Combating Inter-Task Confusion and Catastrophic Forgetting by Metric Learning and Re-Using a Past Trained Model
Authors: Sayedmoslem Shokrolahi
IL MIN KIM
Venue: Accepted by TMLR ()

Abstract: Despite the vast research on class-incremental learning (IL), the critical issues have not yet been fully addressed. In this paper, utilizing metric learning,  we tackle two fundamental issues of class-incremental learning (class-IL), inter-task confusion and catastrophic forgetting, which have not been fully addressed yet in the literature. To mitigate the inter-task confusion, we propose an innovative loss by utilizing the centroids of previously learned classes as negatives and current data samples as positives in the embedding space, which reduces overlaps between the classes of the current and past tasks in the embedding space. To combat catastrophic forgetting, we also propose that the past trained model is stored and re-used for generating past data samples for only one previous task. Based on this, we further propose a novel knowledge distillation approach utilizing inter-class embedding clusters, intra-class embedding clusters, and mean square embedding distances. Extensive experiments performed on MNIST, CIFAR-10, CIFAR-100, Mini-ImageNet, and TinyImageNet show that our proposed exemplar-free metric class-IL method achieves the state-of-the-art performance, beating all baseline methods by notable margins. We release our codes as the supplementary materials.

Published in Transactions on Machine Learning Research (02/2025)
Combating Inter-Task Confusion and Catastrophic Forgetting by Metric Learning and Re-Using a Past Trained Model
Sayedmoslem Shokrolahi
20ss184@quenssu.co
Department of Electrical and Computer Engineering Queen's University
II-Mi Kim
ilmnn kim @queensu.co
Department of Electricol and Computer Engineering Queen's Universily
Reviewed on OpenReview: https: openreview. net/ forum? id= (R
Abstract
Despite the vast research on class-incremental learning (IL), the critical issues have not yet been fully addressed. In this paper, utilizing metrie learning, we lackle two fundamental issues of class- incrementetl learning (clas--L), inter-task confusion and catastrophic forget- ting, which have not been fully addressed yet in the literature. To mitigate the inter-task confusion, we propose an innovalive loss by utilizing the centroids of previously learned classes as negatives and current data samples as positives in the embedding space, which re- duces overlaps between the classes the current and past tasks in the embedding space, To combat catastrophic forgetting, we also propose that the past trained model is stored and re- used for generating past data samples for only one previous task. Based on this, we further propose novel knowledge distillation approach utilizing inter-class embedding clusters, intra-class embedding clusters, and mean square embedding distances. Extensive experi- ments performed on MNIST, 10, CIFAR-100, Mini- Mini-ImageNet, and TinylmageNet show that our proposed exemplar- free metric class-IL method achieves the state-of-the-art performance, beating all baseline methods by notable margins. We release our codes as the supplementary materials.
1 Introduction
Incremental learning (IL) is the learning paradigm in which the model learns from sequential input data without accessing all past data. In any II,, fundamental goal is to remember all seen experiences as much as possible at each point in time. In practice, however, IL easily suffers from a critical issue of catastrophic forgetting (CF) French 1999); De Lange et al. (2021) Zhou et al. (2024) that model entirely or substantially forgets what it has already learned. This poses a significant challenge
scenarios, as the model needs to previously acquired knowledge.
adapt new information without undermining
IL settings can be largely categorized into (i) lask-based and (ii) (ask-free van de Ven et al. (2021). The task-based approach itself includes task-IL, domain-IL, and class-IL van de Ven et al. (2021). ). In task-IL problems, the task identity is always available in training and test, making it the casiest sctting in II. In both domain-IL and class-IL settings, task identity is not provided at the test time. Particularly, in the class-IL, the model must infer the lask identity during the test. phase, which not a requirement of the domain-II. Meanwhile, the task identities are inaccessible during the training and inference phase in task-free cases.
In class-IL, which we focus on in this paper, not all performance degradation can be attributed solely the phenomenon of catastrophic forgetting. Another significant factor contributing to performance decline

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Fixed Trainable
triplets
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Figure 1: Training of the proposed method. To learn the current task without over-fitting, actual current data Da are supplied to the trainable encoder Mq to construct triplet loss, Ltri- To avoid inter-task confusion, using the stored centroids of the past classes, 94-1, as negative samples in conjunction with positive samples extracted from the current dataset Da: we construct the inter-task confusion regularizer, LTCR- To tackle the catastrophic forgetting, we design KD loss LKD by supplying the synthetic past data G3 to both Mr and the stored (fixed) past encoder M three main losses. In the test phase, the trained encoder M₁ is extracted and used as the nearest mean classifier (NCM).
is the confusion between the current task and past tasks, called the inter-task confusion (TTC) Masana et al. (2022) Huang et al. 2022 2023 Nori & KIM 2024). Inter-task confusion arises in class-incremental learning (class-IL) IL) when a model struggles to differentiate between classes belonging to different tasks during testing. This occurs because the classes from distinct tasks are never seen together during training, and the model not explicitly taught to distinguish between them. As a result, the learned features are not optimized to discriminate across tasks, leading confusion when all tasks are evaluated together without access task-specific identifiers. For instance, while each task's classes are trained separately distinguish their own categories, the discrepancy between classes from different tasks remains unresolved, rosulting in misclassifications across tasks. This phenomenon becomes particularly evident when task-IDs must be inferred at test time.
Although these two concepts often have not been elcarly distinguished in the literature, the ITC and the CF should be treated separately because the former refers the confusion between the current and past tasks, whereas the latter refers to forgetting the past tasks. Further analysis of the impact of these two concepts on performance is presented in Subsection 4.5
In recent works IL, many researchers have proposed various approaches to improve the performance of class incremental learning by tackling CF. Mitigating CF can implicitly reduce ITC with different degrees, e.g., replay base method with infinite memory should be able to address both CF and ITC. However, we argue that tackling ITC explicitly will potentially improve the performance further realistic scenarios. Representative methods so could be categorized into four main groups De Lange et al. (202T): (i) replay methods, (ii) rogularization-based methods, (iii) paramcter isolation methods, and (iv) hybrid methods. In the replay methods, part of the data. from previous tasks stored past data are hestiee to alleviate catastrophic forgetting Rebuffi al. (2017): Chaudhry et al. (2019). In the regularization-batt based methods, regularization terms are added to the loss function, possibly combined with the approach of knowledge distillation (KD) Rannen et al. (2017). In the parameter isolation methods, the parameters of the model are controlled to address the issue of forgetting by preventing interference between the current. task and past tasks Serra et al. (2018).
Our proposed approach, shown in Fig, 1 can be categorizod the hybrid method combining regularization and generative replay in the class-IL. II. setting. In scheme, aim to (i) mitigate the inter-task confusion
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and (ii) combat catastrophic forgetting, while we use the triplet loss Liss to train the model My for the current task using the current actual data DR, only which we are assumed to directly access.
First, we pay a special attention to the confusion between the classes of different tasks, ie., the inter-task confusion Masana et al. (2022), ; which results in significant performance degradation in the class-IL. To overcome this challenge, we propose a novel regularization term, LTCR, using the embedding centroids of previously learned classes as negative samples and the embeddings of the data samples of the current task positive samples. The current model Mg is trained such that current classes are located away from previous classes in the embedding space using the positive and negative samples.
Second, catastrophic forgetting is a critical issue in any IL including class-IL. To mitigate the catastrophic forgetting, we store the past model M-1 trained in the last lask time A - and use it (while freezing it) to train the current model M2 in two ways, We first use M to syuthesize past data samples belong to the very last task Gz. which will be used for training Mg. Note that we do not store any actual samples of previous lasks; instead, we synthesize past data samples by storing and re-using past trained (now, fixed) model. We also use M the teacher to teach the current model Mr, the student. This is based on the inspiration that, from the perspective of the past knowledge, Ma-1 1 is the model having such knowledge whereas M₁ is the model to be trained to learn such knowledge. For efficient knowledge distillation (KD) of the past task from Ma-1 to MR. we will design a new loss, LKD, by fully exploiting the properties of embedding structures in class-IL. The main contributions of our work can be summarized as follows:
Using the centroids of previously learned classes as negative samples, we design a regularization term customized to overcome inter-task confusion.
We propose a highly effective KD method the embedding space to combat catastrophic forgetting. To this end, we also propose a method for synthesizing past data samples by storing and re-using past trained model Ma-1- Using MA-1, at current task k, we only generate samples belong to (k 1)-th task.
Extensive simulations are performed, which demonstrate that our proposed scheme achieves the state-of-the-art performance in the setting of class-IL.
2 Related works
2.1 Regularization, Replay, and KD in IL
In II, we must prevent over-fitting in each new task and, at the same time, we must stop forgetting past (asks. For the purpose reducing lorgetting in II, general regularization methods used for handling over- fittings such as dropout Goodfellow et al.] (2013) and early stopping Maltoni Lomonaco (2019) might be used; but they are not very effective in IL. Instead, searching for important weights keep them unchanged with regularization terms is more effective way Bühlmann & Van De Geer (2011)
With advances in generative models, generative replay methods grab enormous attention in II. scenarios. A parallel generator and a solver model were used in Shin et al. (2017) to create synthetic images as replay data in the IL case. More complex issues were investigated in the brain-inspired method van de Ven et al.
2020 They used generated representations in the replay phase instead of using synthetic images. Cost-Free IL PourKeshavarzi et al. (2022) proposed a memory recovery method that helped the current network remember past information without storing data. Error sensitivity modulation experience replay (ESMER) Sarfraz et al. (2023), proposes that the model should prioritize learning from smaller losses to minimize significant feature drift, adjusting learning rates dynamically based on error consistency.
Transferring learned knowledge from the already trained neural network to a new raw nelwork is proved to be useful in many machine learning applications. Most the solutions for this kind of knowledge transfer are based on the concopt of KD Hinton et al. (2015). In II. the distillation of knowledge could be performed across tasks, and various methods used KD-based transfer learning Schwarz et al. (2018); Dhar al. (2019)
Bhat et al.) 2004)) Chen et al. (2024): Liang & Li (2224).
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2.2 Soft-Max Classifiers and Metric Learning in IL
The goal of deep metric learning is to train differentiable model so(:) X - Rp that maps input domain X' to a (compressed) embedding domain I' together with a distance metric d E IR such a way that similar data samples result in a small distance and dissimilar data samples produce a large distance. To this end, loss functions in metric learning need to be properly designed to find iisiaaatttesddssimmlaiittt between samples in the embedding space.
In most static learning scenarios (i.e., the standard non-IL scenarios), using softmax loss in classification problems has proved to provide firm performance. When it comes to IL, however, there exists an inherent deficiency in softmax loss, because softmax loss is essentially focused on drawing lines (i.e., decision bound- aries) between different classes in the embedding space. Fig. 2[a) shows the embeddings of two different classes in task 1. In task 1, because the actual data samples of the two classes are available for training, we can draw a line between the two classes, which is denoted by decision boundary 1. In the next task time (task 2), which shown in Fig. b), new actual data samples for two new classos are provided for training; so, it is again possible to draw a line between the two new classes, denoted by decision boundary 2. However, because the past data samples of task 1 are not accessible anymore, it is difficult to draw the optimal line, denoted by the ideal decision boundary, that distinguishes all the four classes seen so far. Such optimal boundary could be drawn only if all the data samples including the past classes were accessible. This is a fundamental limitation of the approach based on softmax classifiers. We note that sofumax loss does not directly (or explicitly) try to minimize the size of each cluster of embeddings nor maximize the distance between clusters of emboddings in the embedding space. The fundamental difference between static lcarning and IL is that, in II, we do not know where the new embedding clusters will be placed in the embedding space in the future tasks. For this reason, softmax loss might not be the best approach in IL.
In IL, an alternative approach is to use deep metric learning with similarity /dissmiilarity loss function such as a triplet loss. Minimizing the triplet loss encourages putting the same class data samples closer to each other and putting different: class data samples farther from one another, in the embedding space, which results in a smaller size of each embedding cluster of each class and a larger distance between embedding clusters of different classes. Fig. B(a) shows two embedding clusters of two classes in task 1. In task 1, by optimizing the triplet loss, the size of each cluster is minimized and the distance between the two clusters is maximized. As shown in Fig. 3b)) in task 2, two new embedding clusters of two new classes are introduced to the embedding space. Again, by using the triplet loss on the data samples of the two new classes (but not on the data samples of the past two classes), the size of each of the two new clusters is minimized and the distance between the two new clusters is maximized. Then, the chances that any of the two new clusters happen to overlap with any of the old clusters become small in the metric learning, because each of the four clusters was/is is minimized, and two clusters in each task were/are separated as much as possible. This the reason why the approach of metric learning is inherently more suitable for IL.
The triplet loss uses three instances: (i) an anchor (za), (ii) positive data sample (zp) having the same label as the anchor, and (iii) a negative data sample (I.,) having different label. Considering distance metric d(i,.)) on the embedding space (e.g., squared Euclidean distance), the triplet loss is defined as Leri(z) = max(0, d(za, - d( + m) for a single triplet input (Ia: Tpp zn)). The goal is to satisfy d(Ia: zp) - d(ra; zn) + m < O, which means making d(Ia: smaller than d(z,,, xw) by a predefined margin m. During inference, we use the nearest class mcan (NCM) classificr Yu ct al. (2020).
3 Proposed Scheme
3.1 Incremental Learning Formulation
At the initial stage, a model Mo is trained from scratch in the standard non-incremental manner using training dataset. Do containing Co classes in a classification application. Then new datasets Dr, each having additional new C' classes, are sequentially collected and supplied to the model Mr one by one so that M2 is trained only on D2 at cach task in the incremental manner for I...., K, where K is the total number of incremental tasks, The current model Mj does not have any access to the actual past data, D.. = 0, k.......-
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decision boundary'
ideall decision boundary
decision boundary
decision boundary 1
(a) Emmbeddings of two classes task
(b) Extra embeddings two additional classes are added task
Figure 2: Softmax classifiers.
cluster size minimized
cluster distance maximized
cluster size
minimized
cluster size is minimized
cluster distunce maximized
cluster size
minimized
Embeddings of two classes in task 1.
(b) Extra embeddings of two additional classes added task 2.
Figure Metric learning approach.
For performance evaluation in the test phase, we use the average accuracy and forgetting, which are the widely adopted standard performance metric in IL Chaudhry et al. (2019 2018a); Yu et al. (2020). After training all K tasks, the average accuracy Aς is given by Ag = R Σ Ej= ak,j where a,,j is the test accuracy of the model that has been incrementally trained from task to on the held-out test set of task j.
Forgetting defined for the j-th task after the model has been trained incrementally up to task k. where k > j. as in Chaudhry al. (2018ah: of: max (at,s ag.s). Vj < k. Considering of E I-1, 1], defined for j k, our locus lies quantifying forgetting across preceding tasks, and ak the test
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accuracy of the model that has been incrementally trained on the held-out test set of task j. Furthermore, by standardizing against the count of previously encountered tasks, the average forgetting at the k-th task is denoted as O₃ T= j== og.
3.2 Overview of Our Proposed Method
The fundamental idea of our proposed method is to intelligently control the sizes and positions of embeddings of the classes of the current task considering the embedding locations of the past tasks in the embedding space to (i) avoid inter-task confusion and (ii) prevent catastrophic forgetting. The overall structure is illustrated in Fig. | Our proposed model is composed of two encoders (Mx and Mx-1); the current input datasct (Dx), the set of stored centroids of the past classes (94-1); and the generated datasct (Gx) of the past data samples. At the current task k, the encoder denoted by Mr is trained by using Da. Qk-1: and Gk, whereas the other encoder indicated by Mk-1, which was trained in the last task A 1 and has been stored, is fixed. Note that, in Pg-1, only single centroid (not multiple samples) for each past class is stored, which must be stored for NCM. In our proposed method, the current model M& is trained by Leri to learn the current task using the embeddings H2 which are produced when the dataset D₃ of the actual data samples for the current task are supplied as input. To be more precise, H₂ = [hg:.... A&] E Rpx denotes the normalized embedding matrix produced by trainable student model Ms. using real current task datasel. The dimension of embedding space is p and batch size is b.
To address the intertask confusion, we introduce Lren, through which Ms learns how to avoid any confusion between the current lask and the past tasks utilixing previously stored embedding centroids of past classes (14-1) as negatives in conjunction with H₃ as positives.
The other critical issue is to combat catastrophic forgetting. To this end, we use a data generator that is composed of input & (this is initialized as random noises) and the previously trained (now, fixed) encoder Mę-1 in order to generate the synthetic images G3 of the classes of the past task(s). These synthesized past images in Ga are used by M and Ms such that Ma-1 (as the teacher having strong knowledge of Gk) teaches Mg (as the student who has not learned G. yet) about the past knowledge G2. Specifically, Ge is supplied as the inputs to both encoders, M& and M3-1, to produce the embeddings Z and Z respectively. These embeddings are used together to construct the KD loss, LKD- Note that the (fixed) encoder Ma-1 is used for two different purposes in the current task: (i) to generate the synthetic images G5 of the past classes and (ii) to teach My the past knowledge as a teacher. Overall, the proposed total loss function for training Mj is composod of three main terms:
Las. Leri + XLTTRR + LKD.
(1)
where Lesi is the triplet loss used to train the current model Mj with the current available data Da (for implementation details, see Appendix), and the other two losses, LTer and LKD, are explained in more detail in what follows.
3.3 Inter-task Confusion Regularizer, Lrcn, to Combat Inter-task Confusion
This loss, LTCR, is proposed to avoid any confusion between the current task and any past tasks. Ideally, class-IL must be able to accurately differentiate between classes across tasks as well as between classes within each task. In class-IT., however, it is very challenging for the model to effectively discriminate between the classes across tasks because the model is distinctively trained for each individual task. This fundamental challenge is inevitable because the model cannot see the data for the classes together in training when they belong to different tasks. This challenge in class-IL, known as inter-task confusion Masana et al. (2022). is illustrated in Fig. 4b). Note that the triplet loss focuses solely on each task one by one, meaning that it does not make any effort to avoid collision between the cluster of a class belonging to the current task and that of another class belonging to any of the past. tasks, which results in inter-task confusion. To mitigate this inter-task confusion, we propose a regularization term that is specifically designed for the class-IL paradigm.
The fundamental idea of our proposed scheme is that, in metric learning, the cluster centroids are anyway stored in the course of training to be leveraged later for inference and this information be effectively used
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class current task
Inter-task confusion
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(a) In current task, triplct loss (b) The clusters classes current (c) Inter-task Confusion Regularizer, creases (the green arrows) the cluster size task those past tasks might overlap LTCR. increases inter-cluster dis- of each class and increases (the ar- in the embedding space, which inter- tance between classes of different tasks row) the inter-cluster distances between task confusion. This cannot mitigated any two classes of the current task in the by triplet loss. embedding space.
in the embedding space. Specifically, the distances between the data samples (the hollow diamonds and crosses) of the classes of the current task and the centroids (the black squares) of the classes of all past tasks are increased (the orange arrows) by Lrer in the embedding space.
Cluster size of each class in the current task decreased by triplet loss.
Inter-cluster distanees between classes of the current task are increased by triplet loss.
Inter-cluster distances between any classes of the current task and any classes of the past tasks are increased by task confusion regularizer.
Figure Triplet loss, inter-task confusion phenomenon, and inter-task confusion regularizer.
to mitigate inter- task confusion. Specifically, we propose a new loss, LTCR, which utilizes cluster centroids of the classes of all past tasks as negative samples while the positive samples are the randomly selected data points with noise in every class of the current task. In other words, the positives are random subset of embeddings Hg which are produced when the dataset D& of the actual data samples for the current task are supplied as input to trainable model My. This loss encourages the distance between the data samples of the current classes and the centroids of the past classes in the past tasks to be larger than predefined margin mTCR in order to effectively avoid the overlap between classes across distinct lasks, thereby addressing inter-task confusion, as shown in Fig. c). Mathematically, the loss is given by
LICR max (0, MTCR d()p. Vo' 24-1-
(2)
where Ep denotes the positive samples. Also, par indicates the negative samples, which are the centroids of the class v', and Q411 is the set of class indices from the first task up to task k-1. To facilitate increasing the distance effectively, as in the triplet loss, we use a margin MTCR- The size a mini-batch for constructing LICR is the same as in the triplet loss, which is
3.4
KD loss, LKD. to Combat Catastrophic Forgetting
This loss, LKD, is proposed to address the issue of catastrophic forgetting. It is composed of three innovative knowledge distillation loss terms for transferring the knowledge of the previous tasks that had been learned by Ma-1 (the teacher) to the current model Mş (the student) as follows:
LTD maee
(D KD T.KD
intra intter)
(3)

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where A and A are hyper-parameters to control the impact of cach term. To construct these three KD losses, we utilize the synthetic data Gj. of the last task inputs to both Mj and Mx-1- Therefore, we will begin by detailing the process of generating Gg in the following subsection. Subsequently, each of the three KD losses will be explained one by one.
3.4.1 Generating Past Synthetic Data Ga
In II, one of the most effective approaches to prevent catastrophic forgetting is to access some of the previous data in training. This approach, called the replay stralegy, is classified into two lypes: (i) coreset replay Rebuffi et al. (017)) and (ii) generative replay [Sun et al. (2021). In the approach of coreset replay, by storing small amount of actual previous data samples, IL is facilitated. However, this approach cannot be adopted when data privacy matters. In this case, the other approach of generative replay might be considered. GANs are a popular model to be used as generative models in II. Lesort et al. (2019): Cong et all 2020)) Variational autoencoders (VAEs) are also valuable as a generative model in both supervised and unsupervised IL Casclles- Dupré et al. (2021]; p: Kemker & Kanan (2017). In the setting of class-IL, however, incrementally training generalive models such as GANs or VA can be challenging because the training data is presented incrementally. Indeed, discussed in van de Ven et al. (2020), in the class-IL setting, generative replay works well for small data sets (e.g., MNIST LeCun
LeCS et al. 1998) ), but scaling it up to non- small ones (e.g., CIFAR-100 Krizhevsky (2009), TinylmageNet Le & Yang (2015)) ) is not straightforward. Also, because such incremental training of generative models is typically distinct from incremental training of the discriminative model performing classification, the overall training complexity goes up. To address these issues, in this paper, we propose a more scalable and effective approach for generative replay without additionally training a dedicated separate generative model.
The core idea of the proposed replay approach is to store and ro-use a previously trained model for generating synthelic past. images. Specifically, the model M that was trained in the last task time k - 1 is stored and used for the purpose of generating past data samples, which in turn are used to help the training of the current model MA, as shown in Fig. [ Note that we do not introduce any separate or distinct generator such as GANs or VAEs for generating past data samples; instead, al each lask time, we store a single (past trained) model and re-use it for the training of the next. model. Here, the critical question is how to generate past data samples using a trained discriminator M which is discussed in the following.
For generating conditonniiional synthetic images using (fixed) trained model, in Yin et al. (2020), very effective method, called the Deep-Inversion, was proposed. In this paper, we also follow the approach of Yin ltt al. (2020) for generating class-conditionn synthetic images. The fundamental idea of Yin et al. (020) is to minimize the distances of the means and the distances of the variances between the actual images I E D and the synthesized (generated) images & E G. In training, & is initialized by random (Gaussian) noise and gradually updatod to get close to the actual image, x. Mathematically, for a model that was trained on D, the following regularization term Ra($) is used Yin et al. (2020):
Ro(G) Σ (0)0)-((rrlan) ||+ - l1.
where vi(()) and (f) are the mini-batch-win mean and variance, respectively, at the hth convolutional layer when the input to the (fixed) model is é. In the same way, v1(z)) and df(2) are defined for x. In the setting of IT, however, it is not possible to exactly determine viz (x) and (x)) because the model does not have any access to the original past datasct D. Nevertheless, (D) and (x))()) can be estimated by the stored past trained (fxed) model, because the running average statistics are actually stored in the widely-used BatchNorm layers of the model.
In our proposed method, the technique of Yin et al. (020) cannot be directly used, because we work in the embedding space. To make it work in our proposed method, we change the structure of the model (Yin et al. (2020) and we use a different overall loss function. Our approach involves generating class-conditional images in the embodding space by utilizing the embodding centroid of each class. We adopt minimizing the Euclidean distance between the input noise and the class embodding centroids as one term of the loss function (instead of using the softmax layer and cross-entropy as in Yin et al. (2020)), ) and the regularization
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term in 4 as the second term. Overall, using the fixed model (i.e., the past trained model Mx-1), the synthetic images Gg are constructed for target class by the following optimization:
min Lg min ( 14) + No (x)))
(5)
where j is the embedding centroid for the target class of the last task, A is the scale for the regularization loss, and ji is Euclidean distance.
As shown in the past data generator block of Fig. I for training the current model Ma, the generator is composed of the input image & (initialized by the noise) and the fixed (stored) model Ma1 that was trained in the last lask time k 1. In principle, using the model MK-1, one might atlempt to generate the synthetic images for all past classes from the very first task time to the last task time k 1, because ideally M had learned all classes up to task k 1. However, it turns out that such an approach does not work well due to unavoidable forgetting of the past knowledge.
From our experiments, we found that the best IL performance was achieved when M--1 was used to generate the synthetic images of the last task time k - 1 only, compared to the case of synthetic images of the last task time k - 1 and any older tasks. The benefit of generating the synthetic images of the last task time 1 only is that the computational complexity required for generating synthetic past images is substantially lower, which makes our proposed scheme scalable.
Based our extensive experiments, found that the subjective image quality of syuthetic images is important only up to certain extent (i.e., truly high-quality images are not required) when using them in our proposed KD method, allowing us to reduce the number of iterations for generating images without significant per performance loss. The average accuracy of our proposed IL. method versus the number of iterations used for generating past synthetic images for CIFAR-10 is shown in Fig. Faa. As can be seen, increasing the number of itcrations beyond 40 does not further improve the average accuracy of our scheme. In this paper, therefore, we set the number of iterations to 40 for CIFAR-10 and 80 for all the rest datasets (as opposed to 3,000 in Yin et al. (2020)), of which computing complexity is not high. In Fig. 5b),, forty eight samples of generated synthetic images with a ResNet-18 network trained on CIFAR-10 are illustrated. We consider three different iteration number for generating each 16 synthetic images including 20, 40, and 1000 iterations. In this simulation, our setting is A, = 10 with Adam optimization and the learning rate of 0.06. The superior visual quality of synthotically generated images is apparent with 1000 itcrations (bottom 16 images in Fig. b)),, surpassing the quality observed with 40 iterations (middle 16 images in Fig. (()).. However, it is crucial to note that achieving such high pixel-level quality not necessity for our proposed method. Our primary focus lies in capturing the overall distribution within our knowledge distillation approach.
Additionally, our experiments show that the number of required synthetic images is much fewer than the actual images. Based on the experiments, we choose the amount of synthetic data for the last task to be only 25% of the actual data for the current task. It effectively addresses the issue of generation time, which also contributes to training time. To the best of our knowledge, in the literature, no generative replay-based IL method has used such a scalable generating process by re-using a previously stored model both as a lightweight generator and teacher to distill past knowledge into the current model simultancously. The impact of varying ratios of synthetic images is presented in Appendix A.I
3.4.2 MSE Regularization Term, L
Using the synthesized past images GR, we introduce a regularization term, which is inspired by self-supervised learning. Minimizing the distance between two embeddings of two differently augmented versions of single input has proved to be powerful strategy in self-supervised learning Bardes et al. (2022). Inspired by this, we propose to use similar loss term, namely, the Mcan Square Euclidean (MSE) distance regularization term, Lise- Our idea is to prevent the knowledge learned in the last task from being forgotten by minimizing the distance between two embeddings produced respectively by the last model M&-1 (teacher) and current model Mj (student) for the same last data Gg. Specifically, