Does Continual Learning Equally Forget All Parameters?
Authors: Haiyan Zhao
Tianyi Zhou
Guodong Long
Jing Jiang
Chengqi Zhang
Venue: Submitted to ICLR 2023 (2023)

Abstract: Distribution shift (e.g., task or domain shift) in continual learning (CL) usually results in catastrophic forgetting of neural networks. Although it can be alleviated by repeatedly replaying buffered data, the every-step replay is time-consuming and the memory to store historical data is usually too small for retraining all parameters. In this paper, we study which modules in neural networks are more prone to forgetting by investigating their training dynamics during CL. Our proposed metrics show that only a few modules are more task-specific and sensitively alters between tasks, while others can be shared across tasks as common knowledge. Hence, we attribute forgetting mainly to the former and find that finetuning them only on a small buffer at the end of any CL method can bring non-trivial improvement. Due to the small number of finetuned parameters, such ``Forgetting Prioritized Finetuning (FPF)'' is efficient on both the computation and buffer size required. We further propose a more efficient and simpler method that entirely removes the every-step replay and replaces them by only $k$-times of FPF periodically triggered during CL. Surprisingly, this ``$k$-FPF'' performs comparably to FPF and outperforms the SOTA CL methods but significantly reduces their computational overhead and cost. In experiments on several benchmarks of class- and domain-incremental CL, FPF consistently improves existing CL methods by a large margin and $k$-FPF further excels on the efficiency without degrading the accuracy. We also empirically studied the impact of buffer size, epochs per task, and finetuning modules to the cost and accuracy of our methods.

Under review as a conference paper at ICLR 2023
DOES CONTINUAL LEARNING EQUALLY FORGET ALL PARAMETERS?
Anonymous authors Paper under double-blind review
ABSTRACT
Distribution shift (e.g., task or domain shift) in continual learning (CL) usually results in catastrophic forgetting of neural networks. Although it can be alleviated by repeatedly replaying buffered data, the every-step replay is consumnnn and the memory to store historical data is usually too small for retraining all parameters. In this paper, we study which modules in neural networks are more prone to forgetting by investigating their training dynamics during CL. Our proposed metries show that only a few modules are more task-specific and sensitively alters between tasks, while others can be shared across tasks as common knowledge. Hence, we attribute forgetting mainly to the former and find that finetuning them only small buffer at the end of any CL method can bring non-trivial improvement. Due to the small number of finetuned parameters, such "Forgetting Prioritized Finetuning (FPF)" is efficient on both the computation and buffer size required. We further propose a more efficient and simpler method that entirely removes the etery-step replay and replaces them by only k-timee of FPF periodically triggered during CL. Surprisingly, this "k-FPF" performs comparably FPF and outperforms the SOTA CL. methods but significantly reduces their computational overhead and cost. In experiments on several benchmarks of class- and domain-incremental CL, FPF consistently improves existing CL methods by a large margin and k-FPF further excels on the efficiency without degrading the accuracy. We also empirically studied the impact of buffer size, epochs per task, and finetuning modules to the cost and accuracy of our methods.
INTRODUCTION
Empowered by advancing deep learning techniques and neural networks, machine learning has achieved unprecedented promising performance on challenging tasks in different fields, mostly un- der the i.i.d. (independent and identically distributed) offline setting. However, its reliability and performance degenerates drastically in continual learning (CL) where the data distribution or task in training changing over time, the model quickly adapts ously learned weights. This leads to severe bias towards more recent tasks and "catastrophic forget- ting" of previously learned knowledge, which is detrimental to variety of practical applications.
task and overwrites the previ-
A widely studied strategy to mitigate forgetting is experience replay (ER) (Ratcliff, 1990 Robins 1995) and its variants (Riemer al., 2018 [Buzzega al., 2020 Boschini al. (022). which store a few data from previous tasks in a limited memory and train the model using both the current and buffered data. However, they only bring marginal improvements when the memory is too small to store sufficient data for recovering previously learned knowledge, which is common due to the complicated distributions of previous tasks. In contrast, multi-task learning (Caruana 1997) usually adopts a model architecture composed of a task-agnostic backbone network and multiple task-specific adaptors on top of it. While the backbone needs to be pre-trained on large-scale data, the adaptors usually light-weight and can be achieved using few data. In CL, however, we cannot explicitly pre-define and separate the aag-osic parts and -pec-ipe parts. Although previous methods (Schwarz et al. 2018 Zenke al. 2017) have studied to restrict the change of parameters critical to previous tasks, such extra constraint might degrade the training performance and discourage task-agnostic modules capturing shared knowledge.

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In this paper, study fundamental but open problem in CL, ie.. are most parameters task- and sensitively changing with the distribution shift? Or is the catastrophic forgetting mainly caused by the change a few task-specific parameters? It naturally relates to the plasticity-stabiiee
trade-off in biological neural systems (Mermillod et al. 2013): more task-specific parameters improves the plasticity but may cause severe forgetting, while the stability can be improved by increasing parameters shared across tasks. In addition, how many task-specific parameters suffice to achieve promising performance on new task(s)? every-step replay necessary?
To answer these questions, we investigate the training dynamics of model parameters during the course of CL by measuring their changes over time. For different CL methods training with various choices of buffer size and number of epochs per task on different neural networks, we consistently observe that only a few parameters change more drastically than others between tasks. The results indicate that most parameters can be shared across tasks and we only need to finetune few task-specific parameters to retain the previous tasks' performance. Since these parameters only contain few layers of various network architectures, they can be efficiently and accurately finetuned using a small buffer.
The empirical studies immediately motivate a simple yet effective method, "forgetting prioritized finetuning (FPF)", which finetumes the task-specific parameters using buffered data at the end of CL methods. Surprisingly, on multiple datasets, FPF consistently improves several widely-studied CL methods and substantially outperforms a variety of haselines. Moreover, we extend FPF to a more efficient replay-free CL method "k-FPF" that entirely eliminates the cost of every-step replay by replacing such frequent replay with occasional FPF. k-FPF applies FPF only & times during CL. We show that relatively small & suffices enable k-FPF achieving comparable performance with that of FPF+SOTA CL methods and meanwhile significantly reduces the computational cost. In addition, we explore different groups of parameters to finetune in FPF and k-FPF by ranking their sensitivity to task shift evaluated in the empirical studies. For FPF, we compare them under different choices for the buffer size, the number of epochs per task, the CL method, and the network architecture. FPF can significantly improve existing CL. methods by only finetuning S 0.127% parameters. For k-FPF, we explore different groups of parameters, k, and the finetuning steps per FPF. k-FPF can achieve a promising trade-off between efficiency and performance. Our experiments are conducted on a broad range of benchmarks for class- and domain-incrementee CL in practice, e.g., medical image classification and realistic domain shift between image styles.
2 RELATED WORK
Continual Learning and Catastrophic Forgetting A line of methods stores samples of past tasks to combat the forgetting of previous knowledge. ER (Riemer et al.] 2018) applies reservoir sampling (Vitter 1985) to maintain a memory buffer of uniform samples over all tasks. Each mini-batch of ER is randomly sampled from current task and the buffered data. MIR (Aljundi et al. 2019) proposes new strategy to select memory samples suffering the largest loss increase induced by the incoming mini-batch so those at the forgetting boundary are selected. DER and DER++ (Buzzega et al. 2020) apply knowledge distillation to mitigate forgetting by storing the output logits for buffered data during CL. iCaRL. (Rebuffi et al.) (017)) selects samples closest to the representation mean of each class and trains nearest-mean-ee offeeempll--e---rr----ee-- classifier preserve the class information of samples. A-GEM (Chaudhry et al. 2018) constrains new task's updates to not interfere with previous tasks. Our methods are complementary techniques these memory methods. It can further improve their performance by finetuning a small portion of task- mask-specific parameters on buffered data once (FPF) or occasionally (k-FPF).
Another line of work imposes regularization on model parameters or isolates fask-specifir parameters to retain the previous knowledge. oEWC (Schwarz et al. 2018)) constrains the update of model parameters important to past tasks by a quadratic penalty. To select task task-specific parameters, SI (Zenke et al., 2017) calculates the effect of the parameter change on the loss while MAS (Aljundi) et al. 2018) calculates the effect of parameter change on the model outputs when each new task comes. PackNet (Mallya & Lazebnik 2018) and HAT (Serra et al., 2018) iteratively assign a subset of parameters consecutive tasks via binary masks. All these works try to identify critical parameters for different tasks during CL and restrict the update of these parameters. But they can also prevent task-agnostic parameters from learning shared knowledge across tasks. From the
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training dynamics of CL, we identify the parameters sensitive to distribution shift. FPF and k-FPF finetune these parameters to mitigate bias without restricting the update of task-agnostic parameters.
Different modules in neural networks (Ramasesh et al. 2020) shows that freezing earlier layers after training the first task have little impact on the performance of the second task. This is because their unfrozen part covers the last FC layer and many BN parameters, which are the most sensitive/critical according to our empirical study. Moreover, they did not take into account that the earlier layers have much less parameters and capacity than the top layers. (Pham et al., 2022) only studies the effect of different normalization layers on CL while our method investigates the sensitivity of all parameters in different network architectures. Their continual -norm still suffers from the forgetting to task shift. Our methods directly finetune the task tusk-specific layers on the buffered data to eliminate the bias caused by the task drift. (Zhang et al.] 2019) argues different layers play different roles in the representation function. They find that in different architectures, the parameters the top layers(close to input) are more critical and perturbing them leads to poor performance. Our empirical study is consistent with their findings in that the earlier convolutional layer is sensitive to task drift and the induced biases on them lead to catastrophic forgetting.
3 PROBLEM SETUP
Notations We consider the CL setting, where the model is trained a sequence of tasks indexed by t E (1.2...., T). During each task t, the training samples (x, y) (with label y) are drawn from an i.i.d. distribution Dj. Given neural network fe(-) of L layers with parameter θ {0e ( 0, = (02,)i=m:m denote all parameters in layer-f where oy.; denotes parameter-i. On each task, (e) is trained for N epochs. We denote all parameters and the layer-('s parameters at the end of the n--h epoch of task i. by O,, and f2,,. E [I,..., N}. respectively.
Settings In this paper, we mainly focus on class-incremental learning (class-IL) and domain- incremental learning (domain-IL, In class-IL, Dr are drawn from subset of classes C, and {C,)T= for different tasks are assumed to be disjoint. class-IL is a more challenging setting of CL de Ven & Tolias 2019) than task-incremental learning (task-II.) (Lopez-Paz & Ranzato, 2017]. Unlike task-ll., class-ll. cannot access to the task label during inference and has to distinguish among all classes from all tasks. In domain-IL, tasks be learnt remain the same but the domain varies, i.c. the input data distribution Dr changes. The model is expected to adapt to the new domain without forgetting the old ones. The goal of the class-IL and domain-IL. is: ming ((0)= A Σir ([ (V,, (1))], where is the objective function.
Class-IL datasets We conduct class-Il. experiments on Seq-MNIST, Seq-OrganAMNISTT Seq- PathMNIST, Seq-CIFAR-I0, and Seq-TinylmageNet. Seq-OrranAMNIIT and Seq-PathMnist are generated by splitting OrganAMNIST or PathMNIST from McdMNIST (ang et al.) 2021). medical image classification benchmark. CL on medical images is important in practice but also challenging since medical images always come stream with new patients and new deceases. Moreover, medical images of different classes might only have subtle differences that are hard to distinguish. Both Arg-AAITAAMNIIT and Seq-PathMnist consist of 4 disjoint classification tasks. The number of classes per task in Scq-OrganAMMNISS and Scq-PathMnist are [3, 3, 3, 2] and [3, 2, 2] respectively. Meq-M -SFA-CIFAR-10) are generated by splitting the 10 classes in MNISTLeCun et al. (1988) CIIFAR-I0KriZhesss et al. (2009) into five binary classification tasks.
partitions the 200 classes of IinylmageNettLLe & Yang 2015) into 10 disjoint classification tasks with 20 classes per task.
Domain-IL datasets We conduct domain-ILL IL experiments on PACS dataset (Li al. 2017). which is widely used for domain generalization. It can present more realistic domain-shift challenge than the toy-setting of PermuteMNIST (Kirkpatrick et al., 2017). Images in PACS come from seven classes and belong to four domains: Paintings, Photos, Cartoons, and Sketches. In SeC- for CL, each task only focuses on one domain and the sequence of tasks is Sketches - Cartoons + Paintings - Photos (increasing the level of realism over time) (Volpi al. 2021).
Models We follow the standard network architectures adopted in most previous CL works. For Meq-MNIST, following Lopez-Paz Pazz-Paa&& & Ranzato (2017); Riemer et al. (2018),
employ MLP, ie., a fully-comnected (FC) network with two hidden layers, each composed of 100 ReLU units.
Following (Rebuffi et al. 2017: Li al. 2020 Derakhshani et al. 2022). we train ResNet-18 (He
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al. 2016 other five datasets. In addition, also extend our empirical study to another architecture, i.., VGG-11 (Simonyan & Zisserman, 2014) on Seq-CIFAR-10.
FORGETTING OF DIFFERENT PARAMETERS: AN EMPIRICAL STUDY
fundamental and long-lasting question in CL is how the distribution shift impacts different model parameters and why it leads to harmful forgetting. Its answer could unveil the plasticity-stabilee trade-off in CI., where some parameters are plastic and task-specific and thus have to be finetuned before deploying the model, while the stable ones can be shared with and generalized to new tasks. In order to answer this question, we conduct an comprehensive empirical study that compares the train- ing dynamics of different parameters in three widely studied neural networks. We propose novel metric measuring the sensitivity of parameters to distribution shifts. On all the studied networks, helps distinguish between plastic and stale parameters and allocate the task-specific ones.
4.1 MEASURING FORGETTING VIA TRAINING DYNAMICS
To measure and compare the forgetting effects of different parameters, we adopt an intuitive metric compute the change of parameters and investigate their dynamics over CL. In CL, the unstable changes of parameters are mainly caused by the task shift, while the learning within each task usually leads to smooth changes. Hence, the proposed metric focuses on the difference between two consecutive tasks, e.g.. the change of parameters between epoch-n of the two tasks, i.e.,
(1/10>)]10 f1, Its results on different neural networks are displayed in Fig.
4.2 FORGETTING OF DIFFERENT PARAMETERS DURING CL
We first investigate and compare the training dynamics of different parameters three types of neural networks. To gain insights applicable to all CL methods, we exclude any specific CL tech- niques but simply apply SGD to train model on a sequence tasks, without any countermeasure to forgetting. Then, extend the experiment to different CL methods, hyper-parameters (c.g., buffer size), and datasets to verify whether the observations still hold.
1etoyer3
Layer1
layer
Meck
Cory Bick
Drmy Laya:1
Madk)
Cony Mad:3
Drwy Biok
Lavers
12
23
20
23
24
13
24
Treinin
(a) Dynamics of MLP
(b) Dynamics of VGG-11
(c) Dynamics of ResNet-18
Figure 1: The training dynamics of different groups of parameters when applying SGD CL to train three types of deep neural networks. Note the the y-axis is of logarithmic scale.
Dynamics of MIP We train three-layer ML.P (including the classifier) for SNQ-M. Fig. Ta) reports how the metric introduced in Section 4.1 for each layer changes in CL. It shows that the top FC layer (closest to the output) is the most sensitive one with the greatest changes among all the three layers. This is because tasks in class-IL differ on their predicted classes, which are the outputs of the FC layer. Since task shift mainly changes the top FC layer, finetuning it using all-tasks' data help reduce the forgetting.
Dynamics of VGG Fig. (b) shows the training dynamics of parameters in VGG-11 when trained on Seq-CIFAR10. We partition all parameters into several groups, i.c., the bottom convolutional layer (closest to the input), convolutional layers in different blocks, and three top FC layers. The observations on FC layers are consistent with those on MLP: the last FC layer in VGG is much more sensitive to the task shift than other two FC layers. contrast, the sensitivity of all convolutional layers increases the layer becomes closer to the input because they are producing the representations for the input images, whose distribution shift directly impacts the bottom convolutional layer. However, they are still more stable (or less plastic) than the last FC layer. Since task shift mainly changes the bottom convolutional layers (among all convolutional layers), finetuning them be important to alleviate the forgetting.
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Dynamics of ResNet Fig. 1 (c) reports the training dynamics of parameters in ResNet-18 when trained on Seq. -Iq-CIFARIO. In addition to the groups of VGG-11, ResNet-18 applies batch- normalization (BN) layers, which have two groups of parameters, i.c., (1) their weights and bias, and (2) their mean and variance. Unlike MLP or VGG-11, in ResNet-18, BN layers' mean and variance become the most changed parameters. This observation makes intuitive sense hecause the mean and variance of BN layers capture the first and second order moments of the distribution for the latent representations. Except BN mean and variance, the last FC layer and the bottom convolutional layers are still the 2 sensitive groups among the rest parameters. which are consistent with the observations on MLP and VGG-11. The variance of BN weight and bias is relatively large compared to the rest layers, please refer to Appendix for dynamics of BN weight and bias in different groups.
In the above section, we observe that for three types of deep neural networks, parameters are not equally sensitive to the distribution shift in CL. Moreover, only small portion of them are much more sensitive and task-specific than others. This implies that only finetuning these task- speccfcc (or plastic) parameters may suffice to retain the previous tasks. That being said, the empirical study is limited to SGD without applying any other CL techniques and only focuses on class-IL. In the following, extend the studies to different CL methods, buffer sizes, non-standard datasets, and domain-IL, IL, while fixing the model to be ResNet-18.
Continge
Coul
T1ating
(a) OrgaAIITAA
(b) ER(buffer size= 50) (c) ER(baffer size= 2000)
(d) Seq-PACS
Figure 2: The training dynamics of different groups of parameters in ResNet-18: (a) on non-standard dataset;
(b,c) using a different CL method with different buffer sizes; (d) domain- IL setting. Note the the y-axis of logarithmic scale.
Dynamics different scenarios Fig. 2 (a) extends the empirical study medical image dataset Seg-OTT Comparing to Seq-CIFAR-10, it differs on the number of tasks, dataset size, image size, and data type. Despite these differences, the sensitive groups of parameters stays the same. We further replace SGD with ER using two replay buffer sizes, whose results are reported in Fig. (c). The ranking order of parameter groups in terms of sensitivity stays consistent under the change of the replay strategy and buffer size.
Dynamics on domain-IL In domain-IL, IL. as shown in Fig. 2 (d), the training dynamics of different parameters is in line with our observations in class-II: only a small portion of parameters are task-specific. However, one difference worth noting. Since the output classes stay the same across tasks and only the input domain changes, the most sensitive parameters in class-IL, i.e., the last FC layer, becomes equally or less sensitive than the bottom convolutional layer. Hence, the plasticity and stability of parameters impacted by how close they are to the changed data distributions.
5 FORGETTING PRIORITIZED FINETUNING (FPF) METHODS
The above empirical study of the training dynamics on parameters immediately motivates simple but novel method for CL, i.e., "forgetting prioritized finetuning (FPF)", which can be applied to any existing CL method. In the more efficient k-FPF, we further remove the every-step replay and any other CL techniques but simply applies k-times of FPF in SGD training. In Fig. 3 we provide an illustration that compares SGD, replay-based methods and our methods.
SGD
SGD replay FPF
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2
Task3
T
T
TaskN
SGD
replay (replay-based method)
SGD K-FPF
Tack
Task
Tack
Task
Task1
Task
Tock
Tosk N
replay FPF
Figure 3: Comparison of SGD, replay- based method, FPF and K-FPF. SGD trains each task sequentially with- out replay. Replay-based methods train model on buffered data and current data simultaneously. FPF finetunes the most sensitive (plastic) parameters for few iterations using the buffered data at the end of arbitrary CL methods. FPF periodically (regardless of task boundaries) applies FPF for le times over the course of training.
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FPF to improve CL performance. FPF applies light- lightweiigtt finetuning to the most task task-specific parameters using the buffered data after the training of arbitrary CL methods. Hence, it is complementary to any existing CL methods task-specific parameters by finetuning them on the unbiased buffered data. Thereby, it can improve the performance of any existing CL methods without causing notably extra computation.
a correction step to remove their biases in the
k-FPF to improve CL efficiency and performance. FPF is a simple technique that brings non-trivial improvement but is applied after the training of an existing CL method. Unfortunately, many SOTA CL methods require time-consuming replay in every step, which at least doubles the total computation. Since only a few parameters are sensitive during the task shift, can we develop a replay-free and lazy CL that replaces every-stepp seey-sste-- with occasional FPF? We propose k-FPF that applies FPF 1 times during CL. as shown in Fig. 3 Without the costly experience replay, k-FPF can still achieve comparable performance as FPF+SOTA CL methods but only requires nearly half of their computation. We can apply k-FPF with any replay-free method, e.g., SGD, which is usually used as lower-bound for CL methods. We still maintain a small buffer by reservoir sampling but is only for FPF so SGD never accesses it. We lazily apply FPF on the buffer after every T SGD steps (in total k times over kr SGD steps) without knowing the task boundaries.
We propose two variants of k-FPF, i.c., k-FPF-CE+SGD and -DDDD.. 4-FPF-CE+SGL uses the cross-entropy loss to update the sensitive parameters during FPF. In this paper, k-FPF-CE refers to k-FPF-CE+SGD if not specified. The objective of FPF in k-FPF-CE
is: ming. L(0*) & E(a.))n((ce (V. (v. fe(x)) where O* denotes selected groups of task-specific parameters, B refers to the buffered data and Iog is the cross-entropy loss.
&-FPF-KD+SGD to further improve performance Inspired by DER (Buzzega et al. 2020 further propose k-FPF-KD that introduces knowledge distillation (KD) (Hinton al. 2015) to the objective in k-FPF-CE. In this paper, k-FPF-KI refers to k-FPF-KI+SGID if not spec- ified. Same as DER, the pre-softmax responses (i.e. logits) for buffered data at training time are stored in buffer as well. During FPF, the current model is trained to match the buffered logits retain the knowledge of previous models. The objective of FPF in k-FPF-KD is: ming. L(O*) A E(g.))-(llcE(( f=()))] + (E (2,,)((() hz()))] where 2 is the logits of buffered sample IMSE refers to the mean-squared loss, he (zr) computes the pre-softmax logits and À is a syper-paramess
balancing the two terms. Compared to the computation of k-FPF-CE, the additional computation by K-FPF-KD negligible.
Selection of sensitive paramcters for FPF and K-FPF
A key challenge in both FPF and k-FPF is select the task-specific parameters for finetuning. Please refer to A. for the detailed metric of selecting sensitive parameters in different neural net- works. In the experiments later, under different scenarios and on various benchmarks, we evaluate the performance of FPF and k-FPF when selecting different subsets of task-specific parameters ac- cording to the training dynamics studies in empirical study. nutshell, finetuning more sensitive parameters achieve more improvement, which is in line with our findings in empirical studies. For FPF, finetuning one or two the most sensitive groups layers, like the last FC layer, enough to achieve the best performance among all evaluated combinations. In all scenarios, FPF consistently improves CL's performance by a large margin. For k-FPF, finetuning slightly more parameters, i.c., the carlier convolutional layers, achieves the best performance, which is comparable with that of FPF+CL. This is a price of removing replay, which halves the computational cost.
6 EXPERIMENTS
In this section, to compare FPF and k-FPF with SOTA CL methods, we conduct our experiments mainly on ResNet-18. Please refer to the Appendix for the results on other neural networks. We apply FPF and k-FPF to multiple benchmark datasets and compare them with SOTA CL baselines in terms of test accuracy and efficiency. Besides, we also compare the performance of finetuning different parameters in FPF and k-FPF and show that finetuning a small portion of task-specific parameters suffices to improve CL. FPF improves SOTA CL methods by a large margin under all these scenarios while k-FPF achieves comparable performance with FPF but is more efficient.

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Table I: Test accuracy (%) of CL baselines, FPF and k-FPF. "-" indicates that the algorithm is not applicable the setting. For FPF and k-FPF, we report the hest performance among all combinations of parameters Fig. 5
k-FPF-KD applies an additional knowledge distillation loss to the finetuning objective k-FPF-CE. Bold and Bold gray mark the best and sccond hest accuracy.
BUSTER
METHOOS
SFO-ORGANAMNIS SPO-PATHMNIST
CLASS-IL
SRO-CIFAR-10
SiQ-TINY-IMAGENTT
DOMMAIN-IL SEO-PACS
JOINT
91. 21.9250.40
82.47=2.99
$1,05=1.0
41.5720.35
70.85=3.00 90
SGD
13.65=0.07
19.34-0.06
7.10=0.14
31.43=6.3 39
OEWC SCHWARZ 2018
22.36.1.18
6.58.10.12
35.96114.99
(PRANII BT
30.36-2.61
2.43+0.31
A-EPF-CE
75.2111.03
72.88 3.22
57.97-1.53
13:76.0.722
60.20 1.2.81
1-FPF-KD
50.32: 1.66
74.68:4.72
58.50=1.00 00
14.74:0.94
63.15t:1119
ER [RIEMER ET Al. 2018
71.6911.71
51.66.15.88
45.71
8.15
51.5311.110
EPITER
77.60s: 1.93
67,34=2.08
57.08
13.1320.03
65.16:1199
AGEM [CHAUDERY LT AL. 2018
34.1620.11
27,9124.24
19. 09.2920.04
1.22
40.5423.25
FPE+AGEM
73,761:2445
67.04:4.51
55,40:1.91
13.24:0.544
57.33:0.76
ICARL REBUUI 2017
79.6120.56
54.3520.94
59.60
12. 1320.20
EPF-ICARE
$0,24:0.10
71883=1.51
63.95=0.84
17.45-0.38
[BENIAMIN
68.201:3.22 3.27
44.2713.30
41.77:4.24
10.10
45.91133.44
76.92a 1.38
70.08:4.006
12.49=2.97
12:25:00227
18.38
DER [BUZZRGA 2020
73.28: 1.33
54.45--5.02
47.0
FPF-DER
79.6311.21
67.29
57.25
12.62.1.088
61.0911..37
DER++
[BUZZBOA ET AL.
2020
78.222:2.00
62.0013.779
19.13-0.81
12.1240.00
35.7512..1
EPF-DEKEE
80.99=0.11
68.78-2.99
1.99
13.78-00.57
65.28-
GDUMB PRABBU ET AL. 2020
73.29
63.55:15.62
42.18-2.05
3.67
43.291:2.83
1-FPF-CE
81.2810.71
76.72_1.94
64.35.0.67
19.57.0..37
65.901.0.22
L-PPE-KD
85,1620.67
79.20=3.89
66.43=0.50
20.56:00332
66.42:2..21
ER [RIEMER
$0.45 99
$7.54 0s
57.64-4.27
10 09:0 34
$2.72244.1
69.83:2..87
64
18.61
64.27::
AGEM CHAUDERY ET 500
18.00.10.18
27.3311399
19.4710.03
1,1410,110
35.2914.00
FPF+ACTEM
79.86:00
73.32-3.73
57.84=1 18
17.35:00.65
62.40::
ICARL REBURI AL.
2017
$2.9510047
$7.672:1.13
62.2611
1481110.17
EPPRICAR
84.33:0.37
74.35-2.88
67.75-9.67
17.3729.35
FIR [BENAMMN EY AL.
2018
76.62% 1.
40.0824.13
43.52-1.74
11.3320.33
48.50124.67
FPF-FIIR
82.32=00.0 91
75.59-2.64
63.82-0.69
17 17.94+0.56
65.47 13
DEK [BUZEBOA 2020
$2.52m0.52
66.71
$5.98:1.35
11.5420.70
47.632 85
EPF4DER
85.24-0.55
74,80=3.45
67.52-0.8
17. 17.6000.50
65.69t 66
DER +-
RIZZBDA ET M.. 2020
34.25:0.44
71.0925.600
67 0.06--331
74-46.66
57.7777- 54
PPE-DEKFF
85,6710.23
77.37-1.32
69.09.0.74
20.17:0.35
66.8911.32
Implementation Details. We follow the settings in (Buzzega et al. 2020) to train various SOTA CL methods on different datasets, except training each task for only 5 epochs, which is more practical than 50 or 100 epochs (Buzzega al. 2020) for the streaming setting of CL. Since the epochs are reduced, we re-tune the learning rate and hyper-paramett grid-search on validation set of 10% samples drawn from the original training set.
for different scenarios by performing
For both FPF and k-FPF, we use the same optimizer, i.e., SGD with the cosine-annealing learning rate schedule, and finetune the selected parameters with a batchsize of 32 for all scenarios. The finetuning steps for FPF and k-FPF are 300 and 100 respectively. We perform grid-search on the validation set to tune the learning rate and other hyper-parameters. Please refer to the Appendix for the hyper-paramette
explored.
Baseline methods. We apply FPF to several SOTA memory- based CL methods: ER (Riemer et al. 2018), iCaRL (Rebuffi al. 2017), A-GEM (Chaudhry et al. 2018). FDR (Benjamin et al. 2018), DER (Buzzega et al.) 2020), and DER+ ++ Buzzega et al. 2020). Besides, we also compare our methods with GDUMB (Prabhu et al.) 2020 and oEWC (Schwarz et al. 2018). We report the test accuracy of these baseline methods and the best test accuracy of FPF and K-FPF among a few choices of finetuned parameters. We take JOINT as the upper bound for CL, which trains all tasks jointly, and SGD as the lower bound, which trains tasks sequentially without any countermeasure to forgetting. For FPF, k-FPF, and all memory- based methods, the performance with buffer size 200 and 500 are reported. All results reported in Table] are averaged over five trials with different random seeds.
6.1 MAIN RESULTS
FPF considerably improves the performance of all mesory-based CL methods and achieves SOTA performance over all scenarios in class-IL and domain-IL in Table [ For methods with catastrophic forgetting, like AGEM. the accuracy of FPF increases exponentially. The surge of performance illustrates that FPF can climinate bias by finetuning task-specific parameters to adapt to all seen tasks.
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363
(1 Merwoss
Wemeess
(a) Seq-PathMNIST
(b) Timn--mmgeeeeet
(c) Seq-PACS
Figure 4: Comparison of FLOPs and accuracy between FPF, k-FPF and SOTA methods. FPF improves all CL methods by a large margin without notably extra computation. k-FPF consumes much less com- putation but achieves comparable performance as FPF.
K-FPF-CE replaces the costly every-step replay with efficient occasional FPF. In Table I the performance of E-FPF-CE on Seq.PaThMNIST Tee-TTinn-mgahtee and Seq-PACS are better than the best CL methods and its performance than most CL methods, which implies that finetuning the task-specific parameters on small number of buffer during SGD can help retain the previous knowledge and mitigate forgetting, every-step replay is not necessary. In Fig. 4 the number of training FLOPs and accuracy of different methods reported. Compared to the training FLOPs of several CL methods, the computation cost of FPF and k-FPF-CEE is almost negligible. The overall training FLOPs k-FPF-CE is still much less than SOTA CL methods while its performance are better, which show the efficiency of k-FPF-CE.
Aeg-OrganAMNNIST and Seq-Cifar 10 are also better
k-FPF-KD further improves the performance of &-FPF-CE to be comparable to FPF. k-FPF- CE propose the efficiency of CL methods, but its performance is bit worse than that of FPF One of the most difference between k-FPF and FPF is the experience replay during training of CL. Inspired by DER, we propose k-FPF-KD. which uses knowledge distillation match the outputs of previous models on buffered data, hence retaining the knowledge of previous tasks. The results of k-FPF-KD in Table T show that comparable to FPF in most scenarios. Fig. 4 shows that the FLOPs of k-FPF-KD is similar to k-FPF-CE but much less than other CL methods and FPF, and in some cases, it outperforms FPF. k-FPE-KD shows SOTA performance in both efficiency and accuracy.
6.2 COMPARISON OF FINETUNING DIFFERENT PARAMETERS IN FPF AND k-FPF
FPF and k-FPF get the best performance when only small portion of task-specific param- eters are finetuned. In Fig. 5 the accuracy, training FLOPs and number of trainable parameters during finetune of applying FPF or k-FPF to different task-specific parameters in ResNet-18 on Seq-PathMNIST are compared. Over all different scenarios, k-FPF only needs about half FLOPs of FPF with better performance (indicated by Red Stars). When finetuning on different task-specific parameters, FPF performs the best when BN+FC layers are finetuned, which is only 0.127% of all parameters (indicated by Orange Stars). This is consistent with our observations in empirical studies where BN and FC layers are the most sensitive parameters to distribution shift. And the results shows that only finetuning a small portion of task-specific parameters can mitigate catastrophic forgetting and generalize the model.
The phenomenon for k-FPF is little different. (1) In the bottom plot of Fig. when FC layer not selected for finetuning in k-FPF, the performance is much worse. This is because in class-II., the output classes change across tasks so the FC layer is trained to only output the classes for the current task (Hou et al. 2019). In contrast, when applying k-FPF to domain-IL output classes keep the same for different tasks, Fig. T in Appendix shows that finetuning FC layer performs similarly as finetuning other parameters. Hence, the last FC layer is more sensitive in class-IL than in Domain-IL. This also shown Fig. 2 (a), (d). (2) As the red star indicates, k-FPF needs finetune little more parameters (Block3 of convolutional layers, 18.91% % of all parameters) to achieve a comparable accuracy with FPF. Without experience replay during SGD, the model has larger bias on the current task and thus more task-specific parameters are needed to be finetuned. This also indicates that such bias of task-specific parameters is the main reason for catastrophic forgetting. When Block4 (75.22% of all parameters) is finetuned, since is the most stable parameters in our empirical study, the performance of k-FPF degrades.
Peq-PACS, where the
6.3 ANALYSIS OF FPF AND F-FPF IN DIFFERENT SCENARIOS
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Different training FLOPs for
1.0
k-FPF In Fig. ((), we study the trade-off between the training FLOPs and the accuracy of k-FPF on Seq-PathMINIST by changing k and the number of finetuning steps. in the legend refers to the interval of two consecutive FPF. Fixing k, k-FPF saturates quickly as the finetuning steps increase. This implies that k-FPF is efficient on FLOPs to achieve the best performance. For experiments with small k, e.g. k=2, though the computation required is very low, performance cannot be further improved. This implies that FPF needs to be applied on buffered samples more fre- quently to mitigate forgetting. When & is large, e.g., k=41 or 121, the accuracy slightly improves with the price of much more required computation. As the red star in the plot indicates, applying FPF every 1500 training steps can achieve the best computation-accuracy trade-off.
Accuracy
0.4
0.2
F:CPP 563
Acurray steefi--c
0.8
humba of baiiaak paretrset cutts Instans
0.6
0.4
0.0
PCoon gi ForcONs
Bads glockd Biokk 1eoot3 Mord
Basks Bicck12
2296 -Buck11
basic
FPF finetuned Parameters
Figure 5: Comparison of FLOPs, number of finetuned parameters, and accuracy for FPF(Top) and k- (-FPF(Bottom) finetuning different combi- nations of parameters. All FLOPs are normalized together (0.1), J. as well as the number finetuning parameters. "Basis" the x-label refers to "BN+FC+CONVI" Red stars highlight the best accuracy and show both FPF and k-FPF only require to finetune a small portion of task- specifie parameters. k-FPF halves FPF's FLOPS.
0.82
0.34
Suffer 2k2 -50
Nurbe: spolss
Sutter 200
Namber spacts spots
0.2
(1-500)
spocte
21-0
3-1 1000
SM4FC
Boris Ross -Brockt
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g044C
Boskk Rass eBreea
(a) FLOPs-Accuras in K-FPF
(b) Different buffer sizes and training epochs for FPF
Figure 6: (a) Trade-off between FLOPs and accuracy for k-FPF with different and T (the SGD steps between two consecutive FPF). By increasing the finetunine steps per FPF, the accuracy quickly saturates. The best trade-off is highlighted at the top-left corner when &o 9(T 1500). (b) Comparison between ER and FPF+ER finetuning different parameters with different buffer sizes and number of epochs per task. In all scenarios, FPF can significantly improve ER by only finetuning BN+FC.
Different buffer sizes and training epochs for FPF The buffer size and the training epochs task are usually crucial in memory-based CL methods. In Fig. bbb), when the buffer size or number of epochs increases, the performance of ER improves as well. However, increasing the buffer size brings more benefits. When the buffer size or epochs grow too large, the performance of ER seems saturate and increases slowly. For all scenarios, finetuning BN+FC layers are highly effective to alleviate the current task's bias and promote the performance, which is consistent with our observations from the empirical studies.
7 CONCLUSION
We study a fundamental problem in CL, i.e., which parts of a neural network are task-specific and more prone to catastrophic forgetting. Extensive empirical studies in diverse settings consistently show that only small portion of parameters is task-specifie and sensitive. This discovery leads to a simple yet effective "forgetting prioritized finetuning (FPF)" that only finetunes a subset these parameters on the buffered data before model deployment. FPF is complementary to existing CL methods and can consistently improve their performance. We further replace the costly every-step replay with k-times of occasional FPF during CL to improve the efficiency. Such k-FPF achieves comparable performance as FPF+SOTA CL while consumes nearly half its computation. In future work, we will study how to further reduce the memory size required by FPF.

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Under review as a conference paper at ICLR 2023
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A
APPENDIX
A.1 SELECTION OF THE SENSITIVE PART OF DIVERSE TYPES OF NEURAL NETWORKS
We select sensitive parameters according their training dynamics in the early epochs. Examples of the training dynamics for different layers are shown in Fig 1-2 and their ranking does not change over epochs. Specifically, we sort layers by their training dynamics values in descent order. Then we greedily add layers one after another to the sensitive group until the sum of all selected layers' training dynamics exceeds p percent of the sum for all layers, where p a hyper-parameter In our experiments, for models with the batch-norm layer like ResNet- 18, FPF and k-FPF outperforms all baselines when p = 97, when only 18.90% of parameters in the neural network are regarded as sensitive parameters. For other models like MLP and VGG-11, p 70 and only 1.12% and 0.32% of parameters are regarded as sensitive parameters.
A.2 COMPARISON BETWEEN FPF AND THE METHOD FINE-TUNING ALL PARAMETERS
In T we compare FPF with FPF-ALL (which finetunes all parameters) when applied to different methods for two types of CL, i.e., class-IL and domain-IL. The results shows that FPF consis- tently achieve comparable slightly higher accuracy than FPF-ALL by spending significantly less FLOPs. This demonstrates the advantage FPF on efficiency.
Table 2: Comparison of accuracy and FI.OPs between FPF and FPF-AILL,fnettuiig all parameters).
MNNSST
Seq-PACS
Methods
Accuracy
FLOPs(B)
Accuracy
FLOPs(B)
&-EPF-CE
76.72+
21.35
65.90+0.72
148.25
&-FPE-ALL-CE
75.7442.91
43.95
64.48:22.3
174.60
FPF+ER
69.83+2.87
4.68
64.27
24.39
EPF-ALL+ER
70.64+4.00
8.79
63.81+2.33
34.92
FPF+AGEM
73.32-+3.73
7.07
62.40++1.89
18.47
FPF-ALLAAGEM
74.80+3..12
6.66
34.92
PPF+iCaRI.
74.35+44.8
4.27
FPF-ALL+ÍCaRI.
72.77++4.12
8.79
FPF+FDR
75.59++2.64
2.94
6..47+11.13
11.70
EPF-ALL+FDR
74.24-11.48
64.8812.22
34.92
FPF+DER
75.80-13.45
2.96
65.69111.6
18.47
FPF-ALL+DER
74.94
8.79
66.22.10.77
34.92
FPF DER+
77.37-11322
4.68
66.8911.32
24.39
FPF-ALL-DER++
1..16+1.445
8.79
15.19
34.92
A.3 EXPERIMENTS ON THE TASK SEQUENCE CONTAINING TOTALLY DIFFERENT DATASETS
We concatenate the CL tasks from two datasets (i.e., Seq-CIFAR-10 and Seq-PathMNIST) to form a twice-longer task sequence and evaluate the training dynamics of different groups of parameters. The result is shown in Fig 7 The vertical dashed line at epochs 30 is the boundary between the two datasets. Although the two datasets are from different domains and thus have different distributions, the sensitivity of parameters stays consistent with observations tasks from single dataset. This indicates that the sensitive parameters almost do not change across different tasks/datasets so they can be identified at very early stages.
A.4 4 A MORE CLEAR VERSION OF FIG. AND FIG
In Fig and Fig 9 to make Fig and Fig more concise and easy to understand, we draw the barplots of different parts separately.
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10-1
Dynamics of parameters
10-2
Conv Layer
Conv-Bloce Block
10
Conv Block-2
Conv Block
10 4
Conv Block
Mean&Var Layers
BN Weight&Blas Layers
10-5
FC layer
15
25 Training epochs
35
45
Figure 7: The training dynamics different groups of parameters in ResNet-18 when sequentially training Seq-CIFAR-IT and Seq-PathMNIST.
A.5 PERFORMANCE OF VARIOUS METHODS DURING THE TRAINING OF CL
In Tab. 3 and Tab. the average test accuracy of previous tasks at the end of each task during the training CL on Seq- Seq-Pathhe BeggPathMNNSTT and Seq-PACS is reported. The results show that during training. k-FPF can always achieve the best performance among various CL methods. Whenever the training stops, k-FPF can always achieve a model performing well on previous tasks.
Table 3: The average accuracy of previous tasks at the end of each task during the training of CL. on Seq- PathMNIST.
Methods
Task
Task 2
Task 3
Task 4
&-FPF-CE
99,9510.04
95.411:1.96
81.92-12.26
76.724
ER
98.62+1.59
83.06:3..12
74.60=3.18
57.54=3.05
AGEM
99.71=0.19
46.58+33.3
36. 12:
27.33=3.99
iCaRL
99.98+00.02
86.86+55.47
66.6245564
57.67=#1.13
FDR
99,97-10.06
48.06++0.82
55.75-+6.55
40.08
DER
99,9811000
91.92.13.42
76.50.15.77
66.7111..40
DER+
99.95:00.06
94.06116.14
80.35:3.332
71.09-2.600
Table 4: The average accuracy of previous tasks at the end of each task during the training of CL. on Seq-PACS.
Methods
Task
Task 2
Task
Task
4-FPF-CE
70.94:2.02
73.75::2.68
02.3740..4 49
65.90=10.22
56.6419.04
54.3419.44
8..79.18.88
$2.72=4.01
AGEM
47.34+7.35
38.02+55.2
32.70+7.13
35.29=4.94
FDR
58.59-+4.36
54.00++-.01
46.38-14.00
48.50++4.67
DER
48.49-1940
45.28.18.88
34.48-1781
47.63.1388
DER+
55.33117.4
64.43-1..50
50.1941.330
57.77-2.54
A.6 DETAILED DYNAMICS OF BN WEIGHTS AND BLAS IN DIFFERENT GROUPS
In Fig. 10 the training dynamics of BN weights and biases in different groups reported. This provides a fine-grained explanation to the phenomenon in Fig. (c): the bottom BN layer is much more sensitive and task-specific than other BN layers. Consistent with convolutional layers, the deep BN layers are less sensitive to task drift than the shallower ones.
In neural network, lower layers are closer the input. Since the distribution of the inputs changes, the parameters of lower convolutional layers change sensitively to adapt to the distribution shift. The weights and biases of BN, which the scale and shift of the featuremap, will change along
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0.8
FLOPs
0.5
0.2
Metrods
FLOPS CL Mothods
FLOPs A-Frr-CE/Ourl
Accuracy (-Prr-
FLOPs KFPFPADIOUu))
Accuracy A KDIOUm)
AGEM ICARL
FDR
DER DER++
SGD
ER
AGEM ICARL
FDR
DER DER++
SGD
CL Methods
(a) Seq- PattMPTt
1.0
0,20
Accuracy
FLOPs
0.6-
0.10
FLP Methods
0.05
Accuracy
0.2
ROP (9F Mathods
Accuracy of FFRIOUIS) Methoos
FLOPS CPr-cc
Accurbcy of FPF CElOurs)
FLOPS FDFOUr)
k-FPF KDCOursi
0.0
ER
AGEM
ICARL
FDR DER DER++
SGD
ER
AGEM ICARL
FDR
DER DER+
SGD
(b) Seq-Tiny- Inny-ImaeNNet
0.7
8-
FLOPs
Accuracy
0.4
0.3
Meth
0.2
Accuraty of Methods
Accuraty FIF (dun))c Methods
FLOPs
0.1
FLGP k-mm KD(Durs)
Arcurwcy kncruri
0.0
AGEM
DER CL Methods
AGEM
(c) Seq- PACS
Figure 8: Comparison FLOPs accuracy between FPF, k-FPF and SOTA methods. FPF improves all CL methods by a large margin without notably extra computation. k-FPF consumes much less com- putation but achieves comparable performance as FPF.
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Actuncay of
Acoumayy aEPiFaEs
Accuracy of kFFF-CE
Accuracy
FLOR of
FLOPs of ETFFTEE
1LD0 of SGD
FLOPs of FPFICE
FLOPs
Number of Parameters
Number ttllabblee parameters during finetune of FPP
Number of trainadle parometers during fheeune of I-FPP
88
Feom butff eepeeooen gast ball B0att- Ba
Dx Fcon ff oettow''s aadhin Ceue beuc coeeengng gndd galle ganr 6i
gin enstepptton
FPF Finctuned Poramaters
FPF Finstuned Parameters
Figure Comparison of FLOPs, number of finetuned parameters, and accuracy for FPF(Top) and k- FPF(Bottom) finetuning different combinations parameters. All FLOPs are normalized together to (0, as well as the number of finetuming parameters. "Basis" in the x-label refers to "BN+FC+CONVI" .. Red stars highlight the best accuracy and show both FPF and k-FPF only require to finetune small portion of task- specifie parameters. k-FPF halves FPF's FLOPs.
with the convolutional parameters to adjust the distribution of the output featuremap. In the deeper layers, the functionality of each filter is relatively stable, the distribution of the featuremap need not change drastically.
BN BN Matteyy 1
Dynamics parameters
Weight&Bias Black
BN Weight&Bias Block
10-3
Bn Weight&Bias Block
Bn Weight&Bias Block
10
12
14
16
20
22
Training epochs
Figure 10: The training dynamics of different groups of BN weights and biases in ResNet-18.
A.7 RESULTS OF OTHER NEURAL NETWORKS
In the Tab. the results of various CL benchmarks and FPF MLP and VGG-11 are reported. Similar to the results in T by finetuning the most sensitive parameters in MLP and VGG-11, FPF can further improve the performance of all SOTA CL methods and achieve the best perfor- mance. k-FPF-CE also achieves comparable performance as FPF SOTA methods. Our methods generalize to various neural networks.
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Classification results for CL benchmarks and FPF MLP and VGG-11. Bold and underline indicate the best and second best algorithms in each setting.
Table 5:
CLASS-IL
BUFFER
METHODS
SEQ-MNIST(MLP)
SEQ-CIFARIOCYGG-II)
JOINT
95.5810.33
69.50=1073
SGD
19.6440.07
18.71#0.33
OEWC
20.69+1.34
18.46:10.23
GDUMB
90.6011.377
41.65:10.78
k-FPF-CE
90.6310.57
55.45+1.16
ER
86.73+1.03
46.27+1.18
FPF+ER
91.1510.16
53.48+1.08
AGEM
51.03+4.94
19.40+1.09
FPF+AGEM
89.26:10.52
29.8411.37
500
ICARL
58.12+1.94
45.63+1.94
FTF+ICARL
80.83+10499
48.03::0.65
FDR
83.7914.11
45.56+2.23
FPF+FDR
89.67+0.37
15.5
DER
91.1710.94
51.12:2.477
FPF+DER
91.2510.89
57,46#1.15
DER++
91.18+0.74 91.2210067
47.60+3.23
FTF+DER++
54.69
A.8 PERFORMANCE FINETUNING DIFFERENT PARAMETERS FOR FPF AND K-FPF ON DOMAIN-IL DATASET
In Figure I the performance of finetuning different parameters for FPF and k-FPF on domain-IL dataset PAQ- are reported.
A.9 COMPARISON WITH RELATED WORKS (RAMASESH ET AL., 2020
Paper "Anatomy of catastrophic forgetting: Hidden representations and task sementics" shows that freezing bottom layers had little impact the performance of the second task. (i) Their setting is different: our study and most CL methods focus on the performance of ALL tasks. And it is unfair in terms of parameter amount compare freezing effects of multiple layers/blocks (e.g., block 1-3) vs. one layer/block. (ii) Their result is partially consistent with ours since their unfrozen part covers the last layer and many BN parameters, which the most sensitive/critical part finetune in our paper. (iii) The rest difference is due to our finer- finer-grained study on parameters and on > 2 tasks but this paper only studies two tasks and focuses on the second. Table 6 shows the class-IL accuracy at the end of each task if freezing different single ResNet block (bottom to top: block-1 to block-4). At the end of task-2, 22, our observation is the same as this paper and freezing bottom blocks showing little reduction of accuracy. However, at the end of task 3-5, their performance drops and freezing block-1 drops most.
A. HYPER- PARAMETER SEARCH SPACE
In the following, provide list of all the hyper-parameter combinations that were considered for FPF and k-FPF.
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Under review as a conference paper at ICLR 2023
1.0
FLOPs EE
Acturacy ofR
Nunliberr of brälhable därameters during "inetune
FLOPs EPF+ER
Accuracy of FPF+ER
0.8
Accuracy
0.6
0.4
0.2
0.0
Accuracy K-FPF-CE
FLOPs of K-FPF-CE
Number of trainable parameters during finetune
0.8
Accuracy
0.6
0.4
0.2
0.0
BN
FC
CONV1
BN+FC
BN+CONV1
FC+CONV1
Basis+Block Block1
Basis
Basis+ Block2
Basis+BBocck Block+
Basis+ Block3
Basis+ Block1
Block1-3 Blocs+Blockk-3
Basis
FPF Finetuned Parameters
Figure 11: Comparison of FLOPs, number of finetuned parameters, accuracy for FPF(Top) and k- FPF(Bottom) finetuning different combinations of parameters. All FLOPs are normalized together to (0.1), as well as the number of finetuning parameters. "Basis" in the x-label refers to "BN+FC+CONVI". Red stars highlight the best accuracy and show both FPF and k-FPF only require finetune small portion of task-specific parameters. k-FPF halves FPF's FLOPs. Different from the results of k-FPF in class- in PAQ- since the output classes different tasks are always the same, the last FC layer will not have a large bias on particular classes. Only finetuning BN or CONV1 layers for k-FPF can get comparable performance with ER. Similar to class-IL, IL, since experience replay is not allowed during the training of CL method SGD, little more parameters required to be finetuned by F-FPF to get comparable performance with FPF (about 24. 4.992% of parameters).
17

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Under review as a conference paper at ICLR 2023
Table 6: class-IL accuracy of ER the end of each task Seq-CIFAR- 10
Task-1
Task-2
Task-3
Task
Task-5
No Freeze
97.52 0.23 80.53 + 0.80 63.96 + 0.51 58.05 + 1.91 57.03 + 2.29
Freeze conv-1 97.52 0.23 79.62 2.75 63.28 + 2.13 56.11 + 0.61
55.58 + 1.31
Freeze block-1 97.52 = 0.23 18.8813.001 60.07 = 0.61 55.49 + 0.22
Freeze block-2 97.52 0.23 7.39 63.78
56.23
56.55
Freeze block-3 97.52 + 0.23 80.37 + 2.35 64.31 2.23 57.21
+ 0.40 56.52
+ 0.76
Freeze block-4 97.52 0.23 80.68 + 1.53 64.89 + 1.00 53.78
3.37
54.01 2.07
Table The hyper-parameler search space FPF on different datasets. For all experiments FPE, we use the same number of batch size 32 and finetuning steps 300. The hyper-parameter spaces of finetuning different parameters in the models generated by different CL methods are always same for given dataset. ft-Ir refers to the learning rate during finctuning of FPF.
Dataset
Hyper parameter
Values
OrgIIITT Seq-PathMNIST
Ir
[1. 0.3, 0.1, 0.03, 0.01]
Ir
[1, 0.75, 0.3, 0.05, 0.03]
Seq-CIFAR-10
10
Ir
0.3, 0.1, 0.03, 0.01]
Imageee
Ir
0.5, 0.3, 0.075, 0.05]
Seq-PACS
Ir
[1, 0.5, 0.3, 0.03, 0.005, 0.003]
Table 8: The hyper-parametts search space for k-FPF-SGD on different datasets. For all experiments of k- FPF-SGD, the number of batch size 32 and finetuning steps 100. The hyper-parameter spaces of finetuning different parameters always same for a given dataset. Ir refers to the learning rate during training of CL method SGD, ft-Ir refers to the learning rate during finctuning.
Dataset
Hyper-parameter
Values
Seq-OOrgaAAMNIST
Ir ft-Ir
|0.2, 0.15, 0.1, 0.075]
[0.5, 0.2, 0.15, 0.1]
Scq-PathMMIST
Ir
[0.05, 0.03, 0.01]
Ir
[0.1, 0.075, 0.05, 0.03, 0.01]
Seq-CIFA
Ir
[0.05, 0.03, 0.01]
ft-Ir
[0.075, 0.05, 0.03, 0.01]
Seq-Tiny- ImageNtt Ir
[0.075, 0.05, 0.03]
ft-Ir
[0.1, 0.075, 0.05]
Seq-PACS
Ir
[0.05, 0.03, 0.01]
ft-lr
[0.075, 0.05, 0.03, 0.0075
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Under review as a conference paper at ICLR 2023
Table 9: The hyper-parameier search space for k-FPF-KD different datasets. For all experiments of k- FPF-KD, the number of batch size 32 and finetuning steps 100. The hyper-parameter spaces of finetuning different parameters are always same for a given dataset. Ir refers to learning rate during training of CL method SGD. ft-Ir refers to the learning rate during finetuning. is the hyper- paremmter to balance the two losses.
Dataset
Hyper-parameter
Values
ArggOrATNAMNIST
Ir
[0.2, 0.15, 0.1, 0.075]
ft-Ir
[0.5, 0.2, 0.15, 0.1]
0.5, 0.2, 0.1]
Scq-PathMNIST
Ir
10.05, 0.03, 0.01]
Ir
[0.1, 0.075, 0.05, 0.03, 0.01]
X
[1, 0.5, 0.2, 0.1]
Seq-CIFA Seq-CIFAR-10 10
Ir
[0.05, 0.03, 0.01]
ft-Ir
[0.075, 0.05, 0.03, 0.01]
X
[0.5, 0.2, 0.1]
Ir
10.075, 0.05, 0.03]]
ft-lr
10.1, 0.075, 0.05]
X
0.5, 0.2]
Scq-PACS
Ir
[0.05, 0.03, 0.01] [0.075, 0.05, 0.03, 0.0075]
ft-lr
X
[1, 0.5 0.2 0.1]
19


Reviews:
[{"review_id": "s33tmuVQzcH", "reviewer": "Reviewer_hdv9", "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": "\nThe paper studies the dynamics of different layers in continual learning scenarios, mainly by measuring the shift in parameters. The authors show that only a small subset of parameters (e.g., final FC layer, BN stats) are very sensitive to data drift. To exploit this observation, the authors propose forgetting prioritized finetuning (FPF), which only finetunes a small subset of parameters. In addition, they propose k-time FPF, which replaces the every-step experience replay.", "summary_of_the_review": "Overall, I believe this paper is a borderline paper. Although I believe the contributions of this work is limited, I pretty much enjoyed the direction of understanding NN dynamics in CL, which is done rarely in the literature.\n\n**Post-Rebuttal Update:**  \nI want to thank the authors for their response. Given that the authors have addressed most of my concerns, I would like to increase the score.", "strength_and_weaknesses": "### Strengths\n\n\n- The paper is well-written and easy to follow.\n\n\n- The direction of understanding network dynamics in continual learning is very important.\n\n\n- The proposed method is simple and intuitive and performs well.\n\n\n\n### Weaknesses\n\n\n- First, I should say that I am not sure if the drift in parameters is the best perspective for measuring the dynamics of the layers. For instance, in [2], the authors show that small/large euclidean parameter distance does not necessarily correspond to high/low forgetting, which can depend on many other factors. In other words, you given parameters $\\theta$ at the end of task 1, you can simply find $\\theta_1$ and $\\theta_2$ where $| \\theta - \\theta_1 |  < | \\theta - \\theta_2 | $ but the performance of $\\theta_2$ is better than $\\theta_1$. \n\n\n\n- In addition, as the authors mention in Appendix A.4, some of the presented results (e.g., final blocks being more sensitive) are well-established in the literature [1]. While this work dives a little bit deeper into designing FPF and measuring the compute/performance trade-offs, still, the novelty and contribution of this work are limited.\n\n\n\n\n\n**References**:  \n[1] Ramasesh, Vinay Venkatesh et al. “Anatomy of Catastrophic Forgetting: Hidden Representations and Task Semantics.” ICLR 2021.  \n[2] Mirzadeh, Seyed Iman, et al. \"Linear Mode Connectivity in Multitask and Continual Learning. ICLR 2021.\n\n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "lLsFVb7nZNX", "reviewer": "Reviewer_LsHP", "summary": "", "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": "", "summary_of_the_paper": "This paper proposes a simple technique for preventing the catastrophic forgetting problem in continual learning (CL). By showing that there are sensitive parts in neural network model when learning a novel task, the proposed approach (FPF) just fine-tune the sensitive part of a model after learning sequence of tasks. Furthermore, the additional computation cost for performing FPF the sensitive part is somewhat marginal. In the experiments, authors show that applying FPF can drastically increase the performance of baselines.", "summary_of_the_review": "I vote to marginally accept this paper. Though some experiments are missing, and the proposed solutions are somewhat straightforward, finding out which parts are sensitive to the distribution shift in CL has significant contribution.", "strength_and_weaknesses": "**Pros:**\n\nP1. FPF is simple and highly effective, and showing sensitive regions in the parameters of neural network in CL can be a novel finding. \n\nP2. FPF can be easily plugged-in baselines, and it increases the performance significantly. \n\n**Cons:**\n\nC1. In Section 4.1, the notation in the denominator of the metric for the change of parameters is somewhat confusing. Is it $\\theta_{\\ell,n}^{t+1}$? If it is, is it feasible to use this metric for measuring the dynamics of parameters? \n\nC2. Selecting the sensitive part of the neural network is little bit confusing. How can we select the parts when we use much larger architectures (e.g. ResNet-110)? It would be better to specify the standard for selecting the sensitive region.\n\nC3. There is no comparison between FFP and the method that fine-tune all parameters using memory buffer. I think the results are quite different from \"ER\". It would be better to show the comparison between two methods with respect to the FLOPs and the average accuracy. \n\nC4. There is no experiments on the task sequence containing totally different datasets (e.g. CIFAR-100 & MNIST). The trends that Conv & FC layers are sensitive would be different from the experiments in the paper.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "Y31MHe69FM", "reviewer": "Reviewer_8gaT", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper goal is to study which part of specific neural architectures is mostly affected by catastrophic forgetting in Class Incremental (CI) and Domain Incremental (DI) continual learning, to apply specialized fine tuning to those parts with the purpose of reducing interference. The 1-norm of $l$-th layer weight change between consecutive CL tasks is used as metric to measure which layers are affected most. Two finetuning procedures are provided, with one designed to optimize computational cost of memory consolidation. The method can be hot-plugged to several CL methods in literature. ", "summary_of_the_review": "While the paper has good motivations in abstract (finding a general and efficient procedure for parameter consolidation), it fails to deliver convincing insights, due to lack of technical detail, reduced novelty and scarce generality of the results. Overall the weaknesses quite heavily surpass the merit. ", "strength_and_weaknesses": "-- STRENGTHS –\n(+) The empirical analysis is quite articulated both in terms of number of benchmarks being considered as well as in terms of related CL strategies being assessed. The work is mostly empirical, both in its conception and its execution, so this part is quite well-done.\n\n(+) The generality of the approach is certainly positive: the fact that it can be applied to existing CL strategies is a plus, which stems from the simplicity of the approach.\n\n(+) A careful consideration for the computational costs, in a research topic that is often motivated by the necessity of making neural training sustainable, is an added strength and well motivates a part of the work.\n\n-- WEAKNESSES –\n\n(-) Despite the attempt of rooting the work on considerations about task interference and drifts, this paper is mostly based on an rule-of-thumb intuition (quite an unsurprising one) which is not backed up by convincing theoretical nor empirical motivations. The attempt at providing an empirical motivation in Section 4 is unconvincing because of there is no logical consequence between the  results of the experiments and the implementation of the FPF strategy. The hints from the empirical analysis are either trivial (i.e. fine tune only the closer-to-output-layer weights) or very architecture specific (i.e. in some cases it is best to tune the outer layers but also the early layers, but not the middle ones). This kind of insight is not actionable by the community as it is not enough general. \n\n(-) Generality and impact of the strategy are also severely limited by the choice of the CL scenarios. It is straightforward to see how a metric based on instantaneous change in weights between adjacent tasks can work in CI and DI settings, as in these cases there is a clear distinction between tasks at training time, which in the CI setting is also mirrored in task-specific components of the architecture (multi-heads). The work could gain considerable strength if it can be shown that the insights and strategies can work less ideal scenarios, such as class incremental with repetition (reoccurring tasks) and single class incremental learning (no architectural segregation between tasks).\n\n(-) The exact details of the FPF strategies are nowhere to be found. Only a vague description of the intuition is provided by the details of the strategies are not provided. For instance it is not clear (until one reaches the experiments) if a buffer is needed, and what is the strategy to populate it. One would like to know how one chooses the portions of the network to include/exclude in FPF. By reading the paper it should be possible to replicate the strategy on different problems and architectures, but this is not the case given the lack of details in the current formulation. The paper should definitely be extend to include pseudo-code and other formal description of the strategies to make everything reproducible and generalizable. \n\n(-) Linguistic quality is sometimes borderline, especially in parts of the experimental section whose writing might had been rushed. Another round of proofreading is highly advised. \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "Jaf38aLVWS", "reviewer": "Reviewer_pB6S", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper conducts a series of empirical studies for continual learning about the sensitivity of different network parameters, and shows some interesting observations. Based on the observations, this paper explores a Forgetting Prioritized Fine-tuning strategy for continual learning. Empirical results demonstrate its effectiveness.", "summary_of_the_review": "Overall, I like the empirical observation of this paper which may inspire some future research. However, there are still some questions to be resolved. I expect to responses from the authors.\n\n**********Post rebuttal*************\nAfter discussion with the authors and other reviewers, I suggest the authors to improve the paper by further analyzing the found observations about their in-depth reasons and making the proposed method more adaptive regarding the selection of layers and hyper-paramters.", "strength_and_weaknesses": "Upsides:\n+ This paper analyzes the sensitivity of different network parameters in continual learning, and shows some interesting observations.\n+ The empirical studies are solid and the writing is easy to follow.\n+ A new Forgetting Prioritized Fine-tuning strategy is proposed. By lazily conducting replay, the proposed method achieves comparable performance with lower computation costs.\n\n\nDownsides:\n- How to adaptively select the task-specific parameters for fine-tuning? This paper only provides an empirical study for it, but a well-designed adaptive strategy is expected based on your empirical studies. In this case, the contribution of this paper will become more significant.\n- In Table 1, does any specific method perform the best with the proposed FPF? It seems that there is no consistently state-of-the-art method when combining FPF.\n- The colors of Figure 4&5 are too complex, making it hard to understand. It would be better to simplify this figure. \n- Many previous studies find that the higher layers are more sensitive. Please discuss more Figure 7. Why are lower BN layers more sensitive？ There may be some interesting discussions.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject