Is Forgetting Less a Good Inductive Bias for Forward Transfer?
Authors: Jiefeng Chen
Timothy Nguyen
Dilan Gorur
Arslan Chaudhry
Venue: ICLR 2023 poster (2023)
Keywords: continual learning
transfer learning

Abstract: One of the main motivations of studying continual learning is that the problem setting allows a model to accrue knowledge from past tasks to learn new tasks more efficiently. However, recent studies suggest that the key metric that continual learning algorithms optimize, reduction in catastrophic forgetting, does not correlate well with the forward transfer of knowledge. We believe that the conclusion previous works reached is due to the way they measure forward transfer. We argue that the measure of forward transfer to a task should not be affected by the restrictions placed on the continual learner in order to preserve knowledge of previous tasks. Instead, forward transfer should be measured by how easy it is to learn a new task given a set of representations produced by continual learning on previous tasks. Under this notion of forward transfer, we evaluate different continual learning algorithms on a variety of image classification benchmarks. Our results indicate that less forgetful representations lead to a better forward transfer suggesting a strong correlation between retaining past information and learning efficiency on new tasks. Further, we found less forgetful representations to be more diverse and discriminative compared to their forgetful counterparts. 

Published as a conference paper at ICLR 2023
Is FORGETTING LESS A GOOD INDUCTIVE BIAS FOR FORWARD TRANSFER?
Jiefeng Chen
Timothy Nguyen & Dilan Gorur & Arslan Chaudhry DeepMind
Department of Computer Science University of Sieconsin-Madisse Madison, WI 53706, USA jiefengecs wisc. edu
Mountain View, CA
{t (timmthycnguye,, di dil.dggianno lang, ars lanch @ddeemindd com
ABSTRACT
One of the main motivations of studying continual learning is that the problem setting allows a model to accrue knowledge from past tasks to learn new tasks more efficiently. However, recent studies suggest that the key metric that con- tinual learning algorithms optimize, reduction in catastrophic forgetting, does not correlate well with the forward transfer of knowledge. We believe that the con- clusion previous works reached is due to the way they measure forward transfer. We argue that the measure forward transfer to a task should not be affected by the restrictions placed on the continual learner in order preserve knowledge of previous tasks. Instead, forward transfer should be measured by how easy is to learn task given set of representations produced by continual learning on previous tasks. Under this notion of forward transfer, we evaluate different con- tinual learning algorithms on variety of image classification benchmarks. Our results indicate that less forgetful representations lead to a better forward transfer suggesting strong correlation between retaining past information and learning efficiency on new tasks. Further, we found less forgetful representations to be more diverse and discriminative compared to their forgetful counterparts.
INTRODUCTION
Continual learning aims to improve learned representations over time without having to train from scratch as more data or tasks become available. This objective is especially relevant in the context of large scale models trained on massive scale data, where training from scratch is prohibitively costly. However, the standard stochastic gradient descent (SGD) training, relying on the IID assumption of data, results in severely degraded performance
old tasks when the model is continually updated on new tasks. This phenomenon is referred to as catastrophic forgetting (McCloskey & Cohen 1989 Goodfellow al., 2016) and has been an active area of research (Kirkpatrick et al.] [2016]
Lopez-Paz & Ranzato 2017 2017|Mallya & Lazebnik 2018).. Intuitively, the reduction in catastrophic forgetting allows the learner to accrue knowledge from the past, and use it to learn new tasks more efficiently either using less training data, less compute, better final performance or any combi- nation thereof. This phenomenon efficiently learning new tasks using previous information is referred to as forward transfer.
Catastrophic forgetting and forward transfer are often thought of as competing desiderata of contin- ual learning where has to strike balance between the two depending on the application at hand (addelll et al., 2020). Specifically, Wolezyk et al. (2021) recently studied the interplay of forgetting and forward transfer in the robotics context, and found that many continual learning approaches alleviate catastrophic forgetting at the expense of forward transfer. This is indeed unavoidable if the intend to store. However, assuming
capacity of the model is less than the amount of information that the model has sufficient capacity to learn all the tasks simultancously, as in multitask learning, one might think that less forgetful model could transfer its retained knowledge to future tasks when they are similar to past ones.
Work done while interning at DeepMind. I and AC contributed equally.

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Published as a conference paper at ICLR 2023
Split with Random, initt
Split CIFAR-100 with Random, Init
average forward transfer
average forgeting
-1300
Mathhd
AGEE (mi-220
HrT
-220
Mahoo
N01M Inw2et OK in-20
HT
-330
22
(a) Average Forgetting (t better)
(b) Average Forward Transfer (1 better)
Figure 1: Comparing average forgetting with average forward transfer for different continual learn- ing methods using random initialization on the Split CIFAR-100 benchmark. FOMAML has less forgetting and thus better forward transfer.
In this work, therefore, we argue for looking at the trade-off between forgetting and forward transfer in the right perspective. Typically, forward transfer is measured as the learning accuracy on task after the continual learner has already made training updates from the task (Wolezyk et al. [021]] Chaudhry et al. 2019a] Lopez-Paz & Ranzato 2017). However, since such training updates are usually modified to preserve performance on previous tasks (e.g. EWC (Kirkpatrick et al.) 2016)).
competition arises between maximizing learning accuracy and mitigating catastrophic forgetting. Therefore, we argue for a measure of forward transfer that is unconstrained from any training mod- ifications made to preserve previous knowledge. We propose to use auxiliary evaluation of contin- ually trained representations as a measure of forward transfer which is separate from the continual training of the model. Specifically, at the arrival of new task, we fix the representations learned on the previous task and evaluate them on the new task. This evaluation is done by learning a temporary classifier using small subset of data from the new task and measuring performance on the test set of the task. The continual training on the new task then proceeds with the updates to the representa- tions (and the classifier) with the full training dataset of the task. We note that this notion of forward transfer removes the tug of war between forgetting the previous tasks and transfer to the next task, and it is with this notion of transfer that we ask the question are less forgetful representations more transferable?
We analyze the interplay of catastrophic forgetting and forward transfer on several supervised con- tinual learning benchmarks and algorithms. For this work, we restrict ourselves to the task-based continual learning setting, where task information is assumed at both train and test times as makes the aforementioned evaluation based auxiliary classification fixed points easily interpretable. Our results demonstrate that a less forgetful model in fact transfers better (cf. Figure []. We find this observation to be true for both randomly initialized models well as for models that are ini- tialized from a pre-trained model. We further analyse the reasons of this better transferability and find that less forgetful models result in more diverse and easily separable representations making easier to learn classifier head on top. We note that with these results, we want to emphasize that the continual learning community should look the trade-off between forgetting and forward trans- fer in the right perspective. The learning accuracy based measure of forward transfer is useful for end-to-end learning on fixed benchmark and it creates a trade-off between forgetting and forward transfer as rightly demonstrated by Hadsell et al. (2020); Wolczyk et al. (202T). However, in the then-nntttn--- is a dominant paradigm and where one often
era of foundation models where does not know priori the tasks where a foundation model will be finetuned, measure of forward transfer that looks at the capability a backbone model to be finetuned on several downstream tasks is perhaps a more apt measure.
The rest of the paper is organized as follows. In Section we describe the training and evaluation setups considered in this work. In Section 3 provide experimental details followed by the main results of the paper. Section 4 lists down most relevant works to our study. We conclude with Section 5 providing some hints to how the findings of this study can be useful for the future research.
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Linear Probing
Dj+1
Fixed
K-shot Samples
1
Evaluate
Accuracy
Classification
B
By
Feature Extractor
Task Sequence
T
Tj
Tx
Continual Learning
Figure 2: Illustration continual learning and k-shot evaluation process. We continuously train the feature extractor and the classification head on a task sequence Ti, ....... . Tv. O, o the model obtained after training on Tj. To evaluate the forward transfer of $ we use lincar probing on k-shot samples from the next task T1+1 to learn classifier θ and then evaluate the accuracy o 4 on the test set Dj41 from task T₃+1-
PROBLEM SETUP AND METRICS
We consider supervised continual learning setting consisting of a sequence of tasks T (Ti,... TN.. J. A task T; is defined by a dataset Dj {(I;, Vi, t,), consisting of n. triplets, where I E X, y E V, and E T are input, label and task id, respectively. Each Dj = {DJ" Dyyal Djj consists of train, validation and test sets. At given task 'j' the learner may have access to all the previous tasks' datasets (Diteej but it will not have access to the future tasks. We define feed-forward neural network consisting of a feature extractor & X RD and a spec-fpe classifier θ RD T + Vj. that implements an input to output map- ( ④) X x V/. The neural network is trained by minimizing loss ping fy : ()) x 33 + R+ using stochastic gradient descent (SGD) (Bottou 2010). While we consider image classification tasks and cross-entropy loss for each task, the approach would be applicable to other tasks and loss functions as well.
The learner updates shared feature extractor (T) and task-specific heads (0,) throughout the tinual learning experience. After training on each task 'i', we measure the performance of the learner on all the tasks observed far. Let Ace(i,)) (i) be the accuracy of the model Dje after the feature extractor is updated with T, We define the average forgetting metric at task 'i' similar to (Lopez- Paz & Ranzato 2017):
Egt, Σ Acc(i. Acc(j.j).
The average forgetting metric (E [-1, throughout the continual learning is then defined as,
N
AvgEgt N Σ Fgt.-
negative value of Fgt, indicates that the learner has lost performance on the previous tasks, and the negative AvgFgt the more forgetful the representations of the previous knowledge.
Forward Transfer through K-Shot Probing We measure forward transfer in terms of how easy it to learn a new task given continually trained representations. The easiness is measured by learning linear classifier top of the fixed representations using small subset of the data of the task

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Published as a conference paper at ICLR 2023
(refer to Figure 2 for illustration). Specifically, let S 2 Djt1 denote a sample consisting examples per class from 1=+1 and let D2 be the representations obtained after training on task 'j' (see the bottom blob of Figure 2) Let é be the temporary (linear) classifier head learned on top of fixed ; using S We measure the accuracy of this temporary classifier on the test set of task "j+I' and denote it Fwtt.. This is called the forward transfer of learned representations $ the next task j+1'. The average forward transfer throughout the continual learning is then defined as,
N Σ
AvgFwt
Fwt
N
We note that linear probing is an auxiliary evaluation process where model updates during evaluation remain distinct from the updates made by the continual learner while observing a task sequence. Contrary to this, in most prior works (Wolczyk al. 2021 Lopez-Paz & Ranzato 2017), forward transfer is measured after the continual restrict the learning on current task alleviate catastrophic forgetting on the previous tasks. This causes the learner to perform worse on the current task compared to learner that is not trying to mitigate catastrophic forgetting. We sidestep this dilemma by separating the updates made by the continual learner on a new task from the temporary updates made during auxiliary evaluation copy of the model. We also note that similar linear probing, one could finetune the whole model, including the representations, during the auxiliary evaluation. The main argument is to decouple the notion of forward transfer from modifications made by the continual learning algorithm preserve knowledge of the previous tasks.
Teariner learner has made updates on the task. Such updates typically
Feature Diversity In addition to AvgFgt (Equation 1 and AvgEwt* (Equation 2 we also measure how diverse and easily separable the features of our trained models are for analyzing the transferability of the representations. Specifically, let V E mxx the feature matrix computed using the feature extractor b (obtained after training task 'j') on the 'm' test examples of task '+1''. Let Tie be a sub-matrix constructed by collecting the rows of V that belong to class 'c'. Similar to (Wu al. 2021 Yu et al. 2020), define the feature diversity score of $
FDiv, = log VV 11 +I Σ log ay Dj Vi + II,
where |-| is a matrix determinant operator, D/(me))(mm)))))) a, (m)m,="), 0.5, and Cj denotes the number of classes for task 'j. The average feature score throughout the continual learning experience is then defined
N-1 AvgFDiv N Σ FDivy.
The intuition behind using this score that features that enforce high inter-class separation and low intra-class variability should make it easier to learn classifier head on top leading better transfer to next tasks.
EXPERIMENTS & RESULTS
3.1
SETUP
We now briefly describe the experimental setup including the benchmarks, approaches and training details. More details can be found in Appendix A After the experimental details, we provide the main results of the paper.
Benchmarks
Split CIFAR-10:
We split CIFAR-10 dataset (Krizhessky et al. 2009) into disjoint sub-
sets corresponding to 5 tasks. Each task has 2 classes.
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Split CIFAR-100: We split CIFAR-100 dataset (Krizhevsky et al. 2009) into 20 disjoint subsets corresponding to 20 tasks. Each task has 5 classes.
C-FAR-100 Superclasses: We split CIFAR- 100 dataset into 5 disjoint subsets correspond- ing to 5 tasks. Each task has 20 classes from 20 superclasses in CIFAR- (10 respectively.
CLEAR: This is continual image classification benchmark [i et al. (2021), built from YFCC100M (Thome et al. 2016) images, containing the evolution of object categories from years 2005-2014. There are 10 tasks each containing images in chronological order from years 20005. We consider both CLEARIO (consisting of 10 object classes) and CLEAR100 (consisting of 100 object classes) variants of the benchmark.
Split ImageNet: We split ImageNet (Russakovsky et al. 20015) dataset into 100 disjoint subsets corresponding to 100 tasks. Each task has 10 classes.
For all the benchmarks, except split ImageNet, we considered continual learning from randomly initialized model as well as from a pre-trained ImageNet model. For split ImageNet, we only con- sidered continual learning from randomly initialized model.
Approaches
Below we describe the approaches considered in this work. Except for the independent baseline, all other baselines reuse the model i.e. continue training the same model used for the previous tasks.
Independent (IND): Trains model from an initial model (either random initialized or pre-trained) on each task independently.
Finetuning (FT):: Trains single model on all the tasks in sequence, one task at time.
Linear-Probing- Frrobing-Finetuning (LP-FT): LP-FT (Kumar et al. 2021) is the same as FT ex- cept that before each task training, we first learn task-specific classifier θ for the task via linear probing and then train both the feature extractor 4 and the classifier è on the task to reduce the feature drift.
Multitask (MT): Trains the model the data from both the current and previous tasks using the multitask training objective (equation Appendix). The data of previous tasks is used as an auxiliary loss while learning on the current task.
Experience Replay (ER): Uses a replay buffer M = -N MM when learning on the task sequence, where M, stores m examples per class from the task T,. It trains the model on the data from both the current task and the replay buffer when learning on the current task using an ER training objective (equation 7 in Appendix) (Chaudhry et al., 2019b). There are two main differences between MT and ER: (1) MT uses all the data from the previous tasks while ER only uses limited data from the previous tasks; (2) MT chooses the coefficient for the auxiliary loss via cross- valss-validation while ER always set it to be 1.
Projects the gradient when doing the SGD updates so that the average loss on the data from the episodic memory does not increase (Chaudhry al. 2019a). The episodic memory stores m examples per class from each task.
AGEM:
First-order MAML (FOMAML) is meta-learning approach proposed by Finn et We modify FOMAML such that it can be used in the continual learning setting. Sim- ilar to MT, FOMAML uses all the data from the previous tasks when learning the current task. The training objective of FOMAML aims to enable knowledge transfer between dif- ferent batches from the same task. The learning algorithm for FOMAMI. is provided in Appendix A.2
FOMAML:
Architecture and Training details. We use ResNet50 (e et al. 2016) architecture as the feature extractor t on all benchmarks. On CLEARIO and CLEAR100, we use single classification head θ that is shared by all the tasks (single-head architecture) while other benchmarks, separate classification head θ for each task T; (multi-head architecture). We use SGD to update the model parameters and use cosine learning rate scheduling (Loshchilov Hutter, 2016) adjust the learning rate during training. For LP-FT, we use a base learning rate of 0.001 while for other
'The FWC KKrkpptrickk al. 2016) results in Appendix Table
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Split Random,
Split CIFAR-10 with Random, Init
669
average forward transter
0.75
AGG (mm-33)
-1.05
HIT
FCMAM.
4.10
-820
Mahoo
-225
(K inuseg
CLEAR100 Random
CLEAR100 with Random, init
Mithod
average forward transfer
6.09
0.39
lorgetting
6.04
AGD vrn--14
607
FOHMAM
0.5
0.15
(a) Average Forgetting (+ better)
(b) Average Forward Transfer (f better)
Figure 3: Comparing average forgetting with average forward transfer for different continual learning methods using random initialization on the Split CIFAR-10 and CLEARI00 benchmarks.
baselines, we use base learning rate of 0.01. When using a random initialization as the initial model fo- on split CIFAR-10, split CIFAR-100 and CIFAR-100 superclasses, we train the model for epochs per task while on CLEARIO, CLEAR 100 and Split ImageNet, we train the model for 100 epochs per task. When using pre-trained model as the initial model fo. on all benchmarks, we train the model for 20 epochs per task as we found sufficient for training convergence, For CLEARIO and CLEAR100, the results are averaged over 5 different runs with different random seeds each corresponding to different network initialization, where the task order fixed. For other benchmarks, the results averaged over 5 different runs, where each run corresponds to different random ordering of tasks. The results are reported as averages and 95% confidence interval estimates of these 5 runs. For k-shot linear probing, use SGD with fixed learning rate of 0.01. We train the classifier head Ô for 100 epochs on the k-shot dataset Sk training convergence. On CLEAR100, we consider & E (5, 10, 20, 40) while on other benchmarks, we consider & {5, 10, 20, 100).
found sufficient for
3.2 RESULTS
LESS FORGETFUL REPRESENTATIONS TRANSFER BETTER
We assess the compatibility between forgetting and transferability through AvgF gt and AvgFwt* metrics described in Section 2 Figures and show these two metries for Split CIFAR-100, Split-CIFARIO 10 and CLEAR 100, respectively when the continual learning experience begins from randomly initialized model (the comparison on the other benchmarks provided in the Ap- pendix B.I. It can be seen from the figures that if model has less average forgetting, the corre- sponding model representations have a better K-shot forward transfer. For example, on all the three benchmarks visualized in the figures, FOMAML and MT tend to have the least amount of average forgetting. Consequently, the A of these two baselines is higher compared all the other baselines, for all the values of k considered in this work. Note that the ranking of other methods in terms of correspondence between forgetting and forward transfer is roughly maintained as well. This shows that when continual learning experience begins from randomly initialized model. taining the knowledge of the past tasks or forgetting less on those tasks is a good inductive bias for forward transfer.

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Published as a conference paper at ICLR 2023
S AR With FReTDOn
Spit CHAR 30
Sol: CEPAR- 10
Solt OTAR-302 WiS Pre-trann
3p18 UHA6-100 100 th Pre
Svstage -300
(a) AvgE gt (f better)
(b) AvgFwt & (t better)
(c) Upstream Accuracy (f better)
Figure 4: Comparing average forgetting with average forward transfer different continual lcarning meth- ods that train the model from a pre-trained ImageNet model on the Split CIFAR-10 10 and Split CIFAR- -000 benchmarks. We also show the accuracy of the models on the upsteam ImageNet data. Since CIFAR-I0 and CIFAR-100 images have different image resolution than that of ImageNet images, we need to resize the Ima- geNet test images from 224 224 32 32 in order to get meaningful accuracy of the models trained the Split CIFAR-10 and Split CIFAR-100 benchmarks on the upstream ImageNet data (although the accuracy of the pre-trained model on the resized ImageNet test images is significantly reduced).
Recently, Mehta et al. (2021) showed that pre-trained models tend to forget less, compared to ran- domly initialized models, when trained on a sequence of tasks. We build upon this observation and ask if forgetting less on both the upstream (pre-trained) task, and downstream tasks improve the transferability of the representations? Figure shows the comparison between forgetting (left) and forward transfer (middle) on Split CIFAR- 10 and Split CIFAR- 100 when the continual learning experience begins from a pre-trained model (the comparison on the other benchmarks is provided in the Appendix B. It can be seen from the figure that except for LP-FT, less forgetting is good indicator of a better forward transfer. In order to understand, why LP-FT has a better forward transfer, compared to FOMAML and MT, despite having higher forgetting on the continual learning benchmark at hand, we evaluate the continually updated representations on the upstream data (test set of ImageNet). The evaluation results given in the right plot of Figure 4 From the plot, it can be seen that L.-FT has retained better upstream performance (relatively speaking) compared to the other baselines. This follows our general thesis that retaining 'previous knowledge', evidenced here by the past performance on both the upstream and downstream tasks, is good inductive bias for forward transfer. If instead of freezing the representations and just updating the classifier, we finetune the whole model in the auxiliary evaluation, the less forgetful representations still transfer better (refer to Appendix [B.5).
In order to aggregate the metrics across different methods and to see global trend between for- getting and forward transfer, we compute the Spearman rank correlation between AvgFgt and AvgFwt* Table shows the correlation values for different values of 'k' for both randomly initial- ized and pre-trained models. It can be seen from the table that most of the entries are above 0.5 and statistically significant (p < 0.01) showing that reducing forgetting improves the forward transfer across the board.
LESS FORGETFUL REPRESENTATION ARE MORE DIVERSE
We now look at what makes the less forgetful representations amenable for better forward trans- fer. We hypothesize that less forgetful representations maintain more diversity and discrimination in the features making it easy to learn a classifier head on top leading to better forward transfer. To measure this diversity of representations, we look at the feature diversity score AvgFDiv, as defined in Equation 3 and compare it with the average forgetting score AvgFqt. Table shows the results on different benchmarks and approaches. It can be seen from the table that, for randomly initialized models, less forgetting, evidenced by higher AvgFst score, generally leads to repre-
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Random Init
Pretrain
Dataset
k ==
k = 10
A == 20
==
A 10
20
Split CIFAR-I0
0.64
0.56
0.65
0.68
0.66
0.58
Split CIFAR-100
0.92
0.88
0.91
0.86
0.86
0.88
CIFARIO0 100 Superclasses
0.3 (0.11)
0.4 (0.03)
0.4 (0.03)
0.16 (0.40)
0.46 (0.01)
0,62
CLEAR 10
0.7
0.65
0.73
0.43 (0.02)
0.37 (0.04)
0.64
CLEARI00
0.58
0.59
0.53
0.83
0.8
0.81
Split ImageNet
0.85
0.85
0.79
Table I: Spcarman correlation between AvgEgt and AvgEwt" for different k, which computes the correla- tion over different settings (different training methods and random runs). p-values are shown in parenthesis if greater than or equal to 0.01.
Random Init
Pre-trained
Dataset
Method
AvgPgt -28.18 2.97
AvgFDiv
AvgPgt
AvgFDiv
FT
35.59 = 10.52
-29.01 7.97
60.18 = 36.35
LP-FT
-3.39 1 1.06
171.41
13.41
Split
ER (m=50)
-9.18 + 1,50
37.33 + 14.66
-7.15 - 1.97
1.97
66.18 + 35.74
CIFAR-10
AGEM (m=50)
-13.77
2.38
35.79 + 16.34
5.01 -19.26
60.77 + 41.80
MT
-3.88 + 5.86
36.88 = 13.21
4.83
86.88 21.82
FOMAML
-0.75 + 1.39
45.52 7.82
-1.40 0.61
65.26 10.36
-2.833 +
224.27 + 3.63
2.199
263.31 27.46
LP-FT
4.46
382.10
Split
ER (m=20)
9944 1.11
225.95 2.38
-929
281.31 3.59
CIFAR-100
AGEM (m=20)
-18.70 1,00
224.46 + 2.93
-2.05
260.01 = 20.32
MT
-9.35 +: 4.96
225.33 4.66
4..93
277.14 1.314
FOMAML
-3.05 + 0.98
225.87 5.31
4.40
271.56 + 7.45
FT
-14.45 1.02
458.73 + 12.99
0.55
599.29 = 13.65
LP-FT
-2.66 0.53
702443 +.43++4.11 4.10
CIFAR-100
ER (m=5)
-1..3
463.78 7.86
1.443
600.23 23.86
Superclasses
AGEM (m=5)
-12.28
459.65
14.52
0.76
594.70 27.51
MT
-133 4.02
465.47
1. 7.84
-5.50
601.38 16.92
FOMAML
1.99 = 0.76
470.27 5.17
-1.24
620.66 10.34
FT
0.93 = 1.01
76.72 1.70
0.14
265.72 = 1.08
LP-FT
0.81
281.78 + 0.34
ER (m=10)
1.79 0.24
76.76 1.62
+.22
263 1 0.82
CLEARIO
AGEM (m=10)
2.03 0.86
76.00 1.79
0.01
266.36 1.02
MT
79.01
1.41
1.751
265.25
FOMAML
4.49 0.56
77.98
0.84
262.88 1.28
5.06 + 0.29
179.47 1.01
0.13
441.22 0.50
LP-FT
0.00
488.94 :: 0.71
ER (m=5)
5.53 L 0.24
181.39 L. 1.56
0.34
440.48 1 0.79
C0
AGEM (m=5)
4,94 + 0.36
179.12 + 1.03
0..14
441.26 + 0.27
MT
8.65 0.96
186.16 3.31
1.56
444.38 0.41
FOMAML
9.21
184.38 1.58
0.16
440.30 0.71
54.62
271.98
(m=10)
-27.56
289.18 3.99
Split
AGEM (m= 10)
50.53 1.58
274.07 1.20
ImageNet
MT
-16.79 166.99000 0.69
274.88 + 2.13
FOMAMI.
-10.58
0.69
305.63 + 5.59
Table 2: Comparing AvgFgt with AvgFDiv. The numbers for AvgFgt gt are percentages. Bold numbers are superior results.
sentations that have higher AvgFDiv score. Similarly, on pre-trained models, methods with lower overall forgetting between the upstream and downstream tasks, such as LP-FT, leads to the highest AvgFDiv score. These results suggest that less forgetful representations tend to be more diverse and discriminative.
RELATED WORKS
Continual Learning (also known as Life-long Learning) [Ring 1995 Thrun 1995) aims to learn a model on sequence of tasks that has good performance on all the tasks observed far. However, SGD training, relying on IID assumption of data, tends to result in a degraded performance on older tasks, when the model is updated on new tasks. This phenomenon is known as catastrophic forget-
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ting (McCloskey & Cohen 1989 Goodfellow et al., 2014) and it has been main focus of continual learning research. There are several methods that have been proposed to alleviate catastrophic for-
getting, ranging from regularization-basee -basd approaches (Kirkpatrick et al. 2016 Aljundi et al. al.] 2018
Nguyen et al. 2018 /Zenke et al. 0017), to methods based on episodie memory (Lopez-Paz & Ran-
zato| 2017| Chaudhry et al. 201 9a| Aljundi al. 2019 Hayes al.) 2018 Riemer et al. 2019
Rolnick et al.|||| 2018 Prabhu et al. (2020) to the algorithms based on parameter isolation (Yoon et al.
2018
Mallya & Lazebnik 2018 Wortsman et al.) 2020) Mirzadeh et al. 2021b Farajtabar et al.
