ways to control the level of non-stationarity: (1) through the divergence from the IID by changing the total number of classes N and classes per task C, (2) by changing the probability of classes reoccurrence, and, (3) through the frequency of the distribution shift by changing the number of gradient steps per task
4.1 INCREASING THE DIVERGENCE TO IID BY INCREASING THE NUMBER CLASSES
Here control the divergence to IID by varying the total number of classes N in SCoLe scenarios with fixed 2.
Setting: We use CIFAR100 and create different subsets of N classes by subsampling the total number of classes of the train and the test set. A higher N results classes in the test set) and greater divergence from the IID regime (i.e. larger Trask and Telass). We fix number of epochs e = and batch size b = 64 resulting in u = 15 (D, = 900). Results: In Fig. 5 (left) we plot the accuracy of scenarios with different N. We normalized the test accuracy by the IID accuracy on the same data in order to only assess the effect of increasing N on the knowledge accumulation and minimize the effect of increasing the difficulty of the problem.
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Figure 5: Varying N on CIFARIO0 100 dataset (left) for C=2.N impacts divergence from IID and dif- ficulty, Imbalanced class distribution CIFARIO. -- line is the IID training baseline.
Figure 6: (Left) Test acc. when half of the classes is removed at T=500. (Right) Test acc. under a shift in classes distribution at T=500. The impact of shift is smaller for wider models.
This experiment shows that widening the divergence from IID, slows down knowledge accumulation but it still occurs. Reaching IID accuracy would presumably be possible but would require further scaling and/or C' (cf App. Fig. 10).
4.2 CHANGING CLASS OCCURRENCE FREQUENCY
While so far, the task sampling distribution PYY) was uniform, we now make it non-uniform by changing its entropy. Hence, Telass will grow for some classes and decrease for others N = 10 is fixed.
Setup. We plot the model's test accuracy curves for different entropy of p()). As in previous experiments, the class distribution does not change over time in given scenario and instances per classes are balanced within task. Details on the implementation of the entropy control are in App. G.2. Entropy we see that the closer we are to a uniform class distribution for sampling tasks, the steeper is the accumulation curve. This can be attributed nonuniform Telass over classes, leading (a) knowledge accumulation becoming slower for these rare classes and (b) more probable classes are repeated more frequently in the same context, leading possible overfitting.
2.3 corresponds the uniform distribution. Results: In Fig. 5 (right),
Lowering the entropy of the class distribution increase the sparsity of reoccurrence of certain classes, which leads global slowdown of knowledge accumulation.
4.3 THE ROLE OF THE NUMBER OF UPDATES BETWEEN REVISITS
In previous experiments, we have shown that knowledge ac- cumulation reliably occurs for one epoch per task ("online",
e = 1). Here we study the effect increasing the number of epochs per task ("offline")). Larger should result in larger ex-
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pected number of SGD steps between re-occurrence of classes, Welass: and more time for CF.
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Setup. We compare the online setup (e = 1) with the offline one. In the latter, we train on each task until convergence with an early stopping (e.s.) criterion of 5 epochs (e.s. is the strategy of choice for model selection). We fix the batch size b 64, classes per task C = 2 and study CIFARIO (N 10) and CIFAR100 datasets (N 50). CIFARIO has 4500 samples/class resulting in
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Figure 7: (left:) Test acc. in the online setting (e offline setting (train until conver- gence) with N 10. (right:) Same as left, but with N = 50.
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705 the online case. In the offline setup, Telass and Metass are at least times bigger due to e.s. criterion. On the other hand, CIFARIOR dataset comes with 450 samples/class resulting in u 15 but comparable Tctass = 15x x 50 = 750 due to higher Telass (cf.Sec. 2).
Result. In Fig. 7(lftt) for CIFARIO the gap between the online and offline training is small showing that increasing the number of gradient updates does not necessarily slow down knowledge accumula- tion. On this dataset knowledge accumulation dominates forgetting. For CIFAR100 (right) the gap is significantly larger. Given the comparable period size Uptass, this can be explained by (a) a lack of data diversity given the smaller number of samples per class which can lead to overfitting, and (b)

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larger Tclass- The latter implies that (much) larger set of tasks with different classes is seen before an instance of a class is repeated, which can lead to more forgetting. Hence, the number of samples per classes and Tatass are critical for accumulation.
Increasing the number of gradient steps per task can compromise knowledge accumulation when there is risk of overfitting. Nevertheless, it can also keep it high by improving the knowledge of the model on the current tasks. A right trade-off between learning new knowledge and forgetting past ones exists then that does not necessarily push to low divergence with the IID setting. We propose other evidence of this, by varying the number of epochs per task and the batch size in appendix K Fig 17.
Conclusion. The SCoLe framework is convenient for controling the stationarity of the scenarios or creating setups of various difficulty to study knowledge accumulation. In this section, we have shown that knowledge retention and accumulation still happens when increasing the non-stationary. This means that knowledge learned the past can be retained for long periods of training without being forgotten. In the next section, we evaluate how knowledge retention and forgetting happen in SCoLe scenarios with long-term distribution shifts that influence many tasks.
EFFECT OF LONG-TERM DISTRIBUTION SHIFTS
In the experiments presented so far, we sampled classes for each task from the same distribution p(S,; C). Here we create SCoLe scenarios with a shift over time in the class distribution and assess the accumulation of knowledge under long-term shifts - shifts that persist for over several hundreds of tasks. Those shifts may result in very large or infinite Talass for some classes. We evaluate knowledge retention and interference by designing three different shift patterns and evaluate models with increasing width to access whether increasing the width can slow down forgetting (Mirzadeh et al., 2021).
5.1 KNOWLEDGE RETENTION WITH LONG-TERM, CLASS SHIFT
We assess the capabilities of deep neural networks maintain correct prediction on classes that stop appearing. This evaluation of knowledge retention is strict in comparison to related works (Fini et al., 2022: Davari al., 2022) that evaluate knowledge retention by linear probing latent representation. In our setup, knowledge retention in lower layers is not sufficient, and the model also has to maintain knowledge from feature extraction in lower layers to the decision boundaries in the last layer.
Setting: We train on scenario with C' = 2 and uniform p(Y St) on CIFAR1O. We start the training with all classes, after 500 tasks, we remove half the classes from the class distribution. In contrast to standard CL., where distribution shift is usually caused by adding classes, here we remove classes. In such a scenario, the forgetting behavior should be smooth because the error on remaining classes should be low. Results: Fig. 6 (left) shows that even if no new data is introduced to the learner, that is, no interference with old knowledge is possible, the model can still forget when a subset of already learned classes is no longer trained Interestingly, in this setup forgetting is slow and not catastrophic, and knowledge persists during several hundreds of tasks. Moreover, we clearly observe that growing the width of the model increases knowledge retention the point that looks like the model perfectly memorized removed classes for the maximum model size.
5.2 KNOWLEDGE RETENTION WITH CLASS SUBSTITUTION
Similarly to the previous section, we investigate setting with an abrupt shift in the class distribution, however instead of removing classes (shrinking the domain of p(S,; C)), we replace existing classes with new (shift the domain of p(S;; C)). This allows us to investigate the interference and forgetting dynamics that both cause performance drop in this setting. The goal is to assess whether observed knowledge retention can help to slow down forgetting.
Setting: First, 500 tasks are generated from the first 5 classes of CIFARIO (first period), and the second 500 tasks are generated from the remaining 5 classes (second period). There is then no overlap between the classes in the first and second periods. Also here test models with various widths. Results: The results in Fig. 6 (right) show that this sudden class shift creates disturbance in the training process as in classical CL scenarios. Moreover, in the second period of training, the model
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struggles more to learn the tasks than during the first period, meaning the first period does not provide good initialization for later tasks and that the forward transfer is limited in such a regime. This result corroborates the results of Ash & Adams (2020), who witnessed similar phenomenon in a transfer setting. Similarly to the previous section, observe that wider models can better resist to CF. Still, this difference appears less clear, and it could be due to the better knowledge retention of first classes.
5.3 CYCLIC SHIFTS
Here aim to assess whether knowledge retention in DNNs observed
previously persists when we fix Telass to be equal for all classes but varying number of expected SGD updates Uclass before repetitions. To this end we let the distribution p(S;; C*) follow a cyclic patterns.
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Setting: We define a shifting window of W classes as the domain of p(Sr; C)) for N. tasks after which it is shifted by one class or more depend- ing on N and X. Here À the cycle size, i.e. W is exactly the same every A tasks. For example, if the class subset W, before is [0, 1, 2), after a shift will become [1. 2, 3). After À tasks, will be again [0, 1, 2]. We use the full CIFARIO0 dataset (N 100) with 5 classes per task, the window size is W 10, and the cycle size is X E (50, 100, 200, 500], higher À leads to higher Velass. We choose CIFAR 100 because it has more classes than with CIFARIO and allows creating of shifts with longer period. In this experiment, when class leaves the subset window, it needs À W tasks to return leading to equal Telase for all classes.
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We can see in Fig. 8 that increased shift period makes training harder, i... better learning happens if classes reoceur more frequently. Even with the largest period, the model still progresses systematically over time, as seen in Fig. (bottom). Consistently with other experiments, wider models result in better performance, as shown in Figs. 8 (top). These experiments show that SGD-trained DNNs are also capable of long-term retention and can still accumulate even if they do not see some classes for long period of time.
Results:
Figure 8: Cyclic Shifts Experiments: shows the test accuracy averaged over the 10 last tasks for all cycle and model sizes. (bottom) the effect of cyclic shifts for the smaller model.
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Conclusion. Forgetting still happening in long sequences of tasks with long term distribution shifts is expected. However, experiments in this section show that models are capable of long-term knowledge retention, enabling knowledge accumulation even when data not seen for long time. Our results are in line with the findings of Mirzadeh et al. (2021): Wider models forget less in incremental scenarios. Further, we have also shown that the widest models are capable of almost perfect knowledge retention and that with long-term distribution shifts such cyclic shifts, deep neural networks can accumulate knowledge. They can memorize and reuse knowledge from classes not seen since more than 200 hundred tasks.
RELATED WORK
Most scenarios in the continual learning literature study catastrophic forgetting (van de Ven & Tolias, 2019; Lesort et al., 2021b). They are made up of sequence of tasks where data points appear in one task without reoccurring later. Those settings evaluate whether models can remember tasks that they have seen only once. The no reappearance constraint makes the evaluation of CF clearer. Tasks overlap can not interfere with forgetting. However, they cannot evaluate if models accumulate knowledge through time that could be reused with data/tasks reoccurence.
The scenario we propose has some similarities to the CMR (Lin et al., 2022) and OSAKA (Caccia et al., 2020) frameworks. However, in our setting, we do not evaluate fast adaptation, but rather the capacity to learn a solution to a problem from a long sequence of subproblems. Moreover, there is no real concept shift in SCoLe, that is, ((ylx) is fixed over time. Our evaluation protocol is also similar to the ALMA scenario (Caccia et al., 2021), since we evaluate on a fixed test set. However, in ALMA the data distribution does not drift, while in SCoLe there are drifts between tasks. A scenario with a long sequence of tasks was proposed by (Wortsman et al., 2020). Their scenario is composed of various permutations for the permut-MNiST scenario. This scenario also makes it possible to scale
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the number of tasks, but it does not allow to see the progressive knowledge accumulation of SGD witnessed in SCoLe scenarios because there is no task reoccurence.
In Lesort et al. (2021a), the masking method, referred to "group masking". applies gradients only to the outputs of classes within the current batch while training. In particular, the authors showed that this masking is possible while training linear classifier on top of frozen pretrained model. Caccia et al. (2022); Zeno et al. (2018) applied a similar method in continual learning, respectively, in end-to-end training and multihead training, and showed that this method helped mitigate forgetting.
DISCUSSION
Another interpretation of knowledge accumulation (besides the forgetting lens) is through the lens of transfer. Knowledge accumulation is also the result of a positive forward transfer (with SGD). The knowledge learned on task can be reused and improved when the task reoceurs. By this perspective, avoiding forgetting and maximizing forward transfer to the next occurrence, both require some form of knowledge accumulation through time.
Beyond evaluating how SGD forgets, SCoLe is also designed to be a practical evaluation tool to assess knowledge accumulation in a setting with data reoccurrence. SCoLe could be directly transferable to similar real-life settings. For example, a robot that manipulates objects from visual perception or performs semantic segmentation of scenes when moving around. The robot can witness data distribution shifts through time depending on different factors (lightning, rooms, objects), and the same tasks/classes naturally reoccur. Our results suggest that SGD with gradient masking could be very light approach that could serve an embodied agent with restricted compute or memory.
The reoccurence of data could be compared with the action of a replay methods. However, while replay typically emulates an IID distribution, this never happens in SCoLe scenarios. The data streamed by the generative process only provides access to subset of the classes. Moreover, in replay-based methods, the amount of replay and the distribution of replay can be adapted to maximize performance while SCoLe's e's generative process can not be modified during training.
Training dynamics with SCoLe also share similarities with reinforcement learning agents that learn in finite environments, such as video games or simulations. While they learn, the training distribution changes, either because the policy changes or because the agent explores new parts of the environment. This leads to drifts in the local data distribution with reoccurring data as the SCoLe scenarios. In the long run, reinforcement learning agents can still learn policy that is applicable to the entire environment. The results of this paper are in line with this behavior.
8 CONCLUSION
SCoLe is framework for creating continual learning scenarios with long sequences of tasks. It can be adjusted through using several hyper parameters to generate scenarios of varying difficulty and various distribution shifts between tasks. This versatility makes SCoLe a tool to study the ability of deep neural networks to continually learn.
This paper shows that beyond the catastrophic decrease in performance in classical continual learning benchmarks, standard gradient descent is capable of knowledge retention and accumulation. The phenomenon becomes visible when we scale the number of tasks and repeat classes and tasks. To our knowledge, this phenomenon has not been investigated in the literature before. To amplify knowledge accumulation and to increase its impact, we propose to mask gradients of unused classes in SGD training and removing momentum. In the classical continual learning literature the common intuition is that such a simple approach would not be enough to allow accumulation and overcome catastrophic forgetting. However, our results show that knowledge retention and accumulation are sufficient to overcome catastrophic forgetting in SCoLe scenarios. The magnitude of this behavior still depends on the scenario characteristics and notably on the frequency of reoccurence. Our experiments with SCoLe show interesting insights into forgetting, knowledge accumulation, and knowledge retention. We believe that the knowledge accumulation observed with SGD is not restricted to SCoLe training scenarios, the training setups was made to amplify knowledge accumulation. We hope that our framework will inspire further research in this field improve knowledge accumulation deep neural networks in various scenarios.

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REPRODUCIBILITY STATEMENT
For all of our experiments, we use the standard deep neural network architectures and publicly available datasets. We specify all the training details, including datasets for the experiments of knowledge accumulation and distribution shifts in section 3 and respectively. We also show the SCoLe scenario in Fig. 2 and include the pseudo-code for implementation in Appendix D. We provide the code (https: ////a/ooouuuuu 4open. science/ //CVEEGEENCEE 5533/) for all the experimental results presented in the paper. The code base contains all the parameter configurations for running the experiments to reproduce the figures.
REFERENCES
Jordan Ash and Ryan P Adams. On warm-starting neural network training. Advances in Neural Information Processing Systems, 33:3884-3894, 2020.
Samuel J Bell and Neil D. Lawrence. Behavioral experiments for understanding catastrophic forgetting. ArXiv, abs/21 10. 10570, 2021.
Eden Belouadah, Adrian Popescu, and Ioannis Kanellos. A comprehensive study of class incremental learning algorithms for visual tasks. Neural Networks, 135:38-55 2021. ISSN 0893-6080. doi:
https://doi.org/I1 / w0w.f...eumeet.220....oo 12.003. URL https: www. www.nceeiiieiccccoooooo rect com/
sci http:e//errraeeei/i///6633200000
Lucas Caccia, Jing Xu, Myle Ott, Marc' Aurelio Ranzato, and Ludovic Denoyer. On anytime learning at macroscale. arXiv preprint wwxiv:2206.09550 2021.
Lucas Caccia, Rahaf Aljundi, Nader Asadi, Tinne Tuytelaars, Joelle Pineau, and Eugene Belilovsky, New insights on reducing abrupt representation change in online continual learning. In International Conference on Learning Representations, 2022. URL https: /t/p//ppeeeeeieeeeeeeeeeeeeeeeee net for umrum? LddN8MMBBOOUUfb
Massimo Caccia, Pau Rodriguez, Oleksiy Ostapenko, Fabrice Normandin, Min Lin, Lucas Caccia, Issam Laradji, Irina Rish, Alexandre Lacoste, David Vazquez, and Laurent Charlin. Online fast adaptation and knowledge accumulation: a new approach to continual learning. NeurIPS, 2020.
URL https:t/p//. /ttp//aavvvvr///// org/ abs/2003 05856.
MohammadReza Davari, Nader Asadi, Sudhir Mudur, Rahaf Aljundi, and Eugene Belilovsky. Probing representation forgetting in supervised and unsupervised continual learning. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp- 167 16712-16721, 2022.
Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei. Imagenet: A large-scale hierarchical image database. In 2009 IEEE conference computer vision and pattern recognition, pp. leee, 2009.
Arthur Douillard and Timothée Lesort. Continuum: Simple management of complex continual learning scenarios. 2021. URL https: http:s:s//rxxv..xrte abs 221222122222 06253.
Itay Evron, Edward Moroshko, Rachel Ward, Nathan Srebro, and Daniel Soudry. How catastrophic
can catastrophic forgetting be in linear regression? In Conference on Learning Theory, pp. 4028-4079 PMLR, 2022.
Enrico Fini, Victor G Turrisi da Costa, Xavier Alameda-Pineda, Elisa Ricci, Karteek Alahari, and Julien Mairal. Self-supervised models continual learners. In Proceedings of the IEEF/CVF Conference on Computer Vision and Pattern Recognition, pp. 9621-9630, 2022.
Robert M. French. Catastrophic forgetting in connectionist networks. Trends in Cognitive Sciences, 3 14):128-135, 1999. ISSN 13646613. doi: 10.1000SS13644-661199999944444 URL https:// www. www.sciiiccedcc. rect. com/ ses/scienne wwcieencc/aacccccc httpe//aaaiccclaa///////////////
Raia Hadsell, Dushyant Rao, Andrei Rusu, and Razvan Pascanu. Embracing change: Continual learning in deep neural networks. Trends in Cognitive Sciences, 24:1028-1040 12 2020. doi: ...0066).ies.22200.99
10

---

Under review as a conference paper at ICLR 2023
Dan Hendrycks and Thomas Dietterich. Benchmarking neural network robustness common corruptions and perturbations. arXiv preprint arXiv:1903. 2019.
