Online Coreset Selection for Rehearsal-based Continual Learning
Authors: Jaehong Yoon
Divyam Madaan
Eunho Yang
Sung Ju Hwang
Venue: ICLR 2022 Poster (2022)
Keywords: Continual Learning

Abstract: A dataset is a shred of crucial evidence to describe a task. However, each data point in the dataset does not have the same potential, as some of the data points can be more representative or informative than others. This unequal importance among the data points may have a large impact in rehearsal-based continual learning, where we store a subset of the training examples (coreset) to be replayed later to alleviate catastrophic forgetting. In continual learning, the quality of the samples stored in the coreset directly affects the model's effectiveness and efficiency. The coreset selection problem becomes even more important under realistic settings, such as imbalanced continual learning or noisy data scenarios. To tackle this problem, we propose Online Coreset Selection (OCS), a simple yet effective method that selects the most representative and informative coreset at each iteration and trains them in an online manner. Our proposed method maximizes the model's adaptation to a target dataset while selecting high-affinity samples to past tasks, which directly inhibits catastrophic forgetting. We validate the effectiveness of our coreset selection mechanism over various standard, imbalanced, and noisy datasets against strong continual learning baselines, demonstrating that it improves task adaptation and prevents catastrophic forgetting in a sample-efficient manner. 

Published as a conference paper at ICLR 2022
ONLINE CORESET SELECTION FOR REHEARSAL-BASED CONTINUAL LEARNING
Jachong Yoon' Divyam Madaan 2+ Eunho Yang! 1.3 Sung Ju Hwang"
KAIST" New York University? AITRICS
jaehong. atthoy@kaist.a..... sjtwang820kaist.ecc ac.
divyam mad edu,
ABSTRACT
A dataset is a shred of crucial evidence to describe task. However, each data point in the dataset does not have the same potential, as some the data points can be more representative or informative than others. This unequal importance among the data points may have a large impact in rehearsal- -based continual learning, where store subset of the training examples (coreset) to be replayed later to alleviate catastrophic forgetting. In continual learning, the quality of the samples stored in the coreset directly affects the model's effectiveness and efficiency. The coreset selection problem becomes even more important under realistic settings, such as imbalanced continual learning or noisy data scenarios. To tackle this problem, we propose Online Coreset Selection (OCS), simple yet effective method that selects the most representative and informative coreset at each iteration and trains them in an online manner. Our proposed method maximizes the model's adaptation to a current dataset while selecting high-affinity samples to past tasks, which directly inhibits catastrophic forgetting. We validate the effectiveness of our coreset selection mechanism over various standard, imbalanced, and noisy datasets against strong continual learning baselines, demonstrating that it improves task adaptation and prevents catastrophic forgetting in a sample-efficient manner.
INTRODUCTION
Humans possess the ability to learn a large number of tasks by accumulating knowledge and skills over time. Building system resembling human learning abilities is a deep-rooted desire since sustainable learning over a long-term period is essential for general artificial intelligence. In light of this need, continual learning (CL) (Thrun, 1995), or lifelong learning. tackles learning scenario where model continuously learns over a sequence of tasks (Kumar & Daume III, 2012: Li & Hoiem, 2016) within broad research area, such as classification (Kirkpatrick et al., 2017: Chaudhry et al., 2019a), image generation (Zhai et al., 2019), language learning (Li et al., 2019b; Biesialska et al., 2020), clinical application (Lee & Lee. 2020; Lenga et al., 2020), speech recognition (Sadhu & Hermansky, 2020), and federated learning (Yoon et al., 2021). A well-known challenge for continual learning catastrophic forgetting (McCloskey Cohen, 1989), where the continual learner loses the fidelity for past tasks after adapting the previously learned knowledge to future tasks.
Recent rehearsal-basee based continual learning methods adapt the continual model to the previous tasks by maintaining and revisiting a small replay buffer (Titsias et al., 2020; Mirzadeh et al., 2020). However, the majority of these methods store random-sampled instances as proxy set to mitigate catastrophic forgetting, limiting their practicality to real-world applications (see Figure la) when all the training instances are not equally useful, as some of them can be more representative or informative for the current task, and others can lead to performance degeneration for previous tasks. Furthermore, these unequal potentials could be more severe under practical scenarios containing imbalanced, streaming, or noisy instances (see Figure 2). This leads to essential question in continual learning:
How can we obtain coreset to promote task adaptation for the current task while minimizing catastrophic forgetting on previously seen tasks?
'The work was done while the author was student at KAIST.

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Published as a conference paper at ICLR 2022
selsctepreesebaiiee diverse.
Redundancy
and past tasks sinpki
D
Train
Train
Noise
1
Rupplay Cuffer
Cernect Brfleety
(a) Existing baased CL
(b) Online Coresct Selection (OCS)
Figure 1: Illustration of existing rehearsal-based CL and Online Coreset Selection (OCS): (a) Existing rehearsal-basee methods train on all the arrived instances and memorize a fraction of them in the replay buffer, which results in suboptimal performance due to the outliers (noisy or biased instances). (b) OCS obtains the coreset by leveraging our three selection strategies, which discard the outliers at cach iteration. Consequently, the selected examples promote generalization and minimize interference with the previous tasks.
D2
naby fo
Vehticte
Dog
Trafficc Sign
Trank fo
Vehicle
Deg
Trattic Sign
(a) Imbalanced continual learning
(b) Noisy continual learning
Figure Realistic continual learning scenarios: (a) Each task consists of class-ibbllanced instances. (b) Each task has uninformative noise instances, which hamper training.
To address this question, we propose Online Coreset Selection (OCS), a novel method for continual learning that selects representative training instances for the current and previous tasks from arriving streaming data in an online fashion based our following three selection strategies: (1) Minibatch similarity selects samples that are representative to the current task Tr. (2) sample diversity encourages minimal redundancy among the samples of current task Tr. (3) Coreset affinity promotes minimum interference between the selected samples and knowledge of the previous tasks TE, Vk < t. To this end, OCS minimizes the catastrophic forgetting on the previous tasks by utilizing the obtained coreset for future training, and also encourages the current task adaptation by updating the model parameters on the top-x selected data instances. The overall concept illustrated in Figure lb.
Our method is simple, intuitive, and is generally applicable to any rehearsal- -ased continual learning method. We evaluate the performance of OCS on various continual learning scenarios and show that it outperforms state-of-the-ee continual learning benchmarks of varying complexity. We also show that OCS is general and exhibits collaborative learning with the existing tthearsal-bbsed methods, leading to increased task adaptation and inhibiting catastrophic forgetting. To summarize, our contributions are threefold:
rehearsal- -asdd techniques on balanced, imbalanced, and noisy
We address the problem of coreset selection for realistic and challenging continual learning scenarios, where the data continuum is composed of class-imbalanced or noisy instances that deteriorate the performance of the continual learner during training.
We propose Online Coreset Selection (OCS), a simple yet effective online coreset selection method obtain a representative and diverse subset that has high affinity to the previous tasks from each minibatch during continual learning. Specifically, we present three gradient- based selection criteria to select the coreset for current task adaptation while mitigating catastrophic forgetting.
We demonstrate that OCS is applicable to any rchearsal-based continual learning method and exper- imentally validate it on multiple benchmark scenarios, where it largely improves the performance of the base algorithms across various performance metrics.
RELATED WORK
Continual learning. In the past few years, there has been significant progress in continual learning to alleviate catastrophic forgetting (McCloskey Cohen, 1989). The regularization approaches (Kirk- patrick et al., 2017; Lee et al., 2017; Serrà et al., 2018) 8) modify the model parameters with additional regularization constraints to prevent catastrophic forgetting. The architecture approaches (Rusu et al., 2016; Yoon et al., 2018; Xu & Zhu, 2018; Li et al., 2019a; Yoon et al., 2020) utilize network isolation or expansion during continual learning to improve network performance. Another line of research uses rehearsal approaches, which memorize or generate small fraction of data points for previous tasks and utilizes them to retain the task knowledge (Lopez-Paz & Ranzato, 2017: Chaudhry et al., 201 9a; Aljundi al., 2019 9b; Borsos et al., 2020). For example, Gradient- based Sample Selection
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(GSS) (Aljundi al., 2019b) formulates the selection of the replay buffer constraint selection problem to maximize the variance of gradient direction. ER-MIR (Aljundi et al., 2019a) iteratively constructs the replay buffer using loss-based criterion, where the model selects the top-K instances that increase the loss between the current and previous iteration. However, the existing rehearsal- based methods (Rebuffi et al., 2017; Aljundi et al., 2019b;a Chaudhry et al., 2019a;b) do not select the coreset before the current task adaptation and update the model on all the arriving data streams, which makes them susceptible to real-world applications that include noisy and imbalanced data distributions. In contrast, OCS selects the instances before updating the model using our proposed selection criteria, which makes it robust to past and current task training across various CL scenarios.
Coreset selection. There exist various directions to obtain a coreset from a large dataset. Importance sampling (Johnson & Guestrin, 2018; Katharopoulos Fleuret, 2018; Sinha et al., 2020) strengthens the loss/gradients of important samples based on inflencc functions. Kool et al. (2019) connect stochastic Gumbel-top-k trick and beam search to hierarchically sample sequences without replace- ment. Rebuffi et al. (2017) propose herding based strategy for coreset selection. Nguyen al. (2018) 8) formulate the coreset summarization in continual learning using online variational inference (Sato, 2001; Broderick et al., 2013). Aljundi et al. (2019b) select the replay buffer to maximize the variance in the gradient-space. Contrary to these methods, OCS considers the diversity, task informativity and relevancy to the past tasks. Recently, Borsos al. (2020) propose bilevel optimization framework with cardinality constraints for coreset selection. However, their method is extremely limited in practice and inapplicable in large-scale settings due to the excessive computational cost incurred during training. In contrast, our method is simple, and scalable since it can construct the coreset in the online streaming data continuum without additional optimization constraints.
3 REHEARSAL-BASE CONTINUAL LEARNING
We consider learning a model over a sequence of tasks (Ti....,TT)) TT. where each task is composed of independently and identically distributed datapoints and their labels, such that task Ti includes D.- = {x ] ~ X, x Ve. where N, the total number of data instances, and & x 3%. is an unknown data generating distribution. We assume that an arbitrary set of labels for task Tú, Yt- { has unique classes, y, yy = 0, Vt of k. In a standard continual learning scenario, the model learns corresponding task at each step and f-th task is accessible at step only. Let neural network fe : Xi.r + Vir be parameterized by set of weights Q = { ) where L the number of layers in the neural network. We define the training objective at step as follows:
N
minimize Σ (xfe(xe.)) Bt,,)
(1)
where E(-) is any standard loss function (e.g., cross-entropy loss). The naive CL. design where a simple sequential training on multiple tasks without any means for tackling catastrophic forgetting cannot retain the knowledge of previous tasks and thus results in catastrophic forgetting. To tackle this problem, rehearsal- -aased methods (Nguyen et al., 2018; Chaudhry et al., 2019a; Titsias et al., 2020) update the model on randomly sampled replay buffer Cs constructed from the previously observed tasks, where C. (xk.j- yk.,) / Dr, vk t and JR < Ng. Consequently, the quality of selected instances is essential for rehearsal- -hased continual learning. For example, some data instances can be more informative and representative than others to describe a task and improve model performance. In contrast, some data instances can degrade the model's memorization of past tasks' knowledge. Therefore, obtaining the most beneficial examples for the current task crucial for the success of rehearsal- CL methods.
Periclass acc. 75 (%)
Classwise acc. of
Average Fgt. of T.
To validate our hypothesis, we design learning scenario with sequence of two tasks, MNIST
Forgetting of (%)
80
(Ti) + CIFAR-10 (72) using ResNet- 18. Af- ter the standard single epoch training on Ti we update the model weights through a single back- propagation step using randomly selected data point from Tz, and measure test accuracy of its corresponding class and forgetting of the entire dataset of a past task T. Results for indi- vidual impacts 1000 data points from Tz are
28 30
C2 G. cy Class Index of T3 Instances Class Index of instances
Figure 3: Per-class accuracy and average forgetting when a model trained on MNIST (Ti) is updated on single data point at class c on CIFAR- 10 (T2).
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described in Section 3. The influence of each data point from Tz has large disparity not only on the corresponding class accuracy but also on past task's forgetting that results in a very high standard deviation. We emphasize that each data point has different potential impact in terms of forgetting past tasks. Few data points are much more robust to catastrophic forgetting than others, and this can be severe when the influences accumulated during training.
Based on this motivation, our objective is to select the data instances that can promote current task adaptation while minimizing catastrophic forgetting on the previous tasks. We propose selection criterion that selects the subset that maximizes the gradient similarity between the representative instances and the current task dataset. More formally:
1 Evfe (K (XL.n:Ben)) where u= {n nh NcN.), (2) ( v (Di) K nEw
u
maximize& WENs
S
where S is any arbitrary similarity function and u" is an index set that selects top-s informative samples without replacement. However, obtaining a representative subset from the entire dataset is computationally expensive and intractable for online continual learning; therefore, we consider a minibatch as an approximation of the dataset and select few representative data instances at each minibatch iteration. We empirically validate that approximation generally holds across various datasets, network structures, and minibatch sizes in Appendix B and Figure B.9. Consequently, the model iteratively updates the parameters to find the optimal local minima of the loss using informative data points, which obtain similar gradient directions with the averaged gradients of the dataset. In the next section, we propose OCS which consists of simple similarity criterion to achieve this objective. However, similarity criterion is not sufficient to select the representative coreset for online continual learning; hence, we propose diversity and coreset affinity criteria to mitigate catastrophic forgetting.
ONLINE CORESET SELECTION
In this section, we introduce our selection strategies and propose Online Coreset Selection (OCS) to strengthen current task adaptation and mitigate catastrophic forgetting. Thus far, the rehearsal-bane continual learning methods (Rebuffi al., 2017; Aljundi al., 2019b;a; Chaudhry et al., 201 9a;b) populate the replay buffer to preserve the knowledge on the previous tasks. However, we argue that some instances may be non-informative and inappropriate to construct the replay buffer under realistic setups (such as video streaming or imbalanced continual learning scenarios), leading to the degradation of the model's performance. Moreover, it is critical to select the valuable samples for current task training since the model can easily overfit to the biased and noisy data stream, which negatively affects the model generalization. To satisfy these desiderata, we propose minibatch similarity (S) and sample diversity (V) criteria based on our aforementioned assumption to adaptively select the useful instances without the influence of outliers.
Definition (Minibatch similarity). Let b {x yt.n B, denote n-th pair of data point with gradient Se (b and its corresponding label at task Tr- Let (B,)) denote the averaged gradient vector of B, The minibatch similarity S (be.. Bi) between bi, and B, is given by
fi (Ds.n) m. fe (B.)
S (br Bi) = |e (b,, 1| fe (B.)l*
Definition 2 (Sample diversity). Let bi, = {xi,ns 3 E B, denote n-th pair of a data point with gradient V fe (br.a) and its corresponding label at task Te. The sample diversity V (br... Bryb...)) between Dr.n. and all other instances in B, (Brrb.n) is given by
-1
N
Vie (br.)) f (B.,p) We (be,n)l /e (bt,
V (be. B.xbe..)
Σ pf
(4)
N₂
approximation of the current task dataset and compares the minibatch-level similarity between the gradient vector of a data point and its minibatch B3. It measures how well given data instance describes the current task at each training step. Note that selecting examples with the largest minibatch similarity is reasonable when the variance of task instances is low; otherwise, it increases the redundancy among coreset items. In
In particular, minibatch similarity considers minibatch
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contrast, formulate the sample diversity of each data point b B as averaged dissimilarity (i... an average of negative similarities) between a data point itself and other samples in the same minibatch B, and not average similarity. Thus, the measure of sample diversity in Equation (4) negative and the range is 1,
4.1 ONLINE CORESET SELECTION FOR CURRENT TASK ADAPTATION
The model receives a data continuum during training, including noisy or redundant data instances in real-world scenarios. Consequently, the arriving data instances interrupt and hurt the performance of the model. To tackle this problem, we consider an amalgamation of minibatch similarity and sample diversity to select the most helpful instances for current task training. More formally, our online coreset selection for the current task adaptation can be defined as follows:
u argmax (K) S (br.. m B.) + V (br... (Brb...)
{0,..... |B, -1}
(5)
We emphasize that we can obtain the top-k valuable instances for the current task by computing Equation in an online manner. Once the representative coreset is selected, we optimize the following objective for the current task training at each iteration:
minimize 9
Σ
( (z), where B. = B.BB.[u7 [1].
(6)
(B
We consider a selected coreset at each iteration as candidate for the replay buffer. After the completion of each task training, we choose a coreset C, among the collected candidates, or we may also iteratively update C, to maintain the bounded buffer size for continual learning.
4.2 ONLINE CORESET SELECTION FOR CONTINUAL LEARNING
We now formulate OCS for online continual learning, where our objective is to obtain the coreset to retain the knowledge of the previous tasks using our proposed similarity and diversity selection criteria. However, continual learning more challenging the model suffers from catastrophic forgetting and coreset size is smaller than the size of the arriving data streams. Thus, inspired by our observation in Section 3, aim to train the continual learner the selected instances that representative of the current task and prevent the performance degeneration of previous tasks.
We achieve goal by introducing our Coreset affinity criterion A to Equation 5. In partieular, A computes the gradient vector similarity between a training sample and the coreset for previous tasks (C). More formally, A can be defined follows:
Definition 3 (Coreset affinity). Let bt. (Xt.n; Vt.n. } E Bi denote the n-th pair of a data point with gradient Se (b...) and its corresponding label at task Te Further let V (B(e) be the averaged gradient vector of Be, which is randomly sampled from the coreset The coreset affinity A (b.... Be C) between br, and Be is given by
VSe (br..) Se (Be)
A (br,m Be C) [e (b...) Ve (Bc)
While the past task is inaccessible after the completion of its training, selectively populated replay buffer can be effectively used to describe the knowledge of the previous tasks. The key idea is to select the examples that minimize the angle between the gradient vector of the coreset containing previous task examples and the current task examples. Instead of randomly replacing the candidates in the coreset (Lopez-Pad Paz & Ranzato, 2017; Chaudhry et al., 2019a: Aljundi al., 2019b; Borsos et al., 2020), A promotes the selection of examples that do not degenerate the model performance on previous tasks. To this end, we select the most beneficial training instances which are representative and diverse for current task adaptation while maintaining the knowledge of past tasks. In summary, our OCS for training task T, during CL can be formulated as:
u' argmmx(()) (n) 8 (Br, B.) (br,m / Boob...) T (br. Bc) n {O...., [B]] -B1-1)3. (8)
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is a hyperparameter that controls the degree of model plasticity and stability. Note that, during the first task training, we do not have the interference from previous tasks and we select the top-K instances that maximize the minibatch similarity and sample diversity. Given the obtained coreset B, B,[u*], our optimization objective reflecting the coreset C, is as follows:
minimize
1
Σ
(((e())
((e(x),
(9)
Bc
(R.0)EB.
(x.y)EBe
where Be is a randomly sampled minibatch from the coreset C and À is a hyperparameter to bal- ance the adaptation between the current task and past task coreset. Overall training procedure for Online Coreset Selection (OCS) is described in Algorithm 1. To the best of our knowledge, this the first work that utilizes selective online training for the current task training and incorporates the relationship between the selected coreset and the current task instances promote current task adaptation while minimizing the interference with previous tasks.
Algorithm 1 Online Coreset Selection (OCS)
input Dataset (D, (- neural network fe, hyperparameters X, r. replay buffer <- O. buffer size bound J.
1: for task T. = Ti..... Tr do
2: C. 0
Initialize coreset for current task
3: for batch B. D; do
4:
Be + SAMPLE(C)
Randomly sample batch from the replay buffer S (be.. [B) 1 (be.. BB TA (be... Be) Coreset sclection
5:
u' argmax (*)
ne rE.......BB.l 1+1-1)
6:
θ + θ n fe (e [B]] Be) with Equation (9)
7:
C CB
8:
end for
9:
C+ C CUUSEEE SELECT(C,, size J/T) with Equation (8)
Memorize coreset the replay buffer
10:
end for
5 EXPERIMENTS
5.1 EXPERIMENTAL SETUP
Datasets. We validate OCS on domain-incremennal CL for Balanced and Imbalanced Rotated MNIST using a single- head two-layer MLP with 256 ReLU units in each layer, task leskiincrementl CL for Split CIFAR-100 and Multiple Datasets (a sequence of five datasets) with a multi-head structured ResNet- 18 following prior works (Chaudhry et al., 2019;; Mirzadeh et al., 2020; 2021). Additionally, we evaluate on glass-incremental CL. for Balanced and Imbalanced Split CIFAR- 100 with a single-head structured ResNet-18 18 in Table B.9. We perform five independent runs for all the experiments and provide further details on the experimental settings and datasets in Appendix A.
Baselines. We compare OCS with regularization-banneee CL methods: EWC (Kirkpatrick et al., 2017) and Stable SGD (Mirzadeh et al., 2020), rehearsal-basee CL methods using random replay buffer: A-GEM (Chaudhry et al., 2019a) and ER- Reseeverv (Chaudhry al., 2019b), coreset-based methods using CL algorithms: Uniform Sampling. k-means Features (Nguyen et al., 2018) and k-means Embeddings (Sener & Savarese, 2018), and coreset-based CL. methods: iCaRL (Rebuffi et al., 2017), Grad Matching (Campbell & Broderick, 2019), GSS (Aljundi et al., 2019b), ER-MIR (Aljundi et al., 2019a), and Bilevel Optim (Borsos et al., 2020). We limit the buffer size for the echearsal-based methods to one example per class per task. Additionally, we compare with Finetune, a naive CL method learnt on sequence of tasks, and Multitask, where the model trained the complete data.
Metries. We evaluate all the methods on two metrics following the CL literature (Chaudhry et al., 2019a; Mirzadeh al., 2021).
Average Accuracy (A.) is the averaged test accuracy of all tasks after the completion of CL at task Tr. That is, A, D dr,s, where ar,i is the test accuracy of task T; after learning task Te-
2. Average Forgetting (F) is the averaged disparity between the peak and final task accuracy after the completion of continual learning. That is, F - IT- max T-1) (ar, aT,))- (I.....TT....)))

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Table 1: Performance comparison of OCS and other baselines on balanced and imbalanced continual learning. We report the mean and sandard-deviation of the average accuracy (Accuracy) and average forgetting (Forgetting) across five independent runs. The best results are highlighted in bold.
Method
Rotated MNIST
Split CIFAR-100
Multiple Dutasets
Accuracy
Fargetting
Accumcy
Forgetting
Accuracy
Forgetting
Finetune:
(2 1.37)
0.52
40 288)
(4 0.02)
49,8 2.14)
0.23 0.03)
EWC (Kirkpotrick et 2017)
70.7 (:: 1.74)
0.23 (= 0.01)
4t 1.24)
0.48 0.01)
(2 1.89)
0.28 (2: 0.03)
Stable SGD (Mirzadeh al., 2020y
70.8 (sh 0.781
0.10 = 0.02)
57.4 0.91)
0.07 (+ 0.01)
53.4 2.66)
0.16 0.03)
A-GEM (Chaudtry et al., 2019s)
(:t 1.47)
0.42 (= 0.01)
50.7 2.32)
0.19 0.04)
Reseroer (Chandhry at. 2019b)
6s 1.10)
0.21 0.01)
46.9 0.76)
0: 0.03)
Balonced CL
Uniform Sampling
(9.9 1.32)
0.14 (= BDI)
(+: 0.89)
0.05
56.0
2.40)
(#: 0.02)
iCaRL (Rabulii et 2017)
80.7
0.44)
0.13 (= 0.00)
60.3
0.91)
0,04(:2:000
59.4
1.43)
0.07 (:: 0.02)
k-means Features (Sguyen
2018)
c9: 1.50)
0.14 0.01)
59.3
0.06 001)
53.6 1.88
0.14 0.02)
k-meams Finhekding (Smerr & Smeaess, 2018)
80.6 0.54)
0.13 (= (DDI)
(5.5(())
0.06(20001
55.4
1.46)
(# 0.02)
Grad Matching (C (Campbeel & Bruderick, 2019)
78.5 0.56)
0.15 (= 0.01) 60.0 1.24)
0.04(20.00)
$7.8
1.35)
0.08 (2: 0.02)
GSS (Aljundi al., 20196)
76.0 0.581
0.19 0.01)
59.7 1,22)
0.04
0000
60.2
1000
0.07 (+ 0.01)
ER-MIR (Aljundi al., 2019a]
80.7 0.72)
0.14 (= 0.01)
60.2 0.72)
0.04 0.00
56.9 2.25)
(# 0.08)
Bilevel Optin (Bonos et ol., 2020)
80.7 1 0.44)
0.14 ( 0.00)
60.1 (2 1.07)
0.04
0.013
58.1 2:26)
0.08 (2 0.02)
OCS (Ours)
82.5 (::: 0.32)
0.08 (= 0.00)
60.5 (+: 0.55)
0.04 0.01)
61.5 (#: 1.34)
0.03 ( 0.01)
Multiask
89.8 (:t: 0.37)
71.0 0.21)
57.4 0.84)
Finetune
39.8 1.06)
(-54 0.01)
45 1.38)
0.01) 0.17
27.6
3.66)
0.22 (+: 0.04)
Stable SGD (Mirzadeh al., 2020)
52.0
0.19
48.7 (::
0.03 0.00
29.5 4.99
0.20 0.02)
Inbalancd CL
ICaRl. (Rabuiii al., 2017)
Uniform Sampling
71:7 0.69)
61 1.72)
0.09 (= 0.00)
0.15 0.01)
51.2 1.09)
51.0 0.78)
0.02 0.00
0.03
0.0)
43.6(= 2.95)
35.0 3.0))
0.11 (t: 0.03)
0.03)
f-mmcum Feattuees UNguyen et al., 2018)
52.3 1.48)
0.24 (= 0.01)
50.6
1.52)
0.04(20.00)
36.1
1.75)
0.09 (2: 0.02)
h-means Embedding (Sener & Savarese, 2018)
63.2 0.90)
0.13 0.02)
50.4
1,39)
0.03
001
35.6 1.35)
0.11 0.02)
Grad Matching (Camphell Braderick, 2019)
55.6 1.86)
0.18 - 0.02)
51.1
1.14)
0.02
34.6 0.50)
0.01)
GSS (Aljundi el al., 2019h)
68.7 (=: 0.98)
0.18 (= 0.01)
44.5
(2 1.35)
0.04(20000)
(2.9
0.13 (2: 0.01)
ER MIR (Aljundi al., 2019g)
69.3 1.011
0.16 0.01)
44.8
( 1.42)
0.03
0.1
32.3 3.49)
0.15 (+: 0.03)
Bilevel Optim (Bonss et al., 2020)
63.2 (:: 1.04)
0.22 (= 0.01)
44.0
0.86)
0.03
0.01)
35.1
2.78)
0.12 0.02)
OCS (Durs)
76.5 (:) 0.84)
0.08 (= 0.01)
51.4 (c 1.11) 0.02 0.00)
47.5 (2) 1.66)
0.03 (2: 0.02)
Multitak
81.0 (:: 0.95)
48 0.72)
41.4 (= 0.97)
batorces Natated MAR?
Into ancod Rototed MMST
Ealances Rotated MARST
Irica anced hotaned MIST
50D
Call
Kark
24
20
(a) Average test accuracy
(b) First task test accuracy
Figure 4: (a) Average accuracy (b) First task accuracy for balanced/imbalaneed Rotated MNIST during CL.
5.2 QUANTITATIVE ANALYSIS FOR CONTINUAL LEARNING
Balanced continual learning. Table 1 shows the results on the balanced CL benchmarks. First, observe that compared to the random replay based methods (A-GEM and EeR-Reservoir), OCS shows 19% relative gain in average accuracy, 62% and 79% reduction in forgetting over the strongest baseline on Rotated MNIST and Split CIFAR- 100, respectively. Second, OCS reduces the forgetting by 38% and 57% on Rotated MNIST and Multiple Datasets respectively over the coreset-based techniques, demonstrating that it selects valuable samples from the previous tasks. We further illustrate this in Figure 4, where OCS consistently exhibits superior average accuracy and first task accuracy. Third, we show the scalability of OCS with larger episodic memory in Figure 5. Interestingly, iCaRL shows lower performance than uniform sampling with a larger memory buffer for Rotated MNIST, while OCS outperforms across all memory sizes on both datasets. Furthermore, we note that ER-MIR, GSS, and Bilevel Optim require 0.9x, 3.9x, and 4.2x training time than OCS (see Table 5) on TITAN Xp. showing a clear advantage of OCS for the online streaming scenarios.
Imbalanced continual learning. To demonstrate the effectiveness of OCS in challenging scenarios, we evaluate on imbalanced CL. in Table 1. We emphasize that compared to balanced CL. OCS shows significant gains over all the baselines for Rotated MNIST and Multiple Datasets. Notably, it leads to relative improvement of ~ 7% and ~ 9% on the accuracy, 11% and 40% reduction on the forgetting compared to the best baseline for each dataset, respectively. The poor performance of the baselines in this setup is largely attributed to their lack of current task coreset selection, which results in a biased estimate degenerating model performance (see Figure 8). Moreover, we observe that OCS outperforms Multitask for complex imbalanced datasets, perhaps due the bias from the
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Table 2: Performance comparison of OCS and other baselines on varying proportions of noise instances during noisy continual learning. We report the mean and standard-deviation of the average accuracy (Accuracy) and average forgetting (Forgetting) across five independent runs. The best results are highlighted in bold.
Method
0%
40%
60%
Accuraty
Forgetting
Accuracy
Forgeting
Accuracy
Forgetting
Stable SCD (Mizzadeh sl., 2020)
70.8 (+: 0.78)
( 0.02)
56.2 0.95) 0.40 (= 0.81)
56.1 (4: 0.62)
0:40 0.01)
Uniform sampling
79.9 (d: 1.32)
0.14
0.011
74.9 (1: 2.45)
0.20 (= 0.03)
68.3 (1: 3.68)
0.26 (2: 0.05)
iC3RL (Rebufii et al., 2017)
80.7 0.44)
0+13
77.4
(+: 0.60)
0.18
0.01)
71.4 2.63)
0.2 0.05)
k-meams embelding (Sener & Savarese, 2018)
80.6 0.54)
0.13 0.011
78.5 0.86)
0.17 0.00)
77.5 (+: 1.67)
0:26 0.05)
GSS (Aljundi at. 2019b)
76.0 0.58)
(219
71.7
0.95)
0.19 0.01)
68.8 1.02)
0.17 000)
ER-MIR (Aljundi et al., 2019s)
80.7 (+: 0.72)
0.14 0.01)
76
1.34)
0.17
0.01)
73.5 (+: 0.94)
0.18 0.01)
OCS (Ouns)
82.5 (d: 0.32) 0.08 (2 0.000
80.4 (#: 0.20)
0.14 t= 0.00)
80.3 (=: 0.75) 0.10 (= 0.01)
Seluncud Rsluted MNST
Inbulenced No.eice NAST
Selenodd Vulips Desosts
inbllaced Putips Douost
Ckll
CCAL
(a) Rotated MNIST
(b) Multiple Datasets
Figure 5: Performance comparison on various coreset sizes for balanced/imbalanced continual learning.
dominant classes and the absence of selection criteria in Multitask. Similar to balanced CL, OCS leads to superior performance for larger episodic memory in imbalanced CL (see Figure 5).
Noisy continual learning. Next, we evaluate on noisy Rotated MNIST dataset, which is constructed by perturbing a proportion of instances of the original dataset with Gaussian noise ((00 1). Table shows that the addition of noise significantly degrades the performance on all the baselines. In contrast, OCS leads to a relative gain of 43% on accuracy, 20% and 35% reduction in forgetting on 40% and 60% proportion of noisy data. Note that the performance gap is more significant for the higher distribution of noisy examples, supporting our claim that the similarity and diversity across the training examples in the coreset play an essential role for the task adaptation in continual learning.
5.3 ABLATION STUDIES
Effect of gradients. In Table 3, we empirically justify the utilization of gradients (Grad-OCS) compared to the raw inputs (Input-OCS) and feature-rerrssenattonn (Feat-OCS). We observe that Grad-OCS significantly outperforms Input-OCS and Feat-OCS on balanced and imbalanced CL. demonstrating that the gradients are a better metric to approximate the dataset.
Effect of individual components. We further dissect Minibatch similarity (S), Sample diversity (V) and Coreset affinity (AA) in Table 4. Note that selection using S shows reasonable performance as the model can select valuable data points; however, it may select redundant samples, which degrades its performance. In addition, V in isolation is insufficient since it select non-redundant and non ron-representative instances. The combination of S and V improves the average accuracy, but shows marginal improvement the forgetting. To further gain insight into S and V. we interpolate between S and V in Figure 6, where we can observe that an optimal balance of S and V (indicated by the arrows) can further improve the performance of our proposed selection strategy.
Furthermore, A improves the forgetting since the selected candidates have similar gradient direction to the coreset of the previous tasks maximizing their performance. However, A does not consider the current task distribution explicitly and depends on the quality of the memorized replay buffer. We observe that using A in isolation obtains reasonably high performance on simple dagit-based domain- -nceemnnncremtttll CL problems (c.g., Rotated MNIST) due to its inherent high resemblance among same class instances. Consequently, suppressing catastrophic forgetting by selective training based on A shows relatively high impact rather than selective training based on distinguishing more informative or diverse samples. In contrast, AA in isolation for selection is insufficient for complicated and realistic CL problems such as imbalanced CL and multiple datasets, and all the three components (S, V. and A) contribute to the performance of OCS. For Multiple Datasets, selection using only A (58.1%) obtained worse performance in comparison to S + V + A (61.5%) and S + V (58.6%). Further, selection using S + A (59.4* = 2.0%) and V + A (56.4% = 1.3) also obtained 2. 1% and 5.1 11% lower average accuracy than full OCS, respectively.
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Table 3: Ablation study for analyzing the effect of Table 6: Collaborative learning with rehearsal based CL on various datasets with 20 tasks each.
gradients selection for OCS.
Mechod
Balanced Rotated MNIST
Imbalanced Rotated MNIST
MC-SGD (Mizzaleh et al. 2021)
MCSGG + OCS
Accuracy
Forgetting
Accuracy
Forgetinng
Diraset
Accuncy
Fargsting
Aucunay
Forelting
Inpar-CCS
72.7 es 640
0.13 ct son
50.5 170
0.04 it: 500
Per MNIST
$4.6
0.06
86.6
0.02 800)
Peat OCS
21.7 en ea2
0.17 ca 200
30.5 cB 048)
0.03 1
Ro-MNNST
52.3
Gmd-Ocs
82.5 k2
0.08
76.5 14.5c2000
0 is
CIFAR
Table Ablation study to investigate the impact of selection criteria S, V. and A on OCS.
5 ППИク 9
206 to
Method
Nodcy Rot-MNIST (60%)
Multiple Dutasets
0BO
3
Accuracy
Forgetting
Accuracy
Forgeting
H4: Unetuare Leangg
3 Oars tealg)
64.0 ce: L.R:
0.33 0.0
56.3 (t: D4t)
0.10 0.00
Figure 7: Randomly picked coresct examples. Top:
40.1
0,06 000
49.8 (1: 13%
0.05 0.12
Imbalanced Rotated MNIST. Bottom: Noisy Rotated MNIST with 60% of noisy instances.
0.10c1.m
1.1
0: am0
58.6 191)
0.09 ca
80.3 et 6.751
(= 000
61.5 (t: 1.34
oz (z up0
10
Table 5: Running time on Balanced Rot-MNIST.
Method
Training Time
0.25
Interpolation ratio
2.50 0.75
ER-MIR
GSS
0.38 (x0.87)
1.71 h (x3.89)
Silevel Optim
DCS
Figure 6: Interpolat-
Bilevel
1.83 (x4.17)
Figure 8: T-SNE visualization of the selected samples on Imbalanced Rotated MNIST.
ion between S and V.
OCS (Ours)
0.44 (x1.00)
5.4 FURTHER ANALYSIS
Coreset visualization. Next, we visualize the coreset selected by different methods for imbalanced and noisy rotated MNIST in Figure 7. We observe that uniform sampling selects highly biased samples representing the dominant classes for imbalanced CL. and noisy instances for noisy CL. In contrast, iCaRL selects the representative samples per class for imbalanced CL: however, it selects noisy instances during noisy CL. In comparison, OCS selects the beneficial examples for each class during imbalanced CL. and discards uninformative noisy instances in the noisy CL training regime.
T-SNE visualization. We further compare the T-SNE visualization of the selected coreset by Bilevel Optim, GSS and OCS in Figure 8. We observe that the samples chosen by OCS are diverse, whereas Bilevel Optim and GSS select the majority of the samples from the dominant classes. We attribute the representative clusters and diversity in the samples selected by OCS to our proposed S (selects the valuable samples) and V (minimizes the redundancy among the selected samples) criteria.
Collaborative learning with MC-SGD. We remark that OCS can be applied to any rehearsal-based CL method with a replay buffer during training. We empirically demonstrate the effect of collaborative learning with other CL methods in Table 6. In particular, SGD) (Mirzadeh et al., 2021), which encourages the mode connectivity between model parameters for continual and multitask loss and approximates the multitask loss through randomly selected replay buffer. Note that OCS leads to a relative gain of 1.2% to 3.4% on accuracy over MC-SGD on Permuted MNIST, Rotated MNIST, and Split CIFAR-100 datasets. Furthermore, MC-SGD OCS shows considerably lower forgetting, illustrating that OCS prevents the loss of prior task knowledge.
Mode Connectivity SGD (MC-
6 CONCLUSION
We propose Online Coreset Selection (OCS), a novel approach for coreset selection during online continual learning. Our approach modelled as gradient-based selection strategy that selects representative and diverse instances, which are useful for preserving the knowledge of the previous tasks at each iteration. This paper takes the first step to utilize the coreset for improving the current task adaptation, while mitigating the catastrophic forgetting on previous tasks. Our experimental evaluation on the standard balanced continual learning datasets against state-of-the techniques demonstrates the efficiency of our approach. We also show promising results various realistic and challenging imbalanced and noisy continual learning datasets. We further show the natural extension of our selection strategy to existing rehearsal-based continual learning using random-replay buffer. Our future work will focus on improving the selection strategies and exploring ways to utilize unlabelled data stream during training.
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ACKNOWLEDGEMENT
This work was supported by the Engineering Research Center Program through the National Research Foundation of Korea (NRF) funded by the Korean Government MSIT 20 and Institute of Information & communications Technology Planning & Evaluation (ITTP) grant funded by the Korea gMVE) (No (N0.2019-0-00075, Artificial Intelligence Graduate School (pegram(KAIST)
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Organization, The appendix is organized as follows: We first provide the experimental setups, including the dataset construction for balanced, imbalanced, noisy continual learning, and the hyperparameter configurations for OCS and all baselines in Appendix A. Next, evaluate the selection criteria of the baselines for current task training and provide an additional ablation study comparing OCS with current task training uniform selection in Appendix B.
A EXPERIMENTAL DETAILS
Datasets. We evaluate the performance of OCS on the following benchmarks:
1. Balanced and Imbalanced Rotated MNIST. These datasets are MNIST handwritten digits dataset (LeCun et al., 1998) variants containing 20 tasks, where each task applies a fixed random image rotation (between 0 and 180 degrees) to the original dataset. The imbalanced setting contains a different number of training examples for each class in a task, where we randomly select 8 classes over 10 at each task and each class contains 10% of training instances for training. The total amount of training instances at each class can be [5900, 670, 590, 610, 580, 5400, 590, 620, 580, 590], where bold fonts denote the reduced number of instances for selected classes. The size of the replay buffer is 200 for all the rehearsal-based methods.
Balanced and Imbalanced Split CIFAR-100. dataset (Krizhevsky, 2012) variants, where each task consists of five random classes out of the 100 classes. We use the Long-Tailed CIFAR-100 (Cui et al., 2019) for Imbalanced Split CIFAR-100 consisting of n ni,u' samples for each class, where is the class index, n: is the original number of training images, and μ = 0.05. It contains 20 tasks of five random classes out of the 100 classes The size of the replay buffer is 100 (one example per class) for all the rehearsal- based methods.
These datasets are CIFAR-100
3. Balanced and Imbalanced Multiple Datasets. This dataset contains sequence of five benchmark datasets: MNIST (LeCun et al., 1998), fashion-MNIST (Xiao et al., 2017). NotM- NIST (Bulatov, 2011). Traffic Sign (Stallkamp et al., 2011). and SVHN (Netzer et al., 2011), where each task contains randomly selected 1000 training instances from each dataset. This dataset contains five tasks and 83 classes. We use the same strategy as Long-Taiee CIFAR-100 to construct the imbalanced Multiple Datasets with = 0.1. The size of the replay buffer is 83 (one example per class) for all rehearsal-basee methods.
Network Architectures. We use MLP with 256 ReLU units in each layer for Rotated MNIST and a 18 (He et al., 2016) for Split CIFAR- 100 datasets following Mirzadeh et al. (2020). For Rotated MNIST experiments, shared across all the tasks, and the task identity is not provided during inference. In contrast, we use the multi-head structured ResNet- 18 for CIFAR- -10 and Multiple Datasets experiments, where the task identifiers are provided, and each task consists of its individual linear classifier.
a single-heat head architecture, where the final classifier layer is
Implementations. We follow the design of Mirzadeh et al. (2021) for evaluating all the methods. We utilize their implementation for Finetune, EWC (Kirkpatrick et al., 2017), Stable SGD (Mirzadeh et al., 2020), A-GEM (Chaudhry et al., 2019a), ER-Reservoir (Chaudhry al., 2019b) and MC- SGD (Mirzadeh et al., 2021). We adapt the implementation released by Borsos et al. (2020) for Uniform Sampling, iCaRL (Rebuffi al., 2017). k-means Features (Nguyen et al., 2018), k-means Embedding (Sener & Savarese, 2018), Grad Matching (Campbell & Broderick, 2019), and Bilevel Optim (Borsos et al., 2020). Further, we implement GSS (Aljundi et al., 2019b) and ER-MIR (Aljundi et al., 2019a) following the official code relased by the authors. Following iCaRL (Rebuffi et al., 2017), we store a balanced coreset C, (equal number of examples per class) among the collected coreset candidates.
Memory Capacity. Existing rehearsal- continual learning methods (Chaudhry et al., 201 1a;b; Aljundi et al., 2019a; Mirzadeh et al., 2020; 2021) adopt two typical strategies to store data points in the replay buffer at the end of training each task: (L) memorizing a fixed number of data points per task (C,, = J/T), where an index of the task in task sequence i {I.,. the total number of task T. and memory capacity J, (2) fully utilizing the memory capacity and randomly discard stored samples of each task when new data points arrive from next tasks (CC.l J/t), where the current task
T),,
t and an index of the observed task E {I,...,() 1). While both strategies are available, we adopt the
latter strategy for all baselines and OCS. The details of this are omitted in Algorithm for simplicity.
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Table B.8: Performance comparison of baselines for current task adaptation. We report the mean and standand-deviation of the average accuracy and average forgetting across five independent runs.
Table B99: Performance comparison Class- incremental CL on balanced and imbalanced Split CIFAR- 100. We report the mean and standard- deviation of the average accuracy and average forget- ting across five independent runs.
Method
Balanced Rotated MNIST
Imbollaceed Rebaled MNIST
Annrracy
Tengaring
Accumsy
Teegezing
Method
Ralanedd CIPAR-108
Imbulanced Spit CIEAR-101
Fisetuee
(6 1.57)
0.52 0011
0.54 0.01)
Asdracy
Reggrting
Accrncy
Regrring
Stahic SGD
10.8 0.781
0.10 0.033
52.0 0.25)
0.1911 0.00)
Finsuue
C3 0,30
0.33 (+: 6.02)
23 0.30
0.55# 0.01)
Unitun
78M
0.14 0,09
0.02)
Unioons
(6 0.32)
0.25 (t 0.01)
8.7 0.41)
0.14 601)
E-mexra Eait.
Fest.
(8 1.53)
G7 1.060
0414 6.01)
0:15 0.01)
07.2 0.16)
0.12 0.08)
0.101: 0.01)
Gual Metchia
CaRL
k-meare Frat
18.1 0.55)
16 (167)
(8 0.701
0.22 14: (+-601)
0.23 (+ 0.01)
0:11 11: 0.01)
87 0.56
$6 0.57)
012 6.00)
0.1614 601)
0.33 14: 6.02)
Grad Masching
(9 1.11)
0.15 6.11
52.4 (- 1.540
0.19 0.02)
BR-MIL
17 0.55)
0:23 0.01)
73
0.1011: 0.01)
8:08 8.00)
OCS (Qans)
2011 0.73)
9.08 (+: 9.01)
11.1 0.99
0:07 (:: 6,80)
Mubitauk
C 0.37)
cal (1991)
Mulitaik
7L0 0.00
48
Table 10: Performance comparison between uniform training with OCS coreset and original OCS method. (b) Imbalanced Continual Learning
(a) Balanced Continual Learning
Uniform
OCS
OCS
Uniform OCS
OCS
Dataset
Accurncy
Forgening
Accuracy
Forgetting
Datnset
Accuracy
Forgetring
Accurney
Forgetting
Rot MNN-M
50.4 ct 040
0.14 omm
82,5 (2))
0.08 a20
Rot-MNIST
73.6 130
0,11
76.5
0.05
CIFAR
(1.339
CIEAR
51.3 :3:
0.03 42:0
$1. 12 1m
0.02 nam
Mol. Datasets
36.3 14bh
0.08 (2:000
61.5 (2: 1240
0.03 (2 a.1)
Mol. Datnsets
41.
0.05 (.009
47.5
ts 169
0.03 (E 0821
Hyperparameter configurations. Table A.7 shows the initial learning rate, learning rate decay, and batch size for each dataset that are shared among all the meth- ods. Further, we report the best results obtained for E {0.01, 0.05, 0.1, 10, 50, 100} for all the experi- ments. For OCS, we use batch size 100 for Rotated MNIST and 20 for Split CIFAR- 100 and Multiple Dataset. The running time reported in Table 5 was measured on single NVIDIA TITAN Xp. Due to the significant computational cost incurred by the training of Bilevel Optim (Borsos et al., 2020) for online continual learning, we restrict the bilevel optimization procedure to construct the replay buffer at the end of each task training.
Table A.7: Shared Hyperparameter configu- rations among method and baselines for three datasets.
Parameter
Rotated MNIST
Split CIFAR-100
Multiple Datasets
Initial LR
0.005 [0.75, 0.8]
0.15
0.1
IRR decay
0,875
0.85
Batch size
10
10
10
Choice of hy typrpaarameters for OCS. Note that we use the same value of 10, r 1k for all experiments and analyses, including balanced, imbalanced, and noisy CL scenarios for all datasets, which shows that a simple selection of the hyperparameters is enough to show impressive performance. We expect careful tuning would further enhance the performance of OCS.
B ADDITIONAL EXPERIMENTS
Current task adaptation with the baselines. One of our main contributions is the selective online training that selects the important samples for current task training. Therefore, we investigate the application of the other baselines for current task training in Table B.8. It is worth noting that all the rehearsal-basee baselines that utilize their coreset selection criteria for current task adaptation decrease the performance (1.0 9.8%p 4). except Grad Matching (0.5%p 1) on Balanced Rotated MNIST. Moreover, for Imbalanced Rotated MNIST, Uniform Sampling, k-means Features, and k-means Embedding increase the performance 1.9%p, 13.3%p, and 4.0%p compared to Table I respectively. In contrast, iCaRL and Grad Matching criteria decrease the performance by 1.7%p and 3. 3.2%p on Imbalanced Rotated MNIST, respectively. On the contrary, OCS improves the performance for both the balanced and imbalanced scenarios. In light of this, we can conclude that efficient coreset selection plays crucial role in imbalanced and noisy continual learning: therefore, the future rehearsal- -aaessslllbeddddeee continual learning methods should evaluate their method on realistic settings rather than the standard balanced continual learning benchmarks.
Class-incremental continual learning. We also evaluate OCS for balanced and imbalanced class- incremental CL (CIL) setups in Table B.9. We Split CIFAR- 100 dataset to five tasks with memory size of IK for all methods. While the problem is extremely hard to solve, we want to emphasize that OCS outperforms the strongest baseline by 10.61% % and 63.6% on accuracy and forgetting respectively
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Published as a conference paper at ICLR 2022
Gradient dist. for MNIST
Gradient sim. for MIISST
Gradient dist. for CIPAR-10
Grudient sim, for CIPAR-10
0.5
Costie simibrtty
1.00
Covine simllerty
30.4
0.6
dittance
distancc
0.4
0.50
0.2
0.2
0.25
0.3
20
UST
10
56 PANIST
0.00
10
50
1.0 PM
0.0
10
50
100 PMNNST
Minibatch
Minibatch
Minibatch
Minibatch
MNIST dataset using MLP
CIFAR-I0 10 dataset using ResNet-18
Figure B.9: Empirical validation of & distance and cosine similarity between the gradient of the entire dataset and its minibatch gradient. We report the mean and standard deviation the metrics across five independent runs.
for balanced CIFAR-100 dataset, 24.05% and 30% on accuracy and forgetting respectively for imbalanced CIFAR-100 dataset in the CII setting. Note that we report the results for all the baselines using hyperparameter configuration of the main experiments.
Uniform training with OCS coreset. We further analyze the effect of online coreset selection for current task training in Table B. 10a. In particular, we compare uniform sampling for the current task while utilizing the coreset constructed by OCS for the previous tasks (Uniform + OCS) with our original selection scheme utilizing OCS for current and previous tasks. First, observe that Uniform Rotated MNIST and Multiple
+ OCS shows 2.6% and 9.2% relative decrease in performance datasets respectively compared to our original OCS selection strategy. Second, note that Uniform + OCS significantly deteriorates the catastrophic forgetting for all datasets since uniformly sampled examples do not preserve the previous tasks knowledge. Moreover, imbalanced continual learning shows a similar trend in Table B.10b, where Uniform OCS leads drop in both the accuracy and forgetting across all benchmarks. This further strengthens our claim that OCS is essential for the previous tasks and plays vital role in encouraging current- task adaptation.
Table B.11: Ablation study for analyzing the selection with partial gradients in OCS.
OCS with partial gradients. While we consider ResNet-18 as sufficiently deep neural networks, our OCS also can be utilized in extremely deep networks (e.g., ResNet-101) through OCS selection by computing partial gradients of the neural network to reduce the computa- tional cost during online training. This simple modifica- tion is straightforward and validate its potential, we have performed an additional ablation study on Split Tiny- ImageNet in Table 1. R8 contains convolutional layer with first residual block (we
Used Blocks for OCS
Average Accuracy
Average Forgetting
Gradients Usage Ratio
[1
1.2
37.42 aMa
4,70 u944)
6.3
1.2.3.
36.24 ct 119)
4,92 uss)
25.0
1.2.3.
37.06 (2:0))
4.32
100.0
2,3.
96.4
3.4
(2:00
4.85 0.50
93.7
4.
34.75 cL 1.10
5.20 (1 (443)
75.0
name it as a block 'I') and consecutive three other residual blocks (we name them as block 2, 3, and respectively). We have evaluated the variants of OCS which select the coreset based on weights gradients of partial blocks. The first column of the table describes gradients used in OCS selection. That is, the original OCS uses all gradients of all network components ([1,2,3,4)).
Surprisingly, we observe OCS using earlier two blocks (i.e., [1, 2)) show 0.36%p higher performance while using only the 6.3% of gradients compared to the original OCS. We expect that this specific benefit of earlier blocks is due to the different roles of blocks in neural networks. It is well known that earlier layers relatively focus on capturing generic representations while the latter ones capture class- discriminative information. Thus, obtaining the coreset that represents the task-general information and preserves shared knowledge with past tasks is specifically important since generic knowledge is easy to drift and much more susceptible to catastrophic forgetting.
We believe that further investigation of this observation would definitely provide more useful insights for future work and enhance the performance of OCS while greatly reducing the computational costs.
Distance between the whole dataset and its minibatch. To verify our conjecture that a minibatch can approximation of the whole dataset and select few representative data instances each minibatch iteration, we empirically validate that the whole dataset and its minibatch have significant semantic relevancy. More formally, for given subset B,, dataset D,, and >> O, we suppose that the neural network satisfies following equation,
S- (1 N₂
1
Vio(Bi) sc,
(10)
[.
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Published as a conference paper at ICLR 2022
where S" is an arbitrary distance function. To this end, conduct simple experiment using two different datasets (MNIST and CIFAR-10) 10) and network architectures (MLP and ResNet-18) to show that it generally holds various datasets and network architectures. We use 2-layered MLP for MNIST and ResNet-18 for CIFAR- 10 following our main experiments. At each iteration of training, we measure the &2 distance (.) f2(-)) and cosine similarity (-* 1/(sim(-)) between the averaged gradient of the training minibatch and averaged gradient of the entire training dataset. To show that the distance sufficiently small, we also measure the gradient Eg distance between the entire dataset and the irrelevant dataset. Note that we recalculated the gradient for the whole dataset each iteration for all results to correctly measure the distance each step. As shown in Figure B.9, the gradient of larger minibatch shows better approximation to the gradient of the entire dataset for & distance and cosine similarity. Further, note that that even the gradients of an arbitrary subset with a small-sized minibatch is significantly similar to the whole dataset with a small e, and is more evident when compared to the irrelevant gradients from a different dataset, PMNIST (Permuted MNIST) (Goodfellow et al., 2013).
16


Reviews:
[{"review_id": "pcppp5NMh15", "reviewer": "Reviewer_iADy", "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": "STRENGTHS:\n1) The paper is very well written and presented.\n2) The core-set problem is an important and under researched area in continual learning, especially in its online form.\n3) Evaluation is very well executed.\n4) The introduction of diversity as a criteria for core-set selection is interesting.\n\nWEAKNESSES:\n1) As the term “online” appears in the title of the paper, this modality should be better introduced and motivated. A clear explanation appears in the related work at the end of the continual learning paragraph. However, the term remains not properly defined and seems to be related with the problem of imbalance. \nWhat exactly does imbalance mean? In the reviewer understanding the term seems to be defined as in [*] and in (Aljundi 2019b), that is, task distribution is not i.i.d. Given that definition, why selecting the core-set before should provide an advantage? The reviewer understands that the performance is improved, however, the writing states that selecting the core-set before has a dependency on the imbalanced task distribution and that this is an advantage with respect to (Rebuffi et al., 2017; Aljundi et al., 2019b;a; Chaudhry et al., 2019a;b). If this is not the case and the motivation of selecting the core-set before adaptation is because of the good empirical results, then it should be better remarked in the paper.\n\n[*] Chrysakis, Aristotelis, and Marie-Francine Moens. \"Online continual learning from imbalanced data.\" International Conference on Machine Learning. PMLR, 2020.\n\n2) Figure 2 shows a dataset that is not addressed by the method and is somewhat misleading. The \"Multidataset\"  used in the paper does not include the CIFAR dataset (i.e. complex objects like dogs and vehicles).\n\n3) In the reviewer's opinion the claim of large improvement, included in the third contribution, seems to be somewhat a bit bold. For example, in CIFAR-100 balanced and unbalanced learning settings in Tab.1, the performance does not differ too much from the herding strategy used in iCARL (i.e. 60.3 vs 60.5, 51.2 vs 51.4). Although the reviewer noticed that in rotated MNIST and Multidataset improvements are evident, these datasets do not typically “transfer” their performance to larger datasets (i.e., ImageNet) as CIFAR-100 typically does. \n\n4) The validating hypothesis of Fig.3 (i.e. learning from MNIST to CIFAR10) seems to favor diversity, which is exactly what herding is not doing. In herding, examples are selected closer to the class mean of the feature representation in each class. Herding is somewhat orthogonal to diversity. This may partly explain the not improving performance on CIFAR-100. This part should be discussed in depth (i.e., motivate that the method does not mostly favor datasets with diversity). \n\n5) In the reviewer’s opinion the ablation study of the effect of the gradient is not sufficient to justify its usage. As also remarked in the point 3) of this review, the MNIST family datasets typically do not “transfer” their performance to more complex and bigger datasets. In other words, using the gradient on MNIST does not imply that the gradient on CIFAR or bigger datasets is a good choice.\nIs the gradient computationally expensive for deeper neural networks? For example, what happens with one or two more orders of parameters?\n", "summary_of_the_paper": "The paper presents three gradient-based selection criteria to select the core-set for improving adaptation and reducing catastrophic forgetting. Differently from other methods, the proposed approach selects the instances before updating the model.", "summary_of_the_review": "This is a nice and well written paper in which some details need to be clarified. Specifically, imbalance, selecting the core-set before/after adaptation, dataset diversity and selection, the \"transferability\" of performance of the datasets.  ", "strength_and_weaknesses": "", "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": "jMAKn33nVHO", "reviewer": "Reviewer_btdc", "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": "Positive aspects:\n- The proposed approach presents scientific novelty\n- The related work section covers the most relevant papers in the field\n- The experimental validation is extensive and the authors demonstrated the superiority of their approach.\n\nNegative aspects:\n- The idea is in general well-explained, although the paper lacks clarity in some aspects (see the detailed comments below), therefore it could be further improved\n- There are also some issues with the proposed approach which are not clear enough", "summary_of_the_paper": "The author propose a novel approach for online coreset selection, i.e exemplars used in the rehearsal process of past tasks in a continual learning framework. The proposed method is based on the observation that not all the samples in a dataset are equally valuable, but their quality affects model's effectiveness and efficiency. The method selects the most representative and informative samples at each iteration and trains them in an online manner. The approach has been conviently compared with state-of-the art methods and demonstrated its superiority.", "summary_of_the_review": "Please find below my main concerns:\n1. The following statement is not totally clear: \"The naive CL design cannot retain the knowledge of previous tasks and thus results in catastrophic forgetting\". What do you mean by 'naive CL design'? Please reformulate this statement.\n2. Along the paper, you use repeatedly the expression 'target dataset'? What do you mean by 'target dataset' in a continual learning framework? It is confusing: If I have to learn 10 tasks, which one is the target dataset? I guess you refer to the 'current task'. Therefore, please use this formulation instead and change all over the document.\n3. How many representative instances do you select from each mini batch?  Since a sample is presented several times during the training, shouldn't you use an acumulative measure and the final ranking/selection should be done at the end of the training? How do you guarantee the class-balance of the selected core-set? Please plot the distribution of samples per class resulted after the coreset selection process.\n4. I did not understand the equation 3? What index 't' refers to: task ID? How is possible to measure the similarity between a sample and the minibatch it belongs to? Or you consider the similarity between a samples and the batch average? Something is missing there. \n5. Equation 4: Confusing in terms of notations and terminology! You refer as 'cross-batch', but the eq. 4 is about the similarity between samples in the same batch! 'Cross-batch' should not refer to the similarity between a sample from one batch and the samples from different batches? Why the similarity measure in eq. 4 is negative? Please reconsider the notation and formulation of eqs 3 and 4.\n6. Usually, in exemplar-based CL, the memory allocated for exemplar is known and fixed from the beginning. While new tasks are being learned, the number of exemplars from previous tasks is decreased in order to keep the memory size. What strategy do you adopt in your approach regarding the memory capacity where the exemplars are stored?", "strength_and_weaknesses": "", "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": "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": "3d0l6u-SB4h", "reviewer": "Reviewer_mR25", "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": "The reviewer lists the major strengths and weaknesses as follows.\n\n1. Strengths:\nThis paper is well-structured and contains sufficient experiments. Its motivation is meaningful and interesting.\n\n2. Weaknesses:\na. The authors did not explain how big the difficulty is to adapt existing algorithms to online learning. And the way of designing the proposed algorithm for online learning seems straightforward and cannot be regarded as a genuine technical contribution.\n\nb. The algorithm lacks novelty. The core part of the proposed algorithm seems very similar to the core part of 'Asymmetric Multi-task Learning Based on Task Relatedness and Loss'. The three adopted selection strategies do not demonstrate enough novelty, either.\n\nc. Some grammatical errors and typos exist, such as 'let .. is' in definition 3.\n", "summary_of_the_paper": "This paper addresses the problem of coreset selection for realistic and challenging continual learning scenarios. The authors proposed Online Coreset Selection (OCS), a simple yet effective online coreset selection method to obtain a representative and diverse subset.", "summary_of_the_review": "In a nutshell, the reviewer regards this paper as a borderline paper, given the limited technical innovation. \n\nI read the authors' rebuttal. Some of my questions and concerns are replied well. However, I think that the core technique of this work does not advance the research in continual learning significantly. So, I adhere to my previous rating. ", "strength_and_weaknesses": "", "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": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "Not applicable"}, "extra_text": {}}, {"review_id": "0bZxjmbM008", "reviewer": "Reviewer_XVBE", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 3, "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": "This paper proposes an Online Coreset Selection method to select the most representative and informative coreset at each iteration and trains them. The proposed method maximizes the model’s adaptation to a target dataset while selecting high-affinity samples to past tasks, which directly inhibits catastrophic forgetting.\n1. The motivation of this manuscript is not clear. The authors should clearly claim the challenging issues in previous methods.\n2. The authors complement the theoretical explanation of the success of the proposed approach.\n3. While the online coreset selection method adopted in the manuscript seems plausible, it is not exciting.\n\n", "summary_of_the_paper": "This paper proposes an Online Coreset Selection method to select the most representative and informative coreset at each iteration and trains them. The proposed method maximizes the model’s adaptation to a target dataset while selecting high-affinity samples to past tasks, which directly inhibits catastrophic forgetting. Experiments on the benchmark datasets show competitive results compared with baselines.", "summary_of_the_review": "In general the paper is well organized and clearly written. The technical details are easy to follow. Experiments on the benchmark datasets show promising results compared with baselines.\n\n", "strength_and_weaknesses": "", "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": {}}]

Author rebuttal:

Meta-review: The authors propose three strategies for coreset selection in the context of continual learning. In particular, the authors consider class-imbalance and noisy scenarios. The authors run extensive benchmarks and ablation showing that the approach can be effective in practice. All reviewers were positive about this work, but found that the methodological contributions were relatively modest. The clarifications provided by the authors were highly appreciated. I would encourage the authors to revise the paper to incorporate these additional details as there were a number of concepts that reviewers found were not sufficiently documented/explained and lacked clarity. I would also highly encourage the authors to explain their use of "online continual learning" as this reads like a tautology.

Finally, I would like to ask the authors to reflect on their insistance with the reviewers; while we would all want engaging and long discussions about our work, the reality is that reviewing papers and discussing them is time consuming and taxing, especially in the middle of continued pandemic. The authors should be grateful of the time reviewers have spent reading their work and providing feedback, and it is not in the authors' interest to ask for a revision of the scores.
Decision: Accept (Poster)