2020). Besides the algorithmic innovations to reduce catastrophic forgetting, recently some works
looked at the role of training regimes (Mirzadeh et al. 2020) and network architectures (Mirzadeh)
et al.
a0 2022) for understanding the catastrophic forgetting phenomenon.
While a learner that reduces catastrophic forgetting tries to preserve the knowledge of the past tasks, often what is more important is to utilize the accrued knowledge to learn new tasks more efficiently, a phenomenon known as forward transfer (Lopez-Paz & Ranzato 2017 Chaudhry et al.) 9a). In most existing works, the forward transfer to task is measured
the learning accuracy of the task after training on the task is finished. Hadsell et al. (2020) and Wolezyk et al. (202T) argued that continual learning methods that avoid catastrophic forgetting do not improve the forward transfer, in fact, sometimes the catastrophic forgetting is reduced at the expense of the forward transfer (as measured by the learning accuracy). This begs the question whether reducing catastrophic forget- ting is a good objective for continual learning research or should the community shift focus on the forward transfer as there seems to be tug of war between the two?
Contrary to previous work, here, we take an auxiliary evaluation perspective to forward transfer where instead of asking whether reducing forgetting on previous tasks, during training on the current task, improves the current task learning, we ask whether a learner that has less forgetting on previous tasks, results in network representations that can quickly be adapted to new tasks? We argue that this mode of measuring forward transfer decouples the notion of transfer from the restricted updates on the current task employed by a continual learner to avoid forgetting on previous tasks. To the best of our knowledge, most similar to our work is Daved & White (2019): Beauliiu et al. (2020) who also looked at the network representations in the context of continual learning. But they took a converse perspective- -arguing that learning transferable representations via meta-learning alleviates catastrophic forgetting.
5 CONCLUSION
We are interested in understanding how to continuously accrue knowledge for sample efficient learn- ing of downstream tasks. Similar some previous works, here we question what effect alleviating catastrophic forgetting has on the efficiency of learning new tasks. However, by contrast, we study forward transfer by the auxiliary evaluation of continually trained representations learned through the course of training on a sequence of tasks. To this end, we evaluated several training algorithms on a sequence of tasks and find that our forward transfer metric is highly correlated with the amount of knowledge retention (i.e. less negative forgetting score), indicating that forgetting less may serve as a good inductive bias for forward transfer.
The question of how to accrue knowledge from the past tasks to learn new tasks more efficiently ever more relevant with the recent advancements in the large scale models trained using internet scale data, aka foundation models, where we would want to avoid initialization from scratch to save computation time. Our suggested measure of forward transfer, that evaluates continually trained representations, also fits nicely in the context of comparing generalization of different large scale models, where a model that can transfer to multiple downstream tasks is preferred. We are in the of discovering new capabilities of models, as new capabilities emerge with larger scale. The extrapolation of our findings could mean that a less forgetful foundation model - where forgetting is evaluated on the upstream data should be preferred over a forgetful model, the former could transfer better to downstream tasks. This serves as a useful model selection mechanism which can be further explored in future research.
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Supplementary Material
Is Forgetting Less a Good Inductive Bias for Forward Transfer?
A EXPERIMENTAL DETAILS
A. DATASETS
We describe the details of the datasets used in this paper below:
CIFAR-10. The CIFAR-I0 dataset (Krizhevsky al., 2009) consists of 60,000 32x32 color images in 10 classes, with 6,000 images per class. There are 50,000 training images and 10,000 test images. We reserve 10,000 training images as the validation data. So the training set used has 40,000 images. We split the CIFAR-10 dataset into 5 disjoint subsets to create the Split CIFAR-10 10 benchmark. Split CIFAR-10 has 5 tasks corresponding the disjoint subsets and each task has 2 classes. During training, we apply random cropping and random horizontal flip to the training images.
CIFAR-100. The CIFAR-100 dataset (Krizhevsky et al.) 2009) is just like the CIFAR-10. 10, except it has 100 classes containing 600 images each. There are 500 training images and 100 testing images per class. The 100 classes the CIFAR-100 are grouped into 20 superelasses. Each image comes with "fine" label (the class to which it belongs) and "coars" label (the superclass to which it be- longs). We reserve 10,000 training images as the validation data. So the training set used has 40,000 images. We use the CIFAR-100 dataset to create two benchmarks Split CIFAR- 100 and CIFAR- 100 Superclasses. The split CIFAR- 100 benchmark is created by splitting the CIFAR- 100 dataset into 20 disjoint subsets corresponding to 20 tasks. Each task in Split CIFAR- 100 has 5 classes. The CIFAR- Superclasses benchmark is created by splitting the CIFAR-100 dataset into 5 dis- joint subsets corresponding 5 tasks. Each task in CIFAR-100 Superclasses has 20 classes from 20 superclasses respectively. For both Split CIFAR-100 100 and CIFAR- 1-0 Superclasses benchmarks, during training, we apply random cropping and random horizontal flipping data augmentations to the training images.
CLEAR. CLEAR (Lin et al. 2021) is the first continual image classification benchmark dataset with a natural temporal evolution of visual concepts in the real world that spans a decade (2005- 2014). It contains two continual learning benchmark CLEARI0 and CLEARI00, The original CLEARIO has 33,000 training images and 5,500 test images with 10 tasks and 11 classes (including a BACKGROUND class). We Remove the BACKGROUND class and reserve 5,000 training images as the validation data. So the training set used has 25,000 images and the test set used has 5,000 images. The original CLEAR 100 has 99,963 training images and 50,000 test images with 10 tasks and 100 classes. We reserve 19,991 training images as the validation data. So the training set used has 79,972 images. Each task in CLEAR10 (or CLEAR100) contains images from certain year (2005-2014). For both CLEARIO and CLEAR 100 benchmarks, we resize the images to 224 x 224 and use random cropping and random horizontal flipping data augmentations during training.
ImageNet. ILSVRC 2012, commonly known as "ImageNet" (Russakovsky et al. 2015) is large scale image dataset with 1,000 classes organized according to the WordNet hierarchy. It has 1,281,167 training images and 50,000 validation images with labels. It also has 100,000 test im- ages but without labels. We use the validation images as the test set and reserve 300,000 training images (300 images per class) as the validation set. So the training set used contains 981,167 im- ages. We split the ImageNet dataset into 100 disjoint subsets corresponding to 100 tasks. Each task has 10 classes. During training, augmentations. To reduce computational cost, we resize the images to 64 x 64.
random cropping and random horizontal flipping data
A.2 BASELINES
We consider the following approaches for leaning on a sequence of tasks Ti...., Tr. Except for the independent baseline, all other baselines reuse the model (i.e.) continue training the same model
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used for the previous tasks. Specifically, when learning the task T, (i > 1). the continual learning method will use the model fi-1 learned on the previous task T;-1 as an initialization for the model fi, which call model reusing. For the first task T` training, the continual learning method will initialize the model by an initial model fo (either a random intialization or pre-trained model).
Independent (IND). The IND baseline learns on each task independently. That is when learning on the task T, it will train the model from an initial model (either random initialization or pre-trained model) using the Empirical Risk Minimization (ERM) objective:
min (...).D (.to0,,,,((aaaaa ((f,(,, fi
We use the IND baseline as a reference to see how well we can learn on task without learning on other tasks in the task sequence.
Finetuning (FT). Finetuning is simple baseline for continual learning. It trains single model on all the tasks in a sequence. When training the model f; on the current task T,, it doesn' 't use the data from the previous tasks. It uses the ERM objective (equation 4 train the model fi on the current task T; only.
(LP-FT). Sinear-Probing Srbbbin-iinnttning (Kumar et al., 2021) is the same as the Finetuning baseline except that before each task training, we first learn task-specific classifier θ for the task via linear probing and then train both the feature extractor & and the classi- fier θ on the task. That is when learning on the current task Ti we have two-stage training process. In the first stage, we train the classifier O while fixing the feature extractor 4, via the ERM training objective:
Linear-Probing
Grobing-Finetuniig
min (: () O, Φ,)
In the second stage, we train both the classifier O and the feature extractor c via the ERM training objective (equation 4). We only use LP-FT in the setting where the initial model fo is pre-trained model.
Multitask (MT). The Multitask baseline trains the model on the data from both the current task and the previous tasks when learning on the current task T,. uses the following multitask training objective:
2.) + A Eis / (),); (6) min VE...))- 0,, (0,))))
trains a shared feature extractor 4; and task-specific classifiers (0,) for the tasks Ti...., , Tí. The hyperparameter À is chosen from the set {1.0, 0.1, 0.01} based on the average learning accuracy across tasks on the validation set.
Experience Replay (ER). The ER baseline uses replay buffer M = U Ms when learning on the sequence tasks, where M2 stores examples from the task 77. In our work, we restrict the replay buffer M to store only m examples per class from each task. The training objective used by ER is:
min ((e,,, T.) BesjeeBeeeommm.. (1, +.) (,,(0,))_1
(7)
AGEM. AGEM is continual learning method proposed by Chaudhry al. Similar to ER, AGEM also replay buffer (or episodic memory) M UNN MM,, where M, stores only
m examples per class from the task T.. While learning the task T,, the training objective of AGEM
is:
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min (4f(t,) t), J
(8)
s.t. E (4 1),)) S (a (ie-
where Mi - Mg.. The corresponding optimization problem
min 2 9 0112 s.t. g" gres 2 0
(10)
where 9 gradient computed using a batch randomly sampled from the current task solve the objective (equation 8). Gref is a gradient computed using batch randomly sampled from the episodic memory Mi and ğ is projected gradient that we will use to update the model. When the gradient g violates the constraint (equation 9). it is projected via:
go gref gre gref
(11)
FOMAML. MAML is meta-learning approach proposed by Finn et al.) Since there are some differences in the meta-learning setting and the continual learning setting (e.g. meta-learning algo- rithms assume that there is task distribution where we can sample tasks from it while in the con- tinual learning setting, we don't have such task distribution), we cannot directly use the MAML algorithm proposed in Finn et al. (2017). We then modify MAML such that it can be used in the continual learning setting. While learning on the task T,, the training objective we want to solve is:
min Ei ft) + A EEEM En ...... By -D: (. (0)) ft
(12)
where = (1,2, . ,1. D, means sampling a batch from D; and
1 Ub I..... -....... B
(13)
Here, UB....... Bbi f) is model obtained by applying b gradient update steps on the model using b batches BI...., BB. If we use standard SGD for Up and the learning rate is then we have
11 = ft 113 = 1 (9-11) a V ( $13 ((9-1)), 9 = 1,....,,
(14)
The training objective aims to find a model such that it achieves small error on the current task T; and after several gradient update steps some batches from seen task T, [i],, the updated model can achieve small error on other batches from the task 7j. So we want to find a model that enable knowledge transfer between different batches from the same task.
Solving the objective (equation 12 requires computing the second-order gradients, which might be expensive. However, we can the idea first-order MAML (FOMAML) proposed in Finn et al. (2017), which ignores the second derivative terms, to solve the objective. The algorithm of FOMAML presented in Algorithm In our experiments, we simply set a 5 and 1. On Split ImageNet, we set = 1 while on other benchmarks, we set b b= 2.
A.3 ARCHITECTURE AND TRAINING DETAILS
Architecture. We use ResNet50 He et al. 2016 architecture as the feature extractor O on all benchmarks by default. On CLEARIO and CLEAR100, shared by all the tasks (single-heel head architecture) while on other benchmarks, we use a separate classification head O for each task 7; (multi-head architecture).
single classification head θ that
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Algorithm 1 FIRST-ORDER MAML (FOMAML)
Require: A model fi-1 after training on the previous task Ti-1, 1, learning rate a for inner-update, a learning rate 9 for upter, the number of previous tasks used for each training step, the number of gradient update steps 6 for the inner-update and the number of training steps n for the outer-update.
1: fi t f-1
2: Randomly sample a batch from the current task T;, i.c., ~ Di
3: G < (B; f()
4: for my=1, 1,,2......2 do
5: Randomly select indices from the set ( 13 without replacement set 7p-
6:
I I [ {i)
7:
for j do
8:
[u. -.
9:
for 1 do
10:
Randomly sample batch Bj, from D,.
11:
Apply an inner-update step: f!a) + f.. a V 12. end for Randomly sample batch B from Dj.
(B 12 1)
12:
13:
14:
G G V )(9))
15:
end for
16:
Apply an outer-update step: fo s- fc - G.G
17:
end for
18:
return ft
Continual Learning Training Details. We use Stochastic Gradient Decent (SGD) for training models. We use cosine learning rate scheduling (Loshchilov & Hutter 2016) adjust the learning rate during training. Suppose the base learning rate is and the number of training steps for each task is n. Then for each task training, training step f. the learning rate for the SGD update is r. cos fx For LP-FT, we use base learning rate of 0.001 while for other baselines, we use a base 2n learning rate of 0.01. on split CIFAR-10, split CIFAR- 100 and CIFAR- -00 superclasses, we use a batch size of 64. On CLEAR10 and CLEAR 100, we use batch size of 128. On Split ImageNet, we use batch size of 256. When using a random initialization as the initial model fo. on split CIFAR-10, split CIFAR- 100 and CIFAR-100 superclasses, we train the model for 50 epochs per task while on CLEARIO, CLEARIO0 and Split ImageNet, we train the model for 100 epochs per task. When using pre- trainrr model as the initial model fo. on all benchmarks, for 20 epochs per task as we found it sufficient for training convergence. For LP-FT, we perform the linear probing for 10 epochs per task. These training hyper-parameters chosen based on the average learning accuracy across tasks on the validation set.
train the model
K-Shot Linear Probing Training Details. We use Stochastic Gradient Decent (SGD) with a fixed learning rate of 0.01 for linear probing. We train the classifier head é for 100 epochs on the k-shot dataset - as we found it sufficient for training convergence. On CLEAR100, the set of values consider for & is (5, 10, 20, 40) while other benchmarks, the set of values we consider for k is {5, 10, 20, 100}. For each ks we use batch size of min(k (k- c, 50), where e is the number of classes in the task. We don't apply any data augmentations the training images during the k-shot linear probing.
A.4 HYPER-PARAMETERR SELECTION
In this section, we discuss how we select the hyper-parameters.
Continual Learning Training. For different baselines, the shared hyper-parametent are the batch size, the learning rate and the number of training epochs. We do not tune the batch size, but set it to be a fixed number for each benchmark. For the learning rate and the number of training epochs, we choose them based on the average learning accuracy across tasks on the validation data. The range of the learning rate that we consider is 10. 0.01, 0.001, 0.0001). }. We found that setting the learning rate to be 0.01 leads to the best average learning accuracy for all the baselines except LP-FT. For L.--T, we found that setting the learning rate be 0.001 leads to better average learning accuracy.
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We set the number of training epochs to be sufficiently large number such that the average learning accuracy doesn't improve as we increase the number epochs further. For all the baselines, we pick fixed number of training epochs such that all methods converge for each benchmark setting.
K-shot Linear Probing Training. The hyper-parameters the number of training epochs. For each k, we just set the batch size to be min(k c, 50) and do tune it. Note that K-shot linear probing is convex optimization problem. Thus, the number of training epochs will not affect the results across basclines as long as we train for sufficient number of epochs. We found that 100 epochs were more than sufficient for all the baselines to converge for K-shot linear probing. Also, the learning rate will not affect the results much as long we pick reasonable one. Therefore, we simply fix the learning rate to be 0.01.
the batch size, the learning and
B ADDITIONAL EXPERIMENTAL RESULTS
B. COMPARING FORGETTING AND FORWARD TRANSFER
In the main paper, give results for comparing forgetting and forward transfer on some bench- marks. In this section, we provide additional results for comparing forgetting and forward transfer on other benchmarks. shows the results where we use a pre-trained model. We can see that the claims made Section 3.2 still hold here.
Segure[]shows the results where use random initialization and Figure
B.2 EVALUATING AVERAGE ACCURACY AND AVERAGE LEARNING ACCURACY
In this section, we report results for traditional continual learning metrics Average Accuracy and Average Learning Accuracy. The Average Accuracy is defined as:
1 N
AvgAcc
Σ Acc(N,j)-
While the Average Learning Accuracy is defined as:
1
AvgLAce
Acc(j.))
The results reported in Table
B.3 ABLATION STUDY ON THE MODEL ARCHITECTURE
We want to see whether our claims about forgetting and forward transfer also hold when we use different architecture. Thus, on split CIFAR-10, split CIFAR-100, and CIFAR-100 Superclasses benchmarks, we also report results in Figure 7 for using ResNet18 as the model architecture. We only show results for using random initialization since we don't have pre-trained ResNet18 model on ImageNet. From the results, we can see that our claim that less forgetting a good inductive bias for forward transfer still holds.
B.4 CORRELATION BETWEEN AVERAGE FORGETTING AND AVERAGE FEATURE DIVERSITY SCORE
In order to aggregate the metrics across different approaches and to see global trend between forgetting and feature diversity, we compute the Spearman rank correlation between the AvgFçt and AvgFDiv. Table 4 shows the correlation values for randomly initialized models. From the results, we can see that for randomly initialized models, AvgFgt and AvgFDiv generally have positive correlations.
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CIFAR-100 Superclasses with Random, Init
CIFAR-100 Superclasses Random,
0.6
(mmb)
forgeting
04
HOTAML
Hished
-0.325
AGD4 br-d)
-0.15
01
200
CLEARIO with Random, init
CLEARIO with Random
0.06
0.6
Torgetting
FOMAUL
forward
05
0.03
T8 im-1100
0.62
0.4
05
0.00
30
100
Split ImageNet with Random Init
Split ImageNet Random__
Michus
ND
forward transfer
POMAML
04
0.
Viched
mm-1
En (m-000
NT
POMAVI
3.0
300
k
(a) Average Forgetting (f better)
(b) Average Forward Transfer (f better)
Figure 5: Comparing average forgetting with average forward transfer for different continual learning methods
using random initialization the CIFAR-100 Superclasses, CLEARI0 and Split ImageNNtt benchmarks.
B.5 FORWARD TRANSFER THROUGH K-SHOT FINE-TUNING
We also evaluate forward transfer through k-shot fine-tuning (i.e., we fine-tune the entire model including the feature extractor D and the classifier on the k-shot samples S The train- ing hyper-parameters
the same as those of k-shot linear probing, except that to avoid over- fitting while fine-tuning the whole network, we perform cross-validation for the learning rate and the number of training epochs using the validation set. The learning rate is chosen from the set (0.01, 0.001} while the number of training epochs is chosen from the set {10, 50, 100). When using random initialization, the results on the Split CIFAR-I0, Split CIFAR-100, and CIFAR-100 Superclasses benchmarks shown in Figure 8 while the results the CLEARIO, CLEAR100 and Split ImageNet benchmarks are shown in Figure 9 When using a pre-trained model as initial- ization, the results the Split CIFAR-10 Split CIFAR- CIFAR-100 Superclasses, CLEAR10 and CLEAR 100 benchmarks are shown Figure 10
In order to aggregate the metrics across different approaches and to global trend between for- getting and forward transfer, we compute the Spearman rank correlation between the AvgFgt and AvgFwt for the k-shot fine-tuning evaluation. Table shows the correlation values for different
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Cifah 120 Superdasses with Fre-7ah
FFA 120-100 Superclasees
CIPAR-1CO Superclames with Protrnn
-22
CLEARSC Fresrann
CLEARLO
CLEAKLE wIth Pre Dan
1.33
1.
CLEAR100 with Prenrai
0.03
(a) AvgE gt. ( better)
(b) AvgEwt" & (f better)
(c) Upstream Accuracy (f better)
Figure 6: Comparing average forgetting with average forward transfer for different continual learning meth- ods that train the model from pre-trained ImageNet model on the CIFAR-100 Superclasses, CLEAR and CLEAR100 benchmarks. We also show the accuracy of the models on the upsteam ImageNet data. Since CIFAR-100 images have different image resolution than that of ImageNet images, we need to resize the Ima- geNet test images from 224 224 to 32 x 32 order to get meaningful accuracy of the models trained on the CIFAR-100 Superclasses benchmark on the upstream ImageNet data. On CLEAR10 and CLEAR 100 bench- marks, since their images have the same image resolution as the ImageNet images, we don't 't need to resize the ImageNet test images when evaluating the upstream accuracy.
values of 'k' for both randomly initialized and pre-trained models. It can be seen from the table that most of the entries are above 0.5 and statistically significant (p < 0.01) showing that reducing forgetting improves the forward transfer across the board.
From the results, we can see that less forgetting generally leads to better forward transfer. Thus, our claim that less forgetting is good inductive bias for forward transfer still holds.
B.6 ABLATION STUDY ON THE REPLAY BUFFER SIZF
For the Experience Replay (ER) baseline, perform experiments the Split CIFAR- 100 and CIFAR- Superclasses benchmarks to study the effect of the replay buffer size on the AvgFgt and AvgFwt* metrics. The results when using random initialization are shown in Figure 11 while the results when using pre-trained model as initialization are shown in Figure 12 From the results, can see that increasing m usually leads to less forgetting and thus more forward transfer. Therefore, our claim that less forgetting is a good inductive bias for forward transfer still holds.
B.7 RESULTS FOR EWC AND VANILLA L2 REGULARIZATION
In this section, we provide some results for the EWC method (Kirkpatrick et al.] 2016) and the vanilla L2 regularization (a variant of EWC where the fisher information matrix is replaced with an identity matrix) using ResNet18 as the model architecture with random initialization on the Split CIFAR- 10 benchmark. For À in EWC, we consider the range {10, 50, 100, 200} and select the best one based on the performance on the validation data. For À vanilla L2 regularization, we con- sider the range (10, 1, 0.1, 0.01) and select the best one based the performance the validation
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Random Init
Pretrain
Dataset
Method
AvgAcc
AvgLAcc 91.38 1.44
AvgAce
AvgLAce
FT
62.69 5.24
67.56 14.62
95.75 1.02
LP-FT
92.64 + 1.15
95,46 0.13
Split
ER (m=50)
85.56 + 2,46
91.70 + 1.53
90.41 + 1.26
95.90 = 0.35
CIFAR-10
AGEM (m=50)
1..74:3.1.
91.59 1.14
80.22 5.51
95.88 = 1.09
MT
89.70 5.37
92.68 + 0.80
91.48 + 4.32
96.14 0.08
FOMAML
92.77 : 0.40
93.45 0.71
94.61 = 0.50
96.06 # 0.45
FT
57.47
81.31 = 0.93
67.96 1.90
89.64 0.79
LP-FT
85.33 0.59
90.27 0.32
Split
ER (m=20)
72.91 1.19
81.00 0.42
81.51 1.00
89.82 0.20
CIFAR-100
AGEM (m=20)
64.02
81.35
71.77 + 1.59
89.24 1.34
MT
73.90
82.15 0.366
82.74 5.11
90.33 0.38
FOMAML
79.79 +
82.36 + 0.57
85.36 + 1.13
89.63 1 0.64
56.76 0.94
68.92 0.78
70.25 + 0.78
81,53 0.38
LP-FT
78.88 + 0.47
81.22 + 0.53
CIFARI00
ER (m=5)
60.43 2.37
68.63 1.60
72.43 - 0.99
81.36 0.25
Superclasses
AGEM (m=5)
59.28 0.52
69.42 0.67
71.79 + 0.79
81.60 0.25
MT
68.43 3.50
69.54 1.37
77.28 3.19
81.77 0.18
FOMAML
71.48 + 1.82
69.86 2.00
80.11 + 0.45
81.03 +.03=00 0.26
FT
1.1880.4
1 10.19
93.64 + 0.48
93.87 0.21
LP-FT
95.27 0.05
94.70 0.11
ER (m=10)
+.63
71.16 0.24
94.12
CLEARIO
AGEM (m=10)
71.76 0.67
70.22 0.75
93.81 +
94.00 0.13
MT
77.68 + 0.68
73.69 + 0.54
95.04 + 0.64
94.53 0.26
FOMAML
78.51
74.41 0.47
95.16 + 0.22
94.63 0.24
FT
52.38
47.27 0.25
86.47 0.10
86.29
LP-FT
89.56 0.04
88.22 0.06
0.06
ER (m=5)
53.16
46.99
87.25 0.188
86.49 0.07 0.07
CLEAR100
AGEM (m=5)
52.35 0.25
47.25 0.41
86.56 0.16
86.26 +:266000 0.18
MT
59.58 + 1.56
50.94
89.56 0.12
87.96 0.13
0.13
FOMAML
00.99:0.5.
+.69
89.42 + 0.12
87.78 - 0.06
0.06
FT
0.54
0.41
ER (m= 10)
3.550
69.71 +
Split
AGEM (m=10)
16.82 1.30
71.71
0.47
ImageNet
MT
54.68 + 4.13
73.58 0.50
FOMAML
59.73 4.58
71.85 + 1.28
Table 3: Results average accuracy AvgAcc average learning accuracy AvgIAce. All numbers are
percentages.
Dataset
Spearman Correlation
Split CIFAR-10
0.33 (0. 10)
Split CIFAR-100
0.31 (0.13)
CIFAR 100 Superclasses
0.38 (0.06)
CLEARIO
0.46 (0.02)
CLEARION 100
0.80
Split ImageNet
0.81
Table 4: Spearman correlation between Avgl'gt and Avgi vi which computes the correlation over different settings (different training methods and random runs). Here, we random initialization the initial model. p-values shown parenthesis if greater than equal 0.01.
data. Experimenting with EWC on larger models and longer benchmarks is computationally very expensive. The comparison of EWC with FT and vanilla L2 regularization is given in Table 6 It can be seen from the table that less forgetting leads to better forward transfer. Thus, our claim that less forgetting good inductive bias for forward transfer still holds.
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Published as a conference paper at ICLR 2023
Split CIFAR-10 with Random, Init
Split CIFAR-10 10 with Random init
average forward transfer
AG2M Inmo2)
-0.10
0.75
-0.00
Hathod
-0.00
0.00
-0.55
-0 40
Split CIFAR-100 with Random_ init
Split Randem
8.00
Vethed
forward transter
(me23)
-1.
0.5
PONAPL
0.00
Victed
Di (m--20)
-45
NT
POMAPL
102
CIFAR-100 Superclasses with Random, Init
CIFAR-100 Superclasses with Random, init
Mathoe
05
NO
-0.55
ACES (mes) Ex Imws)
-025
10
23
300
k
(a) Average Forgetting (f better)
(b) Average Forward Transfer (f better)
Figure 7: Comparing average forgetting with average forward transfer for different continual learning methods using random initialization the Split CIFAR-10. 10, Split CIFAR- and CIFAR-I00 Superclasses benchmarks. Here, we use ResNet18 the model architecture.
C DISCUSSION
C.I RELATEDNESS OF TASKS AND OUR CONCLUSIONS
We note here that task relatedness bears significant effect on the relationship between forgetting and forward transfer. The benchmarks that we considered in this work either have very similar tasks (CLEAR10/100), where the same classes are observed over a 10 years period, or unrelated tasks (Split CIFAR10/100, ImageNet), where disjoint classes are observed in each task. In both cases, less forgetting improved the forward transfer, although for more similar tasks the improvement more significant as intuitively expected. We did not observe that "unrelatedness" of tasks leads to negative transfer. However, if tasks were negatively related to begin with then less forgetting would intuitively lead to negative transfer. But in experience negatively related tasks are very rare and in practical machine learning systems many tasks can learn from each other (which the basis of transfer learning, multitask learning, etc.). We would like to emphasize that the point of the paper is precisely to show that when tasks are somewhat related, and observed a continual setting, less forgetting improves forward transfer. It is in this setting that some of the previous
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Published as a conference paper at ICLR 2023
Split CIFAR-10 with Random, Init
Split CIFAR-10 10 with Random init
0.00
forward transfer
AG22 (nwwa))
-0.0
Hithod
06
.25
0.00
-0.00
Split CIFAR-100 with Random_ init
Split Init
0.75
Vethed
0.70
(mm23)
forgetting
0000
-0.00
average forward
PONAPL
8.60
-0.35
AGEM yn 201
2m-231
-030
102
CIFAR-100 Superclasses with Random, Init
CIFAR- 100 Superclasses with Random init
Methoel
0.6
(mme))
Torgeting
HOMAML
-0.075
-0.220
-0.225
AGD4 on-s1 0n-11
0.16
02
10
23
300
k
(a) Average Forgetting (t better)
(b) Average Forward Transfer (f better)
Figure 8: Comparing average forgetting with average forward transfer for different continual learning methods using random initialization the Split CIFAR-10. Split CIFAR- 100 and CIFAR-I00 Superclasses benchmarks. Here, we evaluate the forward transfer through k-shot fine-tuning.
works (Hadsell et al.) 2020 Wolczyk et al.) 2021 concluded that less forgetting does not improve end-to-end forward transfer. We show here that even on such tasks less forgetting improves the representational measure of forward transfer.
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Published as a conference paper at ICLR 2023
CLEAR10 with Random, jnit
CLEARIO Random,
0.06
forgettin
4GAM (2122)
forward
0.03
0.5
0.62
9.4
0.00
-0.01
10
300
k
CLEAR1OD with Random init
CLEAR100 with Random_ init
0.50
Hemss
ADLM (mwa]
0.45
3m-3)
0.05
AGaMi (row))
0.55
IT
0.20
Split ImageNet Random init
Split ImageNet with Random init
Mechos
average transfer
AGEN (n0w21)
average forgetting
-1.
im 100
-43
04
-14
0.3
Metted
1m2 mm-1m
-15
02
(a) Average Forgetting (f better)
(b) Average Forward Transfer (f better)
Figure 9: Comparing average forgetting with average forward transfer for different continual learning methods using random initialization on the CLEAR10, CLEAR100 and Split ImageNet benchmarks. Here, we evaluate the forward transfer through k-shot fine-tuning.
Random Init
Pretrain
Dataset
F=
k= 20
k=5
k 10
k 20
Split CIFAR-10
0.5
0.49
0.64
0.57
0.51
Split CIFAR-100
0.92
0.93
0.83
0.87
0.88
0.86
CIFAR 100 Superclasses
0.16 (0.40)
0.24 (0.20)
0.28 (0.14)
0.28 (3.
0.33 (0.07)
0.38 (0.04)
CLEAR10
0.68
(1.68
0.68
0.18 (0.34)
0.25 (0.18)
0.53
CLEAR100
0.6
0.59
0.61
0.87
0.87
0.83
Split ImageNet
0.86
0.81
0.83
Table 5: Spearman correlation hetween AvgFgt: AvtFwt. for different k which computes the corre- lation over different settings (different training methods and random runs). Here, Avg defined like AvgFwt* but instead of using k-shot linear probing for evaluation, we use k-shot fine-tuning evaluation (i.e., fine-tuning the entire model). p- valuues shown in parenthesis if greater than equal to 0.01.
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Published as a conference paper at ICLR 2023
Sp CPARRO WIth Tre-san
Sp CIARR-DD
Soltt OPAR-330 WRY Tre-tran
Sp C3AAR-30
Spllt OPA3-300 frar
ansrage
CFAT-100 Superdiaseo
CIR58: 160 Siperisoree with Pretisin
CLEARES With Fretran
CL FARLD
CLDARSS with The Man
2.00
C.EAR103
CLEAR103
EAR105 Fre-mih
B5--4
(a) AvgE gt ( better)
(b) AvgFwt (t better)
(c) Upstream Accuracy (f better)
Figure 10: Comparing average forgetting with average forward transfer for different continual learning meth- ods that train the model from a pre- pre-trained ImageNet model on the Split CIFAR- 10, Split CIFAR- 100, CIFAR- 100 Superclasses, CIEEAR and 100 benchmarks. We also show the accuracy of the models on the upsteam ImageNet data. Here, we evaluate the forward transfer through k-shot fine-tuning.
Method FT
AvgF 1
AvgFwt* * (k=10)
AvgFwt (k=20)
AvgFwt (k=100)
-32.06 1 4.27
71.57 1 1.87
74.89 1 2.72
79.14 + 2.06
Vanilla L2 Reg. 0.01)
-26.41 3.02
72.68 1 2.28
76.58 + 2.73
80.88 1.92
EWC (A = 100)
-21.99 + 3.51
74.27 + 2.09
77.00 + 2.03
81.98 0.93
Table 6: Results for EWC and Vanilla L2 Regularization using ResNet18 as the model architecture with random initialization on the Split CIFAR- 10 benchmark. À hyper- parampareetter that controls the regularization strength of EWC and Vanilla L2 Regularization. The numbers are percentages.
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Published as a conference paper at ICLR 2023
Split CIFAR-100 Random
Split CIFAR-100 100 with Random, Init
Pated
0.725
forward transfer
ER 18:m--330)
0.700
BR (mm-4000
62
8.935
6.530
8.400
-0.00
55.0m2001
55.00-103)
04.00-403)
CIFAR 100 Superclasses with Random, init
CIFAR-100 Superclasses with Random init
Michoe
Veehes
0.02
21.11m1001
F4 23]
0.55
0m--903)
forgetting
forward
-0.02
-0.66
(a) Average Forgetting (f better)
(b) Average Forward Transfer (f better)
Figure 11: Comparing average forgetting with average forward transfer for the ER method with different play buffer sizes using random initialization on Split CIFAR- CIFAR-100 Superclasses benchmarks.
Split CIFAR-100 with Pre-train
Splil CIFAR-100 with Pre-train
Methoe
0.00
transfer
(m--9)3)
..84
.0.68
average
Pattee
(n-150
14 (m-450)
CIFAR-100 Superclasses with Pre-train
CIFAR-100 Superclasses with Pre-train
0.70
00-29911
forgetting
62
-064
average
0.
5000=201
5k-0-1003
(4.0--403)
102
(a) Average Forgetting (f better)
(b) Average Forward Transfer (f better)
Figure 12: Comparing average forgetting with average forward transfer for the ER method with different replay buffer sizes that trains the model from pre-trained ImageNet model the Split CIFAR-100 and CIFAR-100 Superclasses benchmarks.
25


Reviews:
[{"review_id": "mhA1nAboj8", "reviewer": "Reviewer_CFvX", "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": "The paper demonstrates that mitigating catastrophic forgetting leads to more diverse features that improve the generalization performance on future classification tasks (as measured by learning a classifier on a few data points)\n\nIn continual learning literature, learning is often constrained to prevent forgetting on older data; additionally, the model is evaluated on new tasks at the same time it is trying to prevent forgetting on old information; the constraint on future leanring due to the old tasks can degrade the forward transfer performance. \n\nIn this paper, the authors propose to isolate the impact remembering old information from the forward transfer performance. They measure the forward trasnfer performance in a separate phase by learning a classifier on top of the fixed representations using a few data point, and evaluate the classifier on a held-out set. After the forward transfer performance is measured, the model is updated on the new task using one of the many continual learning methods. \n\nFinally, the authors show that the models that forget less have more diverse features based on a metric that they propose. ", "summary_of_the_review": "\n# Closing thoughts\nI am personally not convinved that the problem setting that the authors consider, separate tasks with task ids, is the meat of the continual learning problem. I also think that the compromise between remembering past information, and future learning is an important one, and we should design algorithms that can make the right compromise based on experience instead of designing a protocol that ignores the compromise. That said, I still think the paper would be useful for a small audience who do care about task incremental with task id settings. \n\nOnce the protocol for hyper-parameter selection is clear and is included, I'm happy to raise my score to an accept because I consider my primary role as to judge the scientific intregity of the work, and not to pass a judgement on the problem setting. \n\n# Update\nChanging score from 5 to 6. The authors have added details of hyper-parameter selection, and added a baseline that main claim in the paper more clear and stronger. I think the paper would be a useful addition to the conference. ", "strength_and_weaknesses": "# Strengths \nThe results in the paper are clear, and support the claims made by the authors---models that forget less demonstrate much better forward transfer performance as per the new definition of forward transfer. Additionally, the paper is clearly written, and all the terms are defined concisely.\n\nThe paper includes a reasonable set of baselines, and the empirical studies cover multiple benchmarks. They report results for randomly initialization networks, and pre-trained models. \n\nThe work has direct implication for the research in transfer learning, and demonstrate that foundation models that are trained to perform well on the base task trasnfer better.\n\n# Weaknesses\n\n1. If the main contribution of a paper is based on empirical results, it is crucial to fully specify the experimental protocol. The paper doesn't include details on how the hyper-parameters were selected for different methods; did the authors tune the hyper-parameters for each method individually? What were the range of hyper-parameters used for this tuning? Why is the base learning rate different for LP-FT and other methods? The experimental protocol must be fully specified in the paper or the appendix for the paper to be accepted. \n\n2. The primary contribution of the paper is the observation that foundation models that do well on the base task (can do all tasks well with little forgetting) are better at transferring than models that don't perform well on the base task (due to forgetting). The notion of continual learning is not the main emphasis of the paper. \n\n3. The compromise between remembering old information, and forward transfer is a crucial aspect of continual learning in my opinion and should not be ignored by designing an experimenl protocol that hides it. A continual learner system, in almost all cases, cannot divide experience in separate tasks, and learn a seperate predictor for each task. ", "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": "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": "c3M1_dei-s2", "reviewer": "Reviewer_2ozN", "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": "This paper presents an experimental analysis of catastrophic forgetting versus forward knowledge transfer when tasks are trained continually. The hypothesis posed by the paper is that, contrary to previous findings in the literature, forward transfer does not necessarily imply more forgetting or vice-versa. The authors propose a reformulation of the forward transfer method, which relies on 'linear probing', i.e. training a simple linear classifier on top of a network trained on previous tasks, and testing this simple classifier on the target task test data. The authors also measure feature diversity as a measure of transferability of representations. In the experiments, the authors test their ideas in five benchmark datasets and compare their results to baselines such as finetuning, multitask learning, example-replay methods and metalearning methods. The authors find that less forgetful representations (features) tend to transfer better to new tasks, and these are also more diverse. ", "summary_of_the_review": "The good aspect that I find in this paper is the research question being examined. I think that papers like this, which are focused on examining fundamental/conceptual questions in the area, are certainly required for its progress. On the other hand, I do not find the findings of the paper 100% convincing, and I find the conclusions too broad compared to the extent of the experiments. Although I appreciate the experimental results, I would be convinced if at least one of the following was addressed (or ideally the two of them): 1) more insights into how task relatedness would affect forgetting and transfer (see one of the items I listed as 'weaknesses'); 2) a theoretical analysis supporting the experimental findings. For these reasons, and although I appreciate the effort of the paper on examining important fundamental questions in continual learning, in this first review phase I consider it marginally below the threshold of acceptance. ", "strength_and_weaknesses": "Strengths: \n- The paper tackles a very important question of whether more (or less) catastrophic forgetting is necessarily associated to more (or less) forward transfer. \n- The paper is clearly written, well aligned with literature in the area and easy to follow.\n\nWeaknesses: \n- The first main weakness that I find in this paper is in the experiments, in particular the testing of linear probing versus other methods. On page 5, architecture and training details, you mention that baseline models are trained for 50 and 100 epochs when training from scratch, depending on the dataset, and for 20 epochs only when trained from a pre-trained model. When using k-shot linear probing, you train for 100 epochs in all cases. How can you justify that this difference in training iterations is not biasing your results (in this case favouring k-shot linear probing)? \n- Although from the experimental results I agree with the statements that \"when continual learning experience begins from a randomly initialized model, retaining the knowledge of the past tasks or forgetting less on those tasks is a good inductive bias for forward transfer\" and a similar statement for pre-trained models later in the text, I think that these statements are missing a very important aspect: relatedness of tasks. Intuitively, if tasks are not related at all then not forgetting may not influence transfer at all, since only negative transfer will occur to unrelated tasks, or even more forgetting will be beneficial, depending on how much the 'direction' of forgetting is towards the new task; if tasks are related, then not forgetting will be certainly beneficial. In your experimental framework, how is task relatedness considered?", "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": "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": "aNfZ0qoYWae", "reviewer": "Reviewer_gCd6", "summary": "", "questions": "", "limitations": "", "rating": 8, "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 paper empirically revisits a previous hypothesis/belief from the continual learning (CL) literature, that catastrophic forgetting is not the only important quantity in CL, and that often CL methods that mitigate forgetting can harm the \"forward transfer\" between tasks.\n\nThe paper offers a new notion of transferability, by proposing an alternative evaluation method: after training a task, one *freezes* the representation learned so far, and uses it for training a $k$-shot linear probing model on the *next* consecutive task.\n\nUsing this alternative evaluation method, the authors experimentally show a positive correlation between low-forgetting and high-transferability, when comparing several different continual/multitask-learning algorithms. Finally, lower forgetting is shown to be somewhat correlated to more diverse representations.", "summary_of_the_review": "The research question is important and interesting. However, it calls for a better motivation and a better comparison to existing work.  \nThe experiments *do* show interesting phenomena, but the methodology lacks some important aspects like I wrote above.", "strength_and_weaknesses": "# Strengths\n1. **Importance of the research question.** The area of continual learning (CL) is rapidly growing and many *heuristic* methods are proposed to mitigate forgetting and solve continual settings. Thus, I find it important to understand the interplay between different quantities of interest, and specifically, between the forgetting and the forward transfer.  \nThe paper challenges common definitions in CL and proposes a new perspective on transferability, yielding interesting results.\n\n---\n\n# Weaknesses\n\n1. **Proposed transferability notion - Motivation, comparison to existing literature and discussion.**\n     While I agree that the proposed evaluation method (using linear probing while fixing the learned representations) makes sense and is *indeed* interesting, I would expect a clearer motivation to be given for it than the one in page 4. There is also place for more discussion.  \n     Why should one prefer this notion of transferability over the one proposed in [Wolczyk et al. 2021]? Why is an auxiliary-linear-probing even interesting when continual learning algorithms are expected to yield a *single* model?  \n     Moreover, [Wolczyk et al. 2021] showed that common CL algorithms do not help to (their definition of) forward transfer, and the \"preserved\" knowledge does not help learning future tasks, either faster (their Figure 3) or better (their Figure 4). In that case, how come these algorithms help linear probing (as seen in the new paper's experiments)? This is a little surprising for me.  \n\n1. **Experimental methodology.**\n\n     1. **Some important CL approaches were not tested.** Specifically, no regularization method (e.g., EWC) or parameter-isolation method (e.g., PackNet) were used. I believe these are more important in the paper's context than meta-learning or multitask approaches (FOMAML and MT).\n\n     1. **It is important to report the average accuracy as well.** The average forgetting and forward transfer cannot tell the whole story.\n\n     1. **There are more immediate/natural experiments to conduct.**\n     The main statement (Section 3.2) is more comparative in nature (i.e., \"less forgetful representations transfer better\") than the one in Wolczyk et al., 2021 (i.e., popular CL methods mitigate forgetting but do not contribute to transferability).  \n     That being said, I feel like comparing *different* CL methods, like done here, can be methodologically problematic (e.g., perhaps LP-FT simply yields better representations that are better for *any* cause, forgetting and transferability included).  \n     The existing experiments *are* interesting, but I believe simpler experiments could be more convincing: Fix the CL method (e.g., rehearsal/regularization), but test the influence of its main hyperparameter (e.g., buffer-size/regularization-strength, respectively) on forgetting and forward transfer.\n\n     1. **Statistical significance of results.** Even though the authors plot the error-bars according to *one* standard deviation (if I am not mistaken), the results for CIFAR-10 are often not statistically significant (see figures 1 and 3). In contrast, for CIFAR-100 the reported results are more siginificant. Consider performing additional repetitions.", "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": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "6mkMbPIcBi", "reviewer": "Reviewer_pY2z", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "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 proposes a new way of measuring forward transfer. They define forward transfer as how easy it is to learn a new task given a set of representations produced by continual learning on previous tasks. And they are looking for an answer to the question of \"whether less forgetful representations are more transferable?\" And the results show that less forgetful representations lead to a better forward transfer.", "summary_of_the_review": "The motivation and the research question of the paper is significant and interesting for the community. If the paper is clearly written and explains the differences/similarities with existing approaches more clearly, it could be a much stronger paper. \n\nUpdate:\nAfter checking other reviews, responses, and the revised version, I change my score to 6. The motivation is more clear now. But I still share the concern of Reviewer 2ozN that the conclusions are too broad compared to the extent of the experiments.", "strength_and_weaknesses": "Strength:\n- I think the motivation of the paper and the question they try to answer is quite significant for continual learning. Studying the relation between the forgetting and the forward transfer is one of the key aspects of continual learning.\n\nWeaknesses:\n- I think the paper lacks motivation that why the proposed definition is better than the existing transferability notions. \n- In my opinion, the paper should be written more clearly. The findings do not contradict to the previous findings but it is written in a way that they contradict. I think that is confusing for the readers. ", "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": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Accept: poster