AFEC: Active Forgetting of Negative Transfer in Continual Learning
Authors: Liyuan Wang
Mingtian Zhang
Zhongfan Jia
Qian Li
Chenglong Bao
Kaisheng Ma
Jun Zhu
Yi Zhong
Venue: NeurIPS 2021 Poster (2021)
Keywords: bio-inspired learning
continual learning
neuroscience
memory
forgetting

Abstract: Continual learning aims to learn a sequence of tasks from dynamic data distributions. Without accessing to the old training samples, knowledge transfer from the old tasks to each new task is difficult to determine, which might be either positive or negative. If the old knowledge interferes with the learning of a new task, i.e., the forward knowledge transfer is negative, then precisely remembering the old tasks will further aggravate the interference, thus decreasing the performance of continual learning. By contrast, biological neural networks can actively forget the old knowledge that conflicts with the learning of a new experience, through regulating the learning-triggered synaptic expansion and synaptic convergence. Inspired by the biological active forgetting, we propose to actively forget the old knowledge that limits the learning of new tasks to benefit continual learning. Under the framework of Bayesian continual learning, we develop a novel approach named Active Forgetting with synaptic Expansion-Convergence (AFEC). Our method dynamically expands parameters to learn each new task and then selectively combines them, which is formally consistent with the underlying mechanism of biological active forgetting. We extensively evaluate AFEC on a variety of continual learning benchmarks, including CIFAR-10 regression tasks, visual classification tasks and Atari reinforcement tasks, where AFEC effectively improves the learning of new tasks and achieves the state-of-the-art performance in a plug-and-play way. 

AFEC: Active Forgetting of Negative Transfer in Continual Learning
Liyuan Wang 1.23
Mingtian Zhang*
Zhongfan Jia
Qian Li
Kaisheng Ma²
Chenglong Bao
Jun 3
Yi Zhong 122*
School of Life Sciences, IDG/McGovern Institute for Brain Research, Tsinghua University. Pekkggg Center for Life Sciences. DDept. Comp. Sci. Tech., Institute for AI, BNRist Center, THBI Lab, Tsinghua University. *AI Center, University College London. 'III. Tsinghua University. Yaau Mathematical Sciences Center, Tsinghua University. [wly19,
tsinghua edu. cn, mingtian zhang. 17@ucl ac. {ligian8, kaisheng, clbao, deszj, wetiggyiithutttssnnggg edu, cn
Abstract
Continual learning aims learn sequence of tasks from dynamic data distribu- tions. Without accessing to the old training samples, knowledge transfer from the old tasks to each new task is difficult to determine, which might be either positive or negative. the old knowledge interferes with the learning the forward knowledge transfer is negative, then precisely remembering the old tasks will further aggravate the interference, thus decreasing the performance continual learning. By contrast, biological neural networks the old knowledge that conflicts with the learning of a new experience, through regulating the learning-triggered synaptic expansion and synaptic convergence. Inspired by the biological active forgetting, we propose to actively forget the old knowledge that limits the learning of new tasks to benefit continual learning. Under the framework of Bayesian continual learning, we develop a novel approach named Active Forgetting with synaptic Oopansion-Convergene namically expands parameters to learn each new task and then selectively combines them, which is formally consistent with the underlying mechanism of biological active forgetting. We extensively evaluate AFEC on variety of continual learning benchmarks, including CIFAR-10 regression tasks, visual classification tasks and Atari reinforcement tasks, where AFEC effectively improves the learning of new tasks and achieves the state-of-the-ae performance alug-and-plan way.
new task, i.e.,
actively forget
(AFEC). Our method dy-
Introduction
The ability to continually learn numerous tasks from dynamic data distributions is critical for deep neural networks, which needs to remember the old tasks by avoiding catastrophic forgetting [18] while effectively learn each new task by improving forward knowledge transfer [17. Due to the dynamic data distributions, forward knowledge transfer might be either positive or negative, and is difficult to determine without accessing to the old training samples. If the forward knowledge transfer negative, i.e., learning new task from the old knowledge is worse than learning the new task on randomly-initiaizze network
Bo I7 then precisely remembering the old tasks will severely interfere with the learning of the new task, thus decreasing the performance of continual learning.
"Corespooning author: Zhu and Y. Zhong.
35th Conference on Neural Information Processing Systems (NcurIPS 2021).

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By contrast, biological neural networks can effectively learn a new experience on the basis of re- membering the old experiences, even if they conflict with each other [8] 5. This advantage, called memory flexibility, is achieved by active forgetling of the old knowledge that interferes with the The latest data suggested that the underlying mechanism of synaptic expansion and synaptic con- vergence (Fig. I see Appendix A for neuroscience background and our biological data). Specifically, the biological synapses expand additional functional connections to learn new experience together with the previously-leaned functional connections (synaptic expansion). Then, all the functional connections pruned to the amount before learning (synaptic convergence).
learning of new experience 29 5
biological active forgetting is to regulate the
Inspired by the biological active forgetting, we propose to actively forget the old knowledge that in- terferes with the learning of new tasks without significantly increas- ing catastrophic forgetting, so
Silent Connection
Functional Connection
Task
as to benefit continual learning. Specifically, we adopt Bayesian continual learning and actively forget the posterior distribution that absorbs all the information of the old tasks with forgetting factor to better learn each new task. Then, we derive a novel method named Active Forgetting (AFEC), which is formally consistent with the underlying mechanism of biological active forgetting at synaptic structures. Beyond regular weight regularization
Task
Expansion
Convergence
Figure I: The biological active forgetting is achieved by regulat- ing the leamnin--triggered synaptic
with synaptic
approaches [12 II 35 21, which selectively penalize changes of the important parameters for the
old tasks, AFEC dynamically expands parameters only for each new task to avoid potential negative transfer from the main network, while the forgetting factor regulates penalty to selectively merge the main network parameters with the expanded parameters, so as to learn a better overall representation of both the old tasks and the new task.
We extensively evaluate AFEC on continual learning of CIFAR-10 regression tasks, a variety of visual classification tasks, and Atari reinforcement tasks (10). where AFEC achieves the state-of-the- art (SOTA) performance. We empirically validate that the performance improvement results from effectively improving the learning of new tasks without increasing catastrophic forgetting. Further, AFEC can be a plug-and-play method that significantly boosts the performance of representative continual learning strategies, such as weight regularization
55
and memory replay 21 J 3
Our contributions include: (1) We draw inspirations from the biological active forgetting and propose novel approach to actively forget the old knowledge that interferes with the learning of new tasks for continual learning; (2) Extensive evaluation on a variety of continual learning benchmarks shows that our method effectively improves the learning of new tasks and achieves the SOTA performance in plug-and-play way: and (3) To the best of our knowledge, we are the first to model the biological active forgetting and its underlying mechanism at synaptic structures, which suggests potential theoretical explanation of how the underlying mechanism of biological active forgetting achieves its function of forgetting the past and continually learning confficting experiences 20
2
Related Work
Continual lcarning needs to minimize catastrophic forgetting and maximize forward knowledge transfer. Existing work in continual learning mainly focuses on mitigating catastrophic forgetting. 2 which selectively penalizes
Representative approaches include: weight regularization [12 M1 33
which allocates ded- which approximates and recovers the old data distributions through storing old training data, their embedding or learning a generative model. In particular, Adaptive Group Sparsity based Continual Learning (AGS-CL) [00] proposed to regularize the group sparsity with separation of the important nodes for the old tasks to prevent catastrophic forgetting, which takes advantages of weight regularization and parameter isolation, and achieved the SOTA performance on various continual learning benchmarks.
changes of the previously-eeamed parameters; parameter isolation
24
10
icated parameter subspace for each task; and memory replay 21
28

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Several studies suggested that forward knowledge transfer is critical for continual learning [17 4. which might be either positive or negative due to the dynamic data distributions. Although it is highly nontrivial to mitigate potential negative transfer while overcoming catastrophic forgetting. the efforts that specifically consider this challenging issue are limited. [3] developed method to mitigate negative transfer when fine-tuning tasks on a pretrained network. For the scenario where the old tasks can be learned again, 26 learned an additional active column to better exploit potential positive transfer. [2 tried to maximize transfer and minimize interference from memory buffer containing a few old training data. Similarly, 6 16 33 attempted to more effectively balance stability and plasticity with the memory buffer in class incremental learning, while 32 stored and updated the old features. By contrast, since pretraining or old training data might not be available in continual learning, mainly focus more restrict yet realistic setting that neural network incrementally learns a sequence of tasks from scratch, without storing old training data. Further, we extend our method the scenarios where pretraining or memory buffer can be used, as well as the scenarios other than classification tasks, such as regression tasks and reinforcement tasks.
3 Method
In this section, we first describe the framework of Bayesian continual learning [2] 20) Under such framework, we propose an active forgetting strategy, which is formally consistent with the underling mechanism of biological active forgetting at synaptic structures.
3.1 Basics of Bayesian Continual Learning
Continual learning needs to remember the old tasks and learn each new task effectively, Let's consider a simple case that a neural network with parameter A continually learns two independent tasks, task A and task B, from their training datasets Dtrain and Dirain 12]
The training dataset of each task
is only available when learning the task.
Bayesian Learning: After learning Dirain the posterior distribution
p( D pl DD (0)p(0)
((Dirain)
incorporates the knowledge of task A. Then, we can get the predictive distribution for the test data of task A:
p p(D Dirain= /
)d0.
As the posterior p(0) Dirain) is generally intractable (except very special cases), we must resort to approximation methods, such as the Laplace approximation [12] other approaches of approximate inference [20]. Let's take Laplace approximation as an example. If p(9 D is smooth and majorly peaked around the mode 0% arg max; log p(0) ( we can approximate it with Gaussian distribution whose mean is 0% and covariance is the inverse Hessian of the negative log posterior (detailed in Appendix B.
Bayesian Continual Learning: Next, we want to incorporate the new task into the posterior, which uses the posterior p(0) ( the prior of the next task [2]
p( O) p(0)D
p(0) D
(1)
D(Draan))
Then we can test the performance of continual learning by evaluating
Diest D Dirain D p(D'ret D 10p(0 D Dirain)
Similarly, p00 D'rain, Digain) can be approximated by a Gaussian using Laplace approximation whose mean is the mode of the posterior:
0%
B A
arg max log p(0) Dirrain .Dirain)
(3)
= arg max log pl (D (0) + log p(0 p( - log p( D(D
trein
(4)
const.
3

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This MAP estimation is also known as the Elastic Weight Consolidation (EWC) 12
A PA. Er...00 0A,))² 2
LEwc (0) = Ln())
(S)
where LB( is the loss for task B and is the label of each parameter. FA is the Fisher Information matrix (FIM) of 0*, Dirain (the computation is detailed in Appendix B.1), which indicates the "importance" of parameter for task A. The hyperparameter À explicitly controls the penalty that selectively merges each 0g to x, to alleviate catastrophic forgetting.
3.2 Active Forgetting with Synaptic
However, if precisely remembering task A interferes with the learning of task B, e.g., task A and task B are too different, it might be useful to actively forget the original data, similar to the biological strategy of active forgetting. Based on this inspiration, we introduce a forgetting factor / and replace p( that absorbs all the information of D'rain with a weighted product distribution S 19
Pmn (6) Dirain 3) p(0) D (1-0)m()1))))))))
(6)
Z
where we use m to denote that we are 'mixing' p(0) and p(0) to produce the new distribution Pm- Z the normalizer that depends on B, which keeps pm [ .3) following Gaussian distribution if p(0) Di and p(0) are both Gaussian (detailed in Appendix B.2). When 3 0, Pm will be dominated by p( and remember all the information about task A. When / 1, Pm will actively forget all the information about task A. Modified from Eqn. our target becomes:
p( D'att Digat Dirain D' ,3) = p(D' D 10)p(0) (
Dirain Digui ,3)00.
We first need to determine 3, which decides how much information from task A is forgotten to maximize the probability of learning task B well. good 3 should be as follows:
arg max D( Darain .3) = arg max / 3
p(D Pm) Dirain ,)d0.
(8)
B
Since the integral is difficult to solve, we can make grid search to determine B, which should be between 0 and 1. Next, p(0) Dtrain, Dirain, () also be approximated by Gaussian using Laplace approximation (the proof detailed in Appendix B.3), and the MAP estimation is
AA arg max log p(0)D raain Drusn .3)
(9)
arg max (1 - B) (log p p(D log p(0)D"r"i)) + log p(0l + const..
Then we obtain the loss function of Active Forgetting with synaptic Expansion-Convergencc (AFEC):
A Σ FA. 02,)²² Σ
de Σ Pe,(0.-00..) 022)²²
LAFRe
(0) (o) 2
(10)
0 are the optimal parameters for the new task and Fe is the FIM of 0: (the computation is detailed in Appendix B) As shown in Fig, 2 we first learn set of expanded parameters O. with LB (0.) to obtain 0 and Fe. Then we can optimize Eqn. (CO), where two weight-merging regularizers selectively merge 8, with 8h for the old tasks and 8%, for the new task. The forgetting factor is integrated into hyperparameter X & B/(1 B) to control the penalty that promotes active forgetting. Therefore, derived from active forgetting of the original posterior in Eqn. C we obtain an algorithm that dynamically expands parameters learn new task and then selectively converges the expanded parameters to the main network. Intriguingly, this algorithm is formally consistent with the underlying mechanism of biological active forgetting (the neuroscience evidence is detailed in Appendix A), which also expands additional functional connections for a new experience (synaptic expansion) and then prunes them to the amount before learning (synaptic convergence).

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As the proposed active forgetting is in- tegrated into the third term, our method can be used in plug-and-play way to im- prove continual learning (detailed in Ap- pendix E, F). Here we use Laplace ap- proximation to approximate the intractable posteriors, which can be other strategies of approximate inference [20] further work. Note that 0r and Fe not stored in continual learning, and the architecture of the main network is fixed. Thus, AFEC does not cause additional storage cost com- pared with regular weight regularization ap- proaches such as [12 35 I 2). Further, it straightforward continual learning of more than two tasks. We discuss it in Appendix B.4 with pseu- docode.
Task
Task
F.F.i.
EWC
0:
Oi
AFEC (ours)
F.F.A
heFei
0:
extend our method
0
Oe:
Now conceptually analyze how AFEC mitigates potential negative transfer in con- tinual learning (see Fig. 2) When learn- ing task B on the basis of task A, regular weight regularization approaches 2 35
Figure Conceptual comparison of EWC and AFEC (ours). ① Synaptic Expansion: Learn the expanded pa- rameters 0g with LB (f.) to obtain 0 and F.. @ Synap- tic Convergence: Learn the main network parameters O with Eqn. (10) for selective weight-merging.
1 selectively penalize changes of the old parameters learned for task A, which will severely interfere with the learning of task B if they conflict with each other. In contrast, AFEC learns set of expanded parameters only for task B to avoid potential negative transfer from task A. Then, the main network parameters selectively merge with both the old parameters and the expanded parameters, depending on their contributions to the overall representations of task and task B.
Experiment
In this section, we evaluate AFEC on a variety of continual learning benchmarks, including: CIFAR- 10 regression tasks, which is toy experiment to validate our idea about negative transfer in continual learning; visual classification tasks, where the forward knowledge transfer might be either positive or negative; and Atari reinforcement tasks, where the forward knowledge transfer is severely negative. All the experiments are averaged by runs with different random seeds and task orders.
4.1 CIFAR-10 Regression Tasks
First, we propose CIFAR-10 regression tasks to explicitly show how negative transfer affects continual learning, and how AFEC effectively addresses this chal- lenging issue. CIFAR-IO dataset [K] con- tains 50,000 training samples and 10,000 testing samples of 10-class colored im- ages of size 32 32. The regression task to evenly map the ten classes around the origin of the two-dimensional coordinates and train the neural network to predict the angle of the origin each class (see Fig.
Task A
Task B
Transfer
180
Figure CIFAR-10 10 regression tasks. Each circle rep- resents the position of class. Task A and Task B use different relative positions. "Transfer" applics the same relative position as Task A. but rotates by several phases.
B.. We change the relative position of the classes to construct different regres- sion tasks with mutual negative transfer, in which remembering the old knowledge will severely interfere with the learning of a new task.
5

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40
Task A
52
Task B
48
Average
Fine-tuning (FT)
Averaged Accuracy (%)
Averaged Accuracy (%)
Averaged Accuracy (%)
MAS (e=1e-4)
30
48
42
MAS (A=1e-2)
MAS (A=1)
20
44
36
EWC (A=1)
EWC (A=1e2)
EWC (A=1e4)
24
AFEC (A=1e4)
EWC AFEC
EWC
MAS
AFEC
Figure 4: Continual learning of two CIFAR-10 regression tasks with two-layer LeNet architecture. Larger strength of weight regularization can better remember the old task but limits the learning of the new task. AFEC can more effectively learn new task while remembering the old task.
As shown Fig. for continual learning of two different regression tasks, regular weight regulariza- tion approaches, such as MAS I1 and EWC [12], can effectively remember the old tasks, but lim- its the learning of new tasks. In particular, larger strength of the weight reg- ularization results in bet- ter performance of the
Table 1: Continual learning of CIFAR-10 regression tasks with various architectures. We present the averaged accuracy (%) of five runs for two- task and ten-task, and five runs of five rotations for transfer experiment.
Methods
LeNer
15
VGGTT
M
VGGLTB 20
ResNer10 7
Fine-tuning
29.23
20.72
46,37 s0.11
46.54 20.20
60.67 e1.52
Two-Task
11:36
30.3
AFBC (ours)
44.45 12.0
77.76 s0.00
86.07 20.24
75.67 11.19
Fine-tuning
46.57 2a.s
18.03 20.00
18.08 2004
54.97 21:1
Ten:
[2
49,95 #1.01
79.39 #1.12
82.91 =0-21
AFEC (ours)
$3.50
82,50
88.31 20.31
85,33 20:31
Fine-tuning
38.93
80.37
84.30
85.69
Transfer
FWC 12
35.87 20:07
76.66 20.4
82.25 20:1
84, 96 20:0
AFEC (ours)
40.90
83.81
86.30
87.80
first task but worse performance of the second task. In contrast, AFEC improves the learning of new tasks on the basis of remembering the old tasks, so as to achieve better averaged accuracy. Note that EWC is equal to the ablation of active forgetting in AFEC, i.e., O, so the performance improvement of AFEC on EWC validates the effectiveness of our proposal. We further demonstrate the efficacy AFEC on variety of architectures and larger amount of tasks (see Table D]
In addition, we evaluate the ability of transfer learning after continual learning of two different regression tasks. We fix the feature extractor of the neural network and only fine-tune a linear classifier to predict a new task that is similar to the first task. Specifically, the similar task applies the same relative position as the first task, but rotates by 60%, 120", 180", 240" 300 Therefore, if the neural network effectively remembers and transfers the relative position learned in the first task, it will be able learn the similar task well. As shown Table [ AFEC can more effectively learn the similar task, while EWC is even worse than sequentially fine-tuning without weight regularization.
4.2 Visual Classification Tasks
Dataset: We evaluate continual learning on a variety benchmark datasets for visual classification, including CIFAR-100, CUB-200-201 and ImageNet- 100. CIFAR-100 [3] contains 100-class colored images of the size 32 x 32, where each class includes 500 training samples and 100 testing samples. CUB-200-201
3 is large-scale dataset including 200 classes and 11,788 colored
images of birds, split as 30 images per class for training while the rest for testing. ImageNet- [ subset of MILSVRC-2011 [23] consisting of randomly selected 100 classes of images and 1300 samples per class. We follow the regular preprocessing pipeline CUB-20000 BUUB-20-200 200-2011 and ImageNet- 100 as 10,, which randomly resizes and crops the images the size of 224 x 224 before experiment.
We consider five representative benchmarks of visual classification tasks evaluate continual learning in different aspects. The first three are on CIFAR- 100, with forward knowledge transfer from more negative more positive (detailed in Fig. 5p while the second two are on large- scale images. (1) CIFAR- 100-SC 34]: CIFAR-100 can be split as 20 superclasses (SC) with 5 classes per superclass dependent on semantic similarity, where each superclass is classification task. Since the superclasses semantically different, forward knowledge transfer in such task sequence is
Benchmark:

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Table 2: Averaged accuracy (%) of all the tasks learned so far in continual learning of visual classification tasks, averaged by 5 different random seeds (see Appendix C for error bar). *AFEC is our method described in Sec. 3.2, while w/ AFEC is the adaptation of our method to representative weight regularization methods (detailed in Appendix E).
CIFAR-100-SC
CIFAR-100
CIFAR-101100
CUB-200 w/ PT
CUB-200 w/o PT
ImageNet- 100
Methods
A1o
An
A1o
Ago
A2
A2+20
As
A1o
As
Au
As
A1u
Fine-tuning
32.58
28.40
40.92
33.53
78.96
37.81
78.75
78.13
31.91
39.82
50.56
44.80
P&C
26
53,48
52.88
70.10
70.21
86.72
78.29
81.42
81.74
33.88
42.79
76.44
74.38
AGS CI. 10
55.19
53.19
71.24
69.99
86.27
80.42
82.30
81.84
32.69
40.73
51.48
47.20
FWC 12
52.25
51.74
68.72
69.18
85.07
77.75
81.37
80.92
32,90
42.29
76.12
73.82
*AFEC (ours)
56.28
55.24
72.36
72.29
86.87
81.25
83.65
82,04
34,36
43.05
77.64
75.46
MAS M
52.76
52.18
67.60
69.41
84.97
77.39
79.98
79.67
31.68
42.56
75.48
74.72
w/ AFEC (ours)
55.26
54.89
69.57
71.20
86.21
80.01
82.77
81,31
34.08
42.93
75.64
75.66
SI [51
52.20
51.97
68.72
69.21
85.00
76.69
80.14
80.21
33.08
42.03
73.52
72.97
w/ AFEC (ours)
55.25
53.90
69.34
70.13
85.71
78.49
83.06
81.88
34.04
43.20
75.72
74.14
RWALK 2
50,51
49.62
66.02
66.
85.59
73.64
80.81
80.58
32.56
41.94
73.24
73.22
w/ AFEC (ours)
52.62
51.76
68.50
69.12
86.12
77.16
83.24
81.95
33.35
42.95
74.64
73.86
relatively more negative. (2) CIFAR-100 [1 The 100 classes in CIFAR-100 100 are randomly split as 20 classification tasks with 5 classes per task. (3) CIFAR- randomly split as 2 classification tasks with 5 classes per task, followed by 20 tasks with 5 classes per task randomly split from CIFAR-100. This benchmark is adapted from ICC to keep the number of classes per task the same as benchmark (1, 2), where the large amounts of training data in the first two CIFAR-10 10 tasks bring a relatively more positive transfer. (4) CUB-200 [[]: The 200 classes in CUB-200-201 are randomly split as 10 classification tasks with 20 classes per task. (5) ImageNet- 21:: The 100 classes in ImageNet- 100 are randomly split as 10 classification tasks with 10 classes per task.
10] : The 10-class CIFAR-10 are
Architecture: We follow I0 to use CNN architecture with 6 convolution layers and 2 fully connected layers for benchmark (1, 2, 3), and AlexNet [44] for benchmark (4, 5). Since continual learning needs to quickly learn usable model from incrementally collected data, mainly consider learning the network from scratch. Following [10), we also try AlexNet with ImageNet pretraining for CUB-200.
First, we consider a restrict yet realistic setting of continual learning without access to the old training data, and perform multi-head evaluation (2). Since AFEC is weight regularization approach, we mainly compare with representative approaches that follow a similar idea, such as EWC [121, MAS [I] SI 35 and RWALK [2]. We also compare with AGS-CL CL I0, the SOTA method that takes advantage of weight regularization and parameter isolation, and P&C 26). which learns an additional active column on the basis of EWC to improve forward knowledge transfer. We reproduce the results of all the baselines from the officially released code of [10] where we do an extensive hyperparameter search and report the best performance for fair comparison (detailed in Appendix C). Then, we relax the restriction of using old training data and plug AFEC in representative memory replay approaches, where we perform single-head evaluation [2] (detailed in Appendix F).
Baseline:
Averaged Accuracy: In Table 2 we summarize the averaged accuracy of all the tasks learned so far during continual learning of visual classification tasks. AFEC achieves the best performance on all the continual learning benchmarks and is much better than EWC [[2]. i.c., the ablation of active forgetting in AFEC. In particular, AGS-CL [0 is the SOTA method relatively small-scale images and on CUB-200 with ImageNet pretraining (CUB-200 w/ PT). While, AFEC achieves a better performance than AGS-CL on small-scale images from scratch and CUB-200 w/ PT, and substantially outperforms AGS-CL on the two benchmarks of large-scale images from scratch. Further, since regular weight regularization approaches generally in re-weighted weight decay form, AFEC can be easily adapted to such approaches (the adaptation is detailed in Appendix E) and effectively boost their performance the benchmarks above.
Knowledge Transfer: Next, we evaluate knowledge transfer the three continual learning bench- marks developed on CIFAR-100 in Fig. 5 We first present the accuracy of learning each new task
7

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70-
CIFAR-100-SC
85
CIFAR-100
85-
CIFAR-10/100
New Accuracy (M)
AFEC
New Task Accuracy
68
New Accuracy
80-
90-
EWC
60-
75-
05-
MAS
SI
65-
70-
60-
RWALK
AGS-CL
50-
P&C
20
15
Number of Taskk
Number Tasks
Number Thnkks
(b)
CIFAR-100-SC
CIFAR-100
CIFAR-10/100
AFEC
FWT (%)
-2-
EWC
8-
FWT
-4-
FWT
SI
RWALK
-12-
-
AFEC
EWC
MAS
RWALK
St
AGS-CL
P&C
AFEC
EWC
MAS
RWALK
Sl
AGS-CL
P&C
AFEC
EWC
MAS
RWALK
S1
AGS-CL
P&C
AGS-CL
P&C
(c)
CIFAR-100-SC
CIFAR-100
CIFAR-10/100
AFEC
BWT (%)
2
BWT (%)
EWC
4
MAS
BWT
8
SI
RWALK
8
APEC
EWC
MAS
RWALK
Si
AGS-CL
PBC
AFEC
EWC
MAS
RWALK
Bi
AGS-CL
PBC
AFEC
EWC
MAS
RWALK AGS-CL.
Si
P&C
AGS-CL
P&C
Figure 5: Knowledge transfer in continual learning. (a) The accuracy of learning each new task in
continual learning. (b) Forward Transfer (FWT), which is from more negative more positive on
CIFAR-100-SCC CIFAR-101 and CIFAR-10/100. (c) Backward Transfer (BWT).
fruit vegetables
large carnivores
small mammals
househood furniture
vehicle
Image
EWC
AFEC
Figure 6: Visualization of predictions of the latest task after continual learning CIFAR-100-SC. present the results on five different random seeds, which determine five different superclasses.
in continual learning, where AFEC learns each new task much better than other baselines. Since continual learning of more tasks leads to less network resources for task, the overall trend of all the baselines is declining. indicating the necessity to improve forward knowledge transfer on the basis of overcoming catastrophic forgetting. Then we calculate forward transfer (FWT) the averaged influence that learning the previous tasks has on a future task, and backward transfer (BWT) [77, i.c., the averaged influence that learning new task has on the previous tasks (detailed in Appendix D). FWT is from more negative to more positive in CIFAR-100-SC. CIFAR- and CIFAR-10/100 while AFEC achieves the highest FWT among all the baselines. The BWT of AFEC is comparable EWC, indicating that the proposed active forgetting does not cause additional catastrophic forgetting. Therefore, the performance improvement of AFEC in Table is achieved by effectively improving the learning of new tasks in continual learning- In particular, AFEC achieves a much larger improvement on the learning of new tasks than P&C, which attempted to improve forward transfer of EWC through learning additional active column. Due to the progressive
i.c..

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parameter isolation, although AGS-CL achieves the best BWT. its ability of learning each new task drops more rapidly than other baselines. Thus, it underperforms AFEC in T
Visual Explanation:
To explicitly show how AFEC improves continual learning, in Fig. 5 we use Grad-CAM (27] to visualize predictions of the latest task after continual learning on 100SR- where FWT is more negative as discussed above. The predictions of EWC overfit the background information since attempts best remember the old tasks with severe negative transfer, which limits the learning of new tasks, In contrast, the visual explanation of AFEC is much more reasonable than EWC, indicating the efficacy of active forgetting to address potential negative transfer and benefit the learning of new tasks.
Plugging-in Memory Replay: We further implement AFEC in representative memory replay ap- proaches in Appendix F, where we perform single-head evaluation [2]. On CIFAR- and ImageNet- 100 datasets, we follow 6 that first learn 50 classes and then continually learn the other 50 classes by 5 phases (10 classes per phase) or 10 phases (5 classes per phase), using a small memory buffer of 20 images per class. AFEC substantially boosts the performance of representative memory replay approaches such as iCaRL 21 LUCIR
9 and PODNet [
4.3
Atari Reinforvement Tasks
Sequence
Sequence 2
Sequence 3
8.0
8.0
AFECC
AFEC!
Nomalazed Acoumulated Roward
Nomakzzdd Accummdatted Rewardd
Normalzaud Aecuizaddcccuuauuuu Accumulated Roward
EWC
AFEC
AFEC!
AFEL??
6.0-
6.0
MAS
MAS
Fine
Fine-turing
Fire-tuiing
4.0
4.0
2.0
2.0-
8
Task
Task
Task
Figure 7: Continual learning of Atari reinforcement tasks. AFEC is our method described in Sec. 3.2, while AFEC² the adaptation of our method to MAS.
Next, we evaluate AFEC in continual learning of Atari reinforcement tasks (Atari games). We follow the implementation of [TC] to sequentially learn eight randomly selected Atari games. Specifically, we applies CNN architecture consisting of 3 convolution layers with 2 fully connected layers [5 for all the methods (detailed in Appendix G). The evaluation metric is the normalized accumulated reward: the evaluated rewards are normalized with the maximum reward of fine-tuning on each task, and accumulated. We present the results of three different orders of task sequence, averaged by five runs with different random initialization.
and identical PPO
For continual learning of Atari reinforce- ment tasks, forward knowledge transfer is severely negative, possibly because the opti- mal policies of each Atari games highly different. We first measure the normalized rewards of learning each task with a ran- domly initialized network, which are 2.16, 1.44 and 1.68 on the three task sequences, respectively. That is to say, the initialization learned from the old tasks results in an averaged per- formance decline by 53.67%. 30.66% and 40.56%, compared with random initialization. Then, we evaluate the maximum reward of learning each new task in Table and the normalized accumulated reward of continual learning Fig. 7 AFEC effectively improves the learning of new tasks and thus boosts the performance of EWC and MAS, particularly when learning more incremental tasks. AFEC also achieves much better performance than the reproduced results of AGS-CL on its officially released code [[O (sce Appendix G for extensive analysis).
Table 3: Averaged performance increase of learning each new task on Atari reinforcement tasks.
Sequence
Sequence
Sequence
AFEC! on EWC
+35.28%
+50.55%
+28.00%
AFEC² on MAS
+30.09%
+61.12%
+26.63%

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Conclusion
In this work, we draw inspirations from the biological active forgetting and propose novel approach to mitigate potential negative transfer in continual learning. Our method achieves the SOTA perfor- mance on variety of continual learning benchmarks through effectively improving the learning of new tasks, and boosts representative continual learning strategies in a plug-and-play way. Intrigu- ingly, derived from active forgetting of the past with Bayesian continual learning, we obtain the algorithm that is formally consistent with the synaptic expansion and synaptic convergence (detailed Appendix A), and is functionally consistent with the advantage of biological active forgetting in memory flexibility [S]. This connection provides potential theoretical explanation of how the underlying mechanism of biological active forgetting achieves its function forgetting the past and continually learning conflicting experiences. We will further explore it with artificial neural networks and biological neural networks in the future.
Limitation and Social Impact
The potential limitations of our work include three aspects: First, we propose method mitigate potential negative transfer in continual learning, so the efficacy of our method might be influenced by the level of negative transfer in task sequence. Second, following [12, assume that all the incremental tasks are independent, which might limit the application of our method to other scenarios such as continual learning of smoothly-changel data distributions. Third, our method needs to learn an additional set of parameters, resulting in more computational cost. Since our work is fundamental research in machine learning, the negative social impacts are not obvious at this stage.
Acknowledgements
This work was supported by NSF of China Projects (Nos. 62061 136001, 61620106010, U19B2034, U181 146, 62076145), Beijing NSF Project (No. JQ19016), Säingua-Pekkng Center for Life Sciences, Beijing Academy of Artificial Intelligence (BAAI). Tsinghua- Huaweei Joint Research Program, grant from Tsinghua Institute for Guo Qiang, and the NVIDIA NVAIL Program with GPU/DGX Acceleration.
10

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12

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Checklist
1. For all authors...
(a) Do the main claims made in the abstract and introduction accurately reflect the paper's
contributions and scope? [Yes] See the abstract and introduction with the manuscript.
(b) Did you descrihe the limitations of your work? [Yes] See the paragraph after Conclu- sion.
(c) Did you discuss any potential negative societal impacts your work? [Yes] See the paragraph after Conclusion.
(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] We carefully read the ethics review guidelines and ensured that our paper conforms to them.
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(c) Did you report error bars (e.g.. with respect to the random seed after running experi- ments multiple times)? [Yes] See Sec.
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13


Reviews:
[{"review_id": "PcaMPzHMrX", "reviewer": "Reviewer_FR4z", "summary": "This paper proposes a new approach for continual learning that actively forgets the old knowledge when learning the new tasks. The approach uses Bayesian continual learning with synaptic expansion-convergence for active forgetting. The paper evaluates the new method on several continual learning benchmarks, including CIFAR10 regression, visual classification, and Atari reinforcement tasks.", "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 synaptic expansion-convergence idea for active forgetting proposed in this paper seems novel for continual learning, although it is quite related to the power EP method by Minka. My main concern with the paper is its clarity, especially in the main technical part of the method. In particular:\n1. The description of the proposed method in Section 3.2 is not very clear. For example, where is \\theta_e in Eq (10)? How is \\theta_e constructed (e.g. by expanding the network architecture or other methods)? How are the weights merged to obtain the original architecture? I find that the illustration in Figure 2 is not understandable. More details should be added here.\n2. The paper should give more details on how to derive Eq (9).\n3. Since the new prior has been changed by Eq (6), how does that affect the computation of the Fisher Information matrix in Eq (10)? More details should be added here, especially when there are more than 2 tasks.\n4. Additionally, more details should be given on how the method can be applied with MAS, SI, and RWALK.\n5. The CIFAR10 regression task in Section 4.1 is not realistic. Why would we want to convert a classification task into such a regression task? It may be better to consider a real regression task. Furthermore, the paper reported average accuracy for this regression task but did not give any explanation on how this average accuracy is computed.\n\n===\n\nThe authors' rebuttal has adequately addressed my concerns. So I increase my score to 6.", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "No potential negative societal impact.", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3"}, "extra_text": {}}, {"review_id": "OqK5cCrDwtr", "reviewer": "Reviewer_we6u", "summary": "This paper proposes a method for continual learning that aims to mitigate the problem of catastrophic forgetting by actively forgetting knowledge from previous tasks. The authors use a Bayesian continual learning framework to design their method. AFEC relies on identifying a set of expanded network parameters which are specific to the new task. The method incorporates a term in the loss function that considers the merge between these parameters and the network parameters being updated for the current task, therefore encouraging active forgetting. Catastrophic forgetting is also controlled by including a term that merges between parameters for old tasks and network parameters for the current task (i.e. the EWC term). Experimental results are reported for datasets on regression, classification and reinforcement learning tasks. These results show some advantages of the method in particular in the forward transfer setting. ", "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 of this paper are: \n- The paper is very well-written, well-structured, and easy to follow. \n- The method explores a new avenue which has been rather ignored in previous continual learning research, in terms of promoting forgetting when appropriate. I believe this is the main strength and novelty of the proposed approach. \n- The contribution is technically sound, and the claims are reasonably supported by the experimental results in a variety of tasks (regression, classification, reinforcement learning)\n\nWeaknesses of this paper are: \n- In the experimental results reported in Section 4.2, it is not clear whether the 5 runs involved 5 different task orders or just 5 different random seeds. This is important as the order of tasks has a direct influence in forward and backward transfer – i.e. learning easier tasks first and then hard ones may give different results than learning hard tasks first and then easier ones. \n- Although it is explicitly mentioned that the set of expanded parameters does not need to be stored for later use, the computational cost of solving Eq. 10 is not mentioned. In particular, does this increase with the size of the network, for example for a rather large number of tasks?\n- Although I appreciate the analogy with biological active forgetting, a clear difference I see of the proposed approach vs. a biological system is the number of tasks. How would AFEC work well for a rather large number of tasks (e.g. hundreds, thousands)? I would believe the trade-off between actively forgetting and retaining knowledge of old tasks would be increasingly challenging with an increasing number of tasks. \n- The use of some language could be improved. For example, the word “significantly” is used in several parts of the paper, although no tests for statistical significance are reported. There is also a typo at the end of the first paragraph of Section 2 (“which toke advantages… ”). \n", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "I would suggest the authors to explicitly mention/point to limitations in terms of complexity of tasks (which implies a larger set of parameters) and number of tasks (which increases the challenge for balancing active forgetting and knowledge retention of old tasks). ", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "3"}, "extra_text": {}}, {"review_id": "7LxnUXpYGKp", "reviewer": "Reviewer_WUG1", "summary": "This paper investigates how to avoid negative transfer in Bayesian continual learning setting.\nThe main contribution is the proposition of an active forgetting mechanisms inspired by biological neural networks for mitigating negative transfer in CL.\nThe experiments on CL benchmarks have been conducted to validate the performances of the proposed method.\n", "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": "Originality:\n  This paper proposes a novel approach -- Active Forgetting with synaptic Expansion-Convergence (AFEC), for reducing the interferes of knowledge from past learning. The method can be a plug-and-play to a CL model for boosting its performance.\n  Relationship to previous works has been explained and relevant literature has been cited appropriately.\n\nQuality:\n  The work is relevant to audience at Neurips and provides reasonable details and code for reproducibility.\n  The authors have conducted experiments on several CL benchmarks to evaluate the effectiveness of the proposed method, and demonstrated SOTA performance.\n\nClarity:\n  The paper is overall clearly written and the method is adequately described.\nIt provides reasonable details and code for reproducibility.\n\nSignificance:\n  The improvement of the proposed method is significant on several CL tasks including regression, classification, and RL.\n\n[After Rebuttal]\nAfter reading other reviewers' comments and the authors responses, I'd like to keep my rating 6 because the authors have addressed an important question in CL and most reviewers' concerns in their responses. They also provide enough details/codes for readers to reproduce the results.", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "Yes", "review_text": "", "extra_scores": {"ethical_concerns": "No", "needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4 hr"}, "extra_text": {}}, {"review_id": "03c-LNGb-xK", "reviewer": "Reviewer_kQj5", "summary": "The paper proposed a continual learning method that attempts to promote better forward transfer among similar tasks. Towards this, the authors attempt to suppress the negative knowledge, the knowledge that impedes learning a new task, from the previous task while learning a new task. This is done by forgetting such knowledge from the previous task without increasing the forgetting catastrophically. The authors claim that such “active forgetting” is biologically inspired. Similar to the Elastic Weight Consolidation (EWC), the authors derive the learning objective, by applying the laplace approximation to the posterior of a new task. The only difference is that the posterior of the previous task is replaced by a weighted product distribution, where a weight of ‘\\beta’ is introduced to capture active forgetting. This change allowed them to derive a new regularization penalty whereby a separate model is trained for a new task and then subsequently merged with that of the previous one. It is in this merging that the negative knowledge of the previous task is eliminated. Experimentally, the authors show strong performance on regression, classification and RL tasks. The authors further show that their method can be added to other regularization- and memory-based methods to improve their performance. \n", "questions": "", "limitations": "", "rating": 6, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "Positives:\n\n- Overall the paper is well-written and intuitively easy to understand. \n- Experiments are conducted thoroughly across various domains. \n\nNegatives:\n\n- Details of the method: It seems that some implementation details of the method are missing and, in fact, difficult to discern from the main learning objective (Eq. 10). Do the authors first train the separate network to obtain the optimal parameters for the new task $\\theta_e^*$, then compute $F_e$ for this optimal model, and finally use Eq. 10 to merge the knowledge from the two tasks/ models? If not, then how is the $\\theta_e^*$ and $F_e$ are obtained? If yes, then would there be an additional $L_B(\\theta)$ term in objective? \n\n- Progress and Compress (Schwarz et al.): It seems that conceptually the method is very similar to the progress and compress (P&C) where a new “active” column/ network is learned for a new task, that is later distilled to the unified model of the previous task. The authors of the present work seem to do the same thing but, of course, the mechanism of merging is different: whereas in P&C knowledge distillation is used, AFEC (present work) uses an additional EWC-type loss. I would want the authors to compare against P&C both theoretically and experimentally. \n\n- Short term measure of negative knowledge: It seems that AFEC takes a short term view of negative knowledge (i.e.) the knowledge that is negative for only the current task. I can imagine scenarios where an orthogonal current task would force the network to remove most of the knowledge from previous task(s), because it was deemed negative for the current task, even though it would have been beneficial for the future tasks. What is the take of the authors on that?\n\n--------------------------------------------\nPost-rebuttal:\n\nI quite likes how objectively the authors responded to the review. While the two-step training for each new task has its drawbacks, I overall quite like the paper. The authors response addressed some of my concerns. Therefore, I am increasing my score to 6.", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "N/A", "review_text": "", "extra_scores": {"needs_ethics_review": "No", "ethics_review_area": "", "time_spent_reviewing": "4"}, "extra_text": {}}]

Author rebuttal:

Meta-review: This work touches on an important problem in Continual Learning that has not been as thoroughly investigated as catastrophic forgetting, namely graceful forgetting (or an active and controlled mode of forgetting) that would allow forward transfer. 
While the need of graceful forgetting has been discussed in the past, there are not many methods that manage to do so in a successful way, and this work proposes a practical way of doing just that. 

Given the reviews, and the active participation of the authors in the discussion (including new experiments) I believe the current manuscript is of interest to the community and matches the expectations from the conference. 
Decision: Accept (Poster)