Saihui Hou, Xinyu Pan, Chen Change Loy, Zilei Wang, and Dahua Lin. Learning a unified clas- sifier incrementally via rebalancing. In The IEEE Conference on Computer Vision and Puttern Recognition (CVPR), June 2019.
Minsoo Kang, Jaeyoo Park, and Bohyung Han. Class-incremental learning by knowledge distillation with adaptive feature consolidation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Puttern Recognition, pp. 16071-16080, 2022.
Diederik P Kingma and Jimmy Ba. Adam: A method for stochastic optimization. arXiv preprint 0rXiv:1412.69888 2014.
Alex Krizhevsky, Vinod Nair, and Geoffrey Hinton. Cifar- 10 (canadian institute for advanced research). URL http:/ /www. cs www.ntooooooooo.......
far html.
Matthias De Lange, Rahaf Aljundi, Mare Masana, Sarah Parisot, Xu Jia, Ales Leonardis, Gregory Slabaugh, and Tinne Tuytelaars. Continual learning: A comparative study on how to defy forgetting in classification tasks. 2019. URL https:
08383.
Timothée Lesort, Thomas George, and Irina Rish. Continual learning in deep networks: an analysis of the last layer. arXiv preprint arXiv:2106.01855 2021a. URL https: /ttppps/////vvvv///ae/eeeea http//axxvv...... abbs/ 21 2106.00 01834.
Timothée Lesort, Hugo Caselles- -Dupré, Michael Garcia-Ortiz, Jean-Frangen Goudou, and David Filliat. Generative models from the perspective of continual learning. In IJCNN International Joint Conference Neural Networks, Budapest, Hungary, Jul 2019a. URL https: //all. scchiees-ovverter fr/hal= 01 954.
Timothée Lesort, Andrei Stoian, and David Filliat. Regularization shortcomings for continual learning. arXiv preprini arXiv: arXiv:1912.0888 19/2.03049, 2019b.
Timothée Lesort, Vincenzo Lomonaco, Andrei Stoian, Davide Maltoni, David Filliat, and Natalia Rodzigodr Continual learning for robotics: Definition, framework, learning strategies, opportunities and challenges. Information Fusion, 58:52 68, 2020. ISSN 1566-2535. doi: wttp://rggg...011....fuuuuuuuu.
URL http:://wett http://wwwwww.ccciciccccttccccct rect. com/ sci peclence/arrticll/iiii//e//e/e http://ii.1115555553333333 93073777.
Timothée Lesort, Massimo Caccia, and Irina Rish. Understanding continual learning settings with data distribution drift analysis. arXiv preprint arXiv:2104.01678, 2021b.
Bill Yuchen Lin, Sida Wang, Xi Victoria Lin, Robin Jia, Lin Xiao, Xiang Ren, and Wen-tau Yih. On continual model refinement in out-of-distribution data streams. arXiv preprint 420.00220,.020 2022.
Seyed Iman Mirzadeh, Arslan Chaudhry, Huiyi Hu, Razvan Pascanu, Dilan Gorur, and Mehrdad Farajtabar. Wide neural networks forget less catastrophically. arXiv preprint arXiv:2110.11526. 2021.
Martin Mundt, Yong Won Hong, Iuliia Pliushch, and Visvanathan Ramesh. A wholistic view of continual learning with deep neural networks: Forgotten lessons and the bridge active and open world learning. 2020. URL httpt: http://axxvvv.oo.. abs//bss////0 2009 01797.
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang. Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. Pytorch: An imperative style, high- performance deep learning library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d' d'Alché-Buc, E. Fox, and R. Garnett (eds.). Advances in Neural Information Processing Systems 32, pp. 0024-8035. Curran Associates, Inc., 2019. URL http::ttttppeeeeee wwweeerss.eeeiiee neurips cc/ hwwp/pape//////// 2015-pytorch-ee an- http:///waaaaaaaaaa/eaoaoaaaoaea pdf.
11

---

Under review as a conference paper at ICLR 2023
Ning Qian. On the momentum term in gradient descent learning algorithms. Neural networks, 12(1): 145-151, 1999.
Vinay Venkatesh Ramasesh, Ethan Dyer, and Maithra Raghu. Anatomy of catastrophic forgetting: Hidden representations and task semantics. International Conference on Learning Representa- fions, 2021. URL https:::tp.........t....tt..tt.t http:///pppweeee.eeeeeee/e htt.:/nrtfforiee htt.frrrmmmmttthhhgddudaaaaa
Sylvestre-Alvise Rebuffi, Alexander Kolesnikov, Georg Sperl, and Christoph H Lampert. icarl: Incremental classifier and representation learning. In Proceedings of the IEEE Conference Computer Vision and Pattern Recognition, pp. 2001-2010, 2017. URL https: /ttp////xxxx/o//o///o abs/1611.0777 07725..
David Rolnick, Arun Ahuja, Jonathan Schwarz, Timothy Lillicrap, and Gregory Wayne. Experience replay for continual learning. Advances in Neural Information Processing Systems, pp. 348-358, 2019. URL https: arxiv.. org/ abs
Gido M van de Ven and Andreas Tolias. Three scenarios for continual learning, arXiv preprint arXiv:1904.07334, 2019. URL attps://arxivv org/ /bsp///b///ie 1ttp/1904.07777
Mitchell Wortsman, Vivek Ramanujan, Rosanne Liu, Aniruddha Kembhavi, Mohammad Rastegari, Jason Yosinski, and Ali Farhadi. Supermasks in superposition. In Proceedings of the 34th International Conference on Neural Information Processing Systems, NIPS'20 20, Red Hook, NY, USA, 2020. Curran Associates Inc. ISBN 9781713829566.
Yue Wu, Yinpeng Chen, Lijuan Wang, Yuancheng Ye, Zicheng Liu, Yandong Guo, and Yun Fu, Large scale incremental learning. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pp. 374-382, 2019. URL https: http://aaxwv..../a/..s/ /wt.a////9....... 13260.
Chen Zeno, Itay Golan, Elad Hoffer, and Daniel Soudry. Task agnostic continual learning using online variational bayes. 2018. URL https: /ttp//aaxvvv/////////eee///.e../ wttpooogggp.//ooooeoeeeeee pttp//dff//.///.//////// 10123, .df.
Bowen Zhao, Xi Xiao, Guojun Gan, Bin Zhang, and Shu-Tao Xia. Maintaining discrimination and fairness class incremental learning. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 13208-13211 13217, 2020.
A REOCCURRENCE STATISTICS
The re-occurrence statistics for SCoLe include (assuming the uniform distribution of classes):
the expected number of tasks between the same class is repeated Telass =
the expected number of tasks between the task is repeated Ttask probability of sampling each task, p 1²)
1 where p is the
p'
Po the probability that the supports S, and S₁ for tasks of k) overlap is (()1())))))))
Note that in standard CL Trask and Telass while p., is O. In vanilla experience replay (ER) (Rol- nick et al., 2019; Rebuffi et al., 2017) which is method for mitigating CF (ef Sec.6), both Talass and Trask and p.
Since ER simulates IDD sctup, all tasks overlap and technically speaking no tasks are identical in this regime. In "standard" CI. with ER this only for future tasks w.r.t past tasks.
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B KL DERIVATION
Pr(x. vl Si)
DKL (p(, (IS)) ((a))))
Σ Pe v/Si) log
p(x, y)
=EX
= E p(aly)p(y|Ss) log plaly)p(uls)) p(zly)p(y) NEY
p(y]St) 1og))ooog log p(y)(st) plu)
Σ
Σ p(alu)=
=EX,SEY
sE
Σ (vES.)
(wes)
N
log log C C
DEY
Since P(y)S.) is uniform over elements set St, it is equal 1 and the uniform p(Y) is evaluated N. Since each of the T tasks equally probable the expected divergence as follows:
N Σ T
N
log N C
E Elog ī
log
C
C LIMITATIONS
In this paper, we investigate the phenomenon of steady knowledge accumulation until convergence when continually training model in long sequences of tasks within finite world despite catastrophic forgetting, However, with increasing complexity of tasks, it takes longer to converge due to slower knowledge accumulation.
Estimating the complexity of SCoLe scenario is challenging and probably impossible in practice. In this condition, is not clear how long the sequence of tasks needs be for given scenario.
It is not guaranteed that the trends observed in this work could be observed in the same way for more challenging datasets such as the ImageNet (Deng al., 2009). However, the size of the chosen datasets make SCoLe ideal for fast experimentation which has helped us to test a large number of hypotheses. This is an advantage that would not exist with larger datasets.
D SCENARIO IMPLEMENTATION
The implementation presented in Figure 9 proposes static version of the scenario. However, the "probability" distribution can be modified through the task sequence to create never-ending drifts or cyclic drifts in the class distribution simply change the balance of the class distribution.
E TRAINING IID BASELINES
The training of the IID baselines has been carried out with the same models as the other training processes. However, they were trained with Adam optimizer to improve performance. They were trained with 100 epochs the full dataset. We experimented with the learning rates of 0.001, 0.01, and 0.1 over 5 seeds and only kept the best performern baselines.
F ADDITIONAL EXPERIMENTS
F.1 INCREASING THE NUMBER OF CLASSES PER TASK
Fig. 10, shows that our training framework also works when the number of classes per task increases. The more classes in the task, the faster the learning curve is. Here, we sample tasks from the entire CIFAR 100 datasct.
F.2 MAKING THE MODEL DEEPER
In these experiments, we train on CIFAR1O with binary tasks and classes sampled uniformly. Fig. 11 shows that depth has low impact in experiments.
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num classes: the total number of classes
classes_ pattess__e__ttker number of tasks per class (2 by default)
probability; vector defining probability of sampling each class for a task (Uniform by default)
rb_epochs: epochs of training per task (I by default)
import numpy np
from continuut scenaries import ClassIncremental
from cont inuum inwum. import CIFAR10
scenario - Class Increeetal (CIFAR10 (config.data train-"!rue),
nbbtasks-nb__lasses
set C1FAR10
train-ralse) tto_taskst
for task index in range (num tasks) classes np. random. ctp.rramccccccccc.....cccaraaa aragae
crum_classes] probability, size=
classcs_per_tasee roplace-Falsc)
create taskset with only selected classes taskset scenario
for epoch range (nb_epochs):
# train the model on "taskset" data l...]
test the model the full test set
Figure 9: Pseudo-Code using continuum (Douillard & Lesort, 2021) to control the distribution imbalance classes.
0.40
dassss task
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task Index
Figure 10: Growing the number classes per task within a task in full CIFAR100 dataset.
F.3 STRUCTURING THE TASK SEQUENCE
Setting: In this experiment, we want to evaluate the role of randomization of classes within tasks. In other words, we try to answer the following question: Is it important that classes are randomly sampled when building tasks? For this, we start with a fixed sequence of binary classification tasks. This sequence is built so that all possible pairs of classes exist and occur only once. By default, training is achieved by repeating training sequence of tasks. We compare this baseline with the same sequence tasks, but for each task, we set the probability that each class is flipped by random to another class. The classes of the initial
this fixed sequence of tasks until the end of the full
sequence tasks is [0, 1] > [0, 2] - [...] + [1 + [1.3] 3] + [8, 9] [0, 1] + [..]]. The values of p are 0, 0,01, 0.1. 0.2, 0.3, 0.4, 0.5, 1. We
that p is the same in the default scenario.
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0.8
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0.3
32
44
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Figure 11: Growing the number of layers in the resnet model. with resnet22.
line represent IID performance
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Figure 12:
Comparison on several sequence tasks with default structure modified by random flip of classes at each task. Scenario created with CIFARIO, 2 classes per task. The randomization of tasks not critical for knowledge accumulation.
Results: The results presented in Fig. 12 show that having fixed sequence of tasks instead of randomized one does not reduce knowledge accumulation in our setting.
F.4 LIMITING THE POSSIBLE PAIRS OF CLASSES IN TASKS
Setting: In this experiment, we want evaluate how important is that all possible pairs classes exist within the full sequence of tasks. For this, we start from the list of all possible tasks and select only a subset of them. When building the task sequence, we only select pairs of classes from the selected list.
The results presented in Fig. show that the presence all possible pairs of classes within the sequence of tasks plays an important role. In fact, without replay to learn discriminative features between two classes, classes must on the same task (Lesort al., 2019b).
Results:
G INCREASING DIFFICULTY
G. REGRESSSIONS
G.2 MODIFICATION OF DISTRIBUTION ENTROPY
To change the entropy of the class distribution, we start with a uniform vector probabilities u. For each class, gives the probability of this class be sampled for task. To create imbalance
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0.7
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Figure 13: Comparison of SCoLe scenario when selecting only a subset of all possible pairs of classes within tasks. We vary the proportion of pairs kept and plot test accuracy.
60
y==0.55x+50.88
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10a Acturacy
40
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Figure 14: Regression of test accuracy over last tasks on three seeds with entropy on CIFARIO (left) and number of classes CIFAR 100 (right). More details of the experiments in Sec. 4
in class probabilities, we slightly modify this vector using u' - s- + reumpy. Crrtipyyaanng((C) X. with C the number of classes and and the hyperparameter that decides how much the distribution is modified. We choose empirically X = 2=C for slight imbalance. To increase the imbalance in the distribution, we multiply u' by itself d times. The complete experimentation tests the values of 0, 1, 2, 5 and 10. Note that d = 0 means that the distribution is uniform (cf. Appendix Sec. G.2 for the Python implementation and the probability vectors for each d).
Probability vectors for ten classes and À 0.05 with different entropy parameters (rounded with 3 decimals).
entropyy 0 (0.1, 0.1 0.1 0.1 0.1, 0.1 0.1 0.1, 0.1,0.1] cntropy=2.303
entropy_decreatt = + [0.129, 0.123, 0.116, 0.11, 0.103, 0.097, entropy=2.285
entropy_decrease- decrease = 2 + (0.161, 0.145, 0.13, 0.116, 0.103, 1110001014|133311000000000000000 0.068, 0.058, 0.049) entropy=2.237
entropy_decrease 5 (0.264, 0.204, 0.156, 0.117, 0.087, 0.063, 0.044, 0.031, 0.013) entropy=1.985
cntropy_decreace = 10 - [0.424, 0.254, 0. 148, 0.083, 0.046, 0.024, 0.012, 0.006, 0.003, 0.001] entropy=1.537
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nun classes: the total number of classes
lambda: hyper-parameter (2+C)
antropy_decrease: parameter that control the scale of the Imbalance
import numpy as no
prob_vec vec = ones cou_ccaasses) / num_classee
introduction of slight imbalance
prob_vec prob_vee (1/num np, np.arange (num_classes)
lambda
prob_vec /= reoo_vec.sure
prob_vec vec - prob_ vec+ entrray (prob_vec**
entropy_decrease) sum
we shuffle the vector so for each experiments the imbalance is not the same
np. randon. seed (config.seee np. random. shuffle (prob_vec)
for task_ in range (nun_tasks);
selected_classes = ra.random. choice (np.arange (10), p-prob_vec size-2, replace=False: the can create the task and train the model. l...]
Figure 15: Pseudo-Code control the distribution imbalance in classes.
H COMPUTE
This project was realized with the use of internal clusters. Each run was performed with a single GPU, mostly NVIDIA GeForce RTX 2070, Quadro RTX 8000, and Tesla V100-SXM2-32GB, The total amount of time required for the runs is 202 days.
I ARCHITECTURES NEURAL NETWORK FIRST EXPERIMENT
Architecture of the convolutional neural network used in Sec.3.
import torch. in as nn
relu nn. (n.ReLU()
convl nn nn.Conv2 (1, 10, Bernel_sizess
conv2 nn. Cn.Conv2 (10, 20, sirnel_size=5) maxpoc12 nn. MaxPoel1d [kernel_size-2 fcl Lww.ainn (320, 50)
head nn. Ln.iine (50, 10)
Forward pass with pytorch
x dimension is (1,28,28)
relu (maxpoo12 (convl (x)) relu (maxpoo12 (conv2 (x))
X
X relu (x))
head(x)
Figure 16: Pseudocode describing the architecture used for experiments in Sec.3
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J FORGETTING
In long task sequences becomes difficult and costly to track the forgetting on all tasks seen so far, hence estimate forgetting by looking locally how learning new task makes the model forget the one just before. We calculate local forgetting, which is the amount of forgetting in a task induced by learning the next task. Note: we only compute forgetting with non-overlapping classes between two tasks.
Pioeat (1) N-C
- Aty JED.
A Ar-1,97
With 3% the set of classes in task t and At,==/ the accuracy realized on class j at task t. Flocat averages the forgetting generated in classes that are in the current task. Then, total forgetting F averages local forgetting tasks seen to far and is computed as:
T
Σ Flocal())
(2)
K ACCUMULATION AND IID
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task index
Figure 17: We simulate situation closer to IID training by changing the epochs number per task (top) (lower is closed to iid) 'and growing batch size (bottom). Getting closer to the IID setting does not necessarily lead to better performance.
As discussed in Section 4.3, on a fixed number of epochs, increasing the batch size brings the training closer to IID training, while for a fixed batch size, growing the number of epochs per task makes the training further from IID. In this section, investigate whether scenarios closer to IID training provide better performance. Growing the number of epochs or decreasing the batch size have the same impact: both increase the number of gradient steps within task. There are, therefore, two forces that oppose each other, learning the current task and forgetting the past ones. On average, the algorithm should learn more about the current task than forget about the past ones expect to be able to converge to global solution.
Setting: In this setting. we experiment with CIFAR10 with classes per task. Then we vary (1) the batch sizes and (2) the number of epochs per task to evaluate if minimum number of epochs with maximum batch size (the closest IID training) maximizes performance.
Fig. 17 (right) shows that the decrease in batch size during one epoch, i.e., getting further away from the IID training, increases the knowledge accumulation speed and final performance. We hypothesize that this result is due to higher number of gradient steps for smaller batch size. If that was the case, experiments with different batch sizes would lead to the same accuracy, but with diverse number of tasks. However, in Fig. 17 (right), larger batch size leads to lower accuracy, which discards the hypothesis. Hence, in this experiment, moving further from IID training performs better, which is counterintuitive. An explanation for this is that, the beginning of task, knowledge
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accumulation is superior to the knowledge degradation caused by forgetting. Therefore, training longer on each task improves the final knowledge accumulation. In the same way, Fig. 17 (left) shows that increasing the number of epochs per task accelerates knowledge accumulation in the number of tasks seen. However, we grow the number of epochs to a certain point, the knowledge accumulation slows down. This figure shows that there is trade-off to find in terms of number of gradient steps converge faster and better.
To conclude, this experiment shows that training in settings that close possible IID (low number of gradient steps per task) does not always improve knowledge accumulation speed and performance.
L INFLUENCE OF EXACT DATA REPETITION
In most our experimentation, when a class reappears, the exact same data is fed to the model. In this experiments, we want to investigate the influence of this. We compare training with exact same data and with data modified by random data augmentation.
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Figure 18: Tinylmagenet 50/5, epoch per task: Addition of random augmentation at each task with various severity. The augmentation slows down knowledge accumulation but does not prevent.
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Figure 19:
TiyyImagenet 50/5, 5 epochs per task: when growing the number of epochs per task, the slight data augmentation improves results of exact data repetition.
Setting: We use the augmentations proposed in Hendrycks & Dietterich (2019) that simulate common perturbation and corruption proposed in images. At each task, a new augmentation is selected and applied with severity I. We selected our augmentation among, "no corruption", "gaussian noise". "shot noise", "împulse noise", "speckle noise". "gaussian blur", "defocus blur", "motion blur", "zoom blur". "fog", "snow", "spatter", "contrast", "brightness", "saturate",, "elastic transform" " and "glass blur". The minimized the chance of having the exact data several times, and the augmentation applied to the data is variate and significant. We use subset of 50 the Tinylmagenet dataset with 5 classes per task.
19

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Under review as a conference paper at ICLR 2023
Our results presented in Fig. 20. It shows that the augmentation applied to each image to minimize the chances having the exact same images does not compromise the accumulation of knowledge. Moreover, Fig. 19 shows that when growing the number of epochs per task, the augmentation can improve performance over exact data repetition.
Results:
M FREQUENCY OF OCCURRENCE VS CLASS ACCURACY
0.8
Class Test Accuracy
0.6
wrn width factor
wrn_width
0.4
2
0.2
16
0.0
-4
-3
-2
-1
Log10 Proba
Figure 20: Lower bound the model learn at 80% accuracy and forgets directly after, Upperbound the model learnd up to 80% each task and never forget after. This representation helps to understand the continual learning capabilities models at each frequency of re-occurence. Each point is the expected performance for a given probability given the model three different seeds.
To understand better how model learn and forgets, can analyze the expected performance for various frequency occurrence.
Setting: Our goal is to better understand continual learning capabilities of models and algorithms by representing the expected performance on each class versus frequency occurrence. In this setting, train CIFARIO0 dataset with SGD (Ir 0.1, momentum 0) on one epoch per task. All classes have different probability to be sampled when huilding task. We use wide resnet model to show that this representation helps to disentangle models capabilities.
Results: The results of this experiments, show that we can differentiate models off different capabilities through this lens. This representation helps describe capabilities of models optimizer and better understand final performance. We also propose to plot the behaviour of a model that would catastrophically forget or model that perfectly remember assuming performance of 80% on each class when training on it.
20


Reviews:
[{"review_id": "xxJwrk-PhcU", "reviewer": "Reviewer_E4AE", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The main claim of the paper is that it challenges “common assumptions about catastrophic forgetting”. The premise for this claim is that a common assumption is that catastrophic forgetting equals forgetting everything and that therefore knowledge accumulation is not possible. The main result of the paper is experimentally disproving this “common assumption” by demonstrating that catastrophic forgetting does not necessarily equate to forgetting everything and that knowledge accumulation is possible.", "summary_of_the_review": "I found this paper an interesting read. I think considering continual learning setups where tasks or classes re-occur is a promising research direction (although in itself not novel, see some references below) that could indeed lead to important new insights. But I’m afraid I do not think the current paper provides substantial new insights.", "strength_and_weaknesses": "I found this paper an interesting read. I think considering continual learning setups where tasks or classes re-occur is a promising research direction (although in itself not novel, see some references below) that could indeed lead to important new insights. But I’m afraid I do not think the current paper provides substantial new insights.\n\nThe main claim of the paper is that it challenges “common assumptions about catastrophic forgetting”. The premise for this claim is that a common assumption is that catastrophic forgetting equals forgetting everything and that therefore knowledge accumulation is not possible. The main result of the paper is experimentally disproving this “common assumption” by demonstrating that catastrophic forgetting does not necessarily equate to forgetting everything and that knowledge accumulation is possible.\n\nIt surprises me that the authors consider it to be a common assumption that catastrophic forgetting equals forgetting everything. I do not agree with this premise. Let’s consider a simple example. This assumption means that after training on a new task, information of past tasks is no longer contained in the network. In other words, a network first trained on task 1 and then on task 2, should have the same task 1 performance as a network only trained on task 2. It is clear that in general this is not the case. (Except perhaps for class incremental settings, but this can be remedied with a simple trick: see for example https://arxiv.org/abs/2106.01834, which the authors are aware of.)\n\nWith this premise gone, the paper loses its fundament and main contribution.\n\nIn Fig 3 the authors make an attempt to convince the reader that the assumption that catastrophic forgetting corresponds to forgetting everything is common / reasonable, but this example is problematic (in fact, it might even disprove the point the authors try to make).\nIn Fig 3A, it is shown that when the authors train a standard neural network in a standard way on their protocol, there is no increase in performance over time. The authors say this result is in accordance with “the common catastrophic forgetting phenomenon”. But it actually is not. If always everything would be forgotten except for the current task, performance should be constant near 20%. Performance however drops to 10%. I expect this might be due to the learning rate being too high and the model collapsing onto one particular class.\n\nFinally, I’d like to encourage the authors to take note of the following papers that also consider continual learning setups where tasks or classes re-occur:\n- Stojanov et al. (2019, CVPR) https://openaccess.thecvf.com/content_CVPR_2019/html/Stojanov_Incremental_Object_Learning_From_Contiguous_Views_CVPR_2019_paper.html \n- Cossu et al. (2022, Frontiers AI) https://www.frontiersin.org/articles/10.3389/frai.2022.829842/full \n\nEspecially the first paper seems to have results that allow analogous conclusions to those presented in the current paper.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "lJi0lHLhqi", "reviewer": "Reviewer_DHkU", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "\nThe paper studies Continual Learning (CL) under a specific framework called SCoLe (Scaling Continual Learning). The major difference between SCoLe and CL is the sparse and controllable appearance of previous tasks and data when the number of tasks is very large. In addition, the paper proposes under the SCoLe framework, DNNs trained with gradient descent only accumulate knowledge without any supplementary CL mechanism. \n\n\nThe authors provide various designed experiments to study knowledge accumulation via different optimization methods and the impact of data shift. They show that continual fine-tuning yields knowledge accumulation under many scenarios (especially online learning scenarios) when previous data reoccur. ", "summary_of_the_review": "Overall, while I find some assumptions of the SCoLe framework not realistic, I believe the work provides an interesting contribution regarding knowledge accumulation in continual learning. The contributions could have been stronger if the authors had validated their hypothesis under a more realistic benchmark (please see the weakness section).", "strength_and_weaknesses": "\n**Strengths:**\n\n- I believe the SCoLe framework is interesting, and showing that DNNs are capable of knowledge accumulation for a long time is a novel contribution.\n\n- The experiments are carefully designed and can support the claims of the paper. \n\n\n\n\n**Weakness:**\n- The main assumption of the SCoLe framework is not aligned with the typical CL assumption of not revisiting the past. In many real-world scenarios, the same data will not reoccur in the future. Hence, I believe it would be interesting if the authors could modify at least one experiment to validate their hypothesis on a more challenging benchmark. For instance, the authors could augment the images of each task differently and, by controlling the augmentation, measure the knowledge accumulation under various settings. I believe this experiment is crucial for the paper.\n\n\n**Questions:**\n- Could the authors explain the \"gradient masking\" mechanism more clearly? Isn't masking the gradients based on the classes similar to having a multi-head classifier (at training time)?", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "B7UkHxn1DK9", "reviewer": "Reviewer_Pyx6", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper argues that when the number of tasks are increased in a continual learning setting, catastrophic forgetting ceases to be a problem and a simple SGD training with gradient masking keeps on accumulating knowledge. Towards this, the authors propose a framework, called SCoLe, where the authors repetitively sample tasks from a fixed number of classes of small datasets. The authors show that the full test set performance increases with the number of tasks, and that if a training setting moves away from the IID training, for example by increasing the number of epochs per task or the total number of classes in a dataset, the test set performance remains low. Overall, the proposed claims are not well-justified and the training setting looks trivial – closer to IID training. \n", "summary_of_the_review": "Please refer to the strengths and weaknesses section above for details.", "strength_and_weaknesses": "**Strengths**\n\n1. The premise of studying continual learning in the presence of large number of tasks and drawing conclusions from it is a worthwhile goal. \n2. Overall the paper is well-written and easy to follow. \n\n**Weaknesses**\n\n1. **Contrived setup**: Overall the setup seemed very contrived and does not justify the claims regarding catastrophic forgetting made in the paper. The authors took small datasets MNIST, CIFAR10 & 100 etc, and repeatedly sampled large number of tasks (up to 1000) consisting of small number of disjoint classes, sometimes even 1 class per task, repeating classes between the tasks, and measured the trajectory of test performance of that dataset (on all classes). It is quite intuitive to think that in such a setup if you control the number of epochs per task properly and keep the total number of classes low, you’ll closely approximate the IID training and your test set performance would increase overtime (barring overfitting). But this doesn’t tell you anything about the catastrophic forgetting. It is quite intuitive that if you keep on observing new classes (along with repeatedly observing previous classes) your overall test performance would keep on increasing. \n\n2. **When the setup is closer to IID training there is less catastrophic forgetting, when the setup is far there is more CF**: Even in the given setup, if one closely looks at the experiments, it seems that when one is closer to the IID setting, the overall test set performance remains high. Similarly, if one moves away from the IID setting, the test set performance degrades. For example, in Fig 7 when the authors compare single-epoch (closer to IID) vs multi-epoch training (farther from IID), and experiments are slightly challenging CIFAR100 (N=50) there is a significant gap between the single- vs multi-epoch performance. It seems that only in very specific situations, when the total number of classes are small and the SGD steps per task are small, or when the setting is closer to IID, the test set performance increases with the number of tasks. This makes the overall results less interesting and trivial.\n\n\n3. **Measuring CF through test set performance**: The notion of forgetting is not clear in this work. What the authors measure is the full test set performance and show that with the data/ task repetition that performance increases. If the data is removed from the mix, cf. Fig 6, the performance of those classes degrades. All this one can observe in a single-task multi-epoch training as well. Perhaps the authors could properly define the notion of forgetting. For example, measuring the performance of a task when it is seen again and plotting that over time.\n\n4. Overall, the learning setting seems contrived and experiments do not justify the claims made in the paper.  Some results on increasing the width resulting in less forgetting (Mirzadeh et al.), and warm starting decreasing the generalization performance (Ash & Adams) are already well-known in the literature. \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "1: The contributions are neither significant nor novel."}, "extra_text": {}}, {"review_id": "1BnhhbJ0FHn", "reviewer": "Reviewer_3eiy", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a new evaluation setting for Continual Learning in the setting of large number of tasks with recurring tasks. The authors propose SCoLe, an experimental framework for this setting and report their findings throughout the manuscript. The key claimed insight is the observation that Continual Learning is possible in a specific setting (reoccurring tasks, SGD without momentum, masking of output layer) without further restrictions.", "summary_of_the_review": "This paper simply states a well-known observation and produces no new insights. ", "strength_and_weaknesses": "Weaknesses:\n- The manuscript does not contain any new or unexpected insights. The fact that task re-occurrence lessens the problem of Continual Learning is not only well known but arguably the main reason that a large part of the CL literature is dedicated to rehearsal and pseudo-rehearsal techniques (i.e. the deliberate enforcing of re-occurrence, proposed as early as 1995). The authors seem to be aware of this \"The reoccurence of data could be compared with the action of a replay methods\" but do not carry out such a comparison. It is expected that a suitable replay technique would perform significantly better, especially in the more difficult SCoLe settings (e.g. Figure 5 left). It is also worth mentioning that scheduled task reoccurrence did indeed feature in highly cited earlier CL publications (e.g. [1][2]) but was regularly critiqued and does disappeared from the literature unless present in real CL problems (e.g. language modelling). Furthermore, the masking of the output layer is an existing technique well known and discussed in other works. \n- The abstract does not clearly mention re-occurrence in the data distribution, merely \"long sequences of tasks sampled from a finite environment\" initially leading me to believe the authors found a profound insight that questioned the entire existence of the catastrophic forgetting phenomenon. This should be rephrased so as not to be misleading. \n- SCoLe itself can barely be considered a contribution and would in most other submissions be merely considered the specific evaluation setting used in this work. \n\n[1] Kirkpatrick, James, et al. \"Overcoming catastrophic forgetting in neural networks.\" Proceedings of the national academy of sciences 114.13 (2017): 3521-3526.\n[2] Schwarz, Jonathan, et al. \"Progress & compress: A scalable framework for continual learning.\" International Conference on Machine Learning. PMLR, 2018.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "1: The contributions are neither significant nor novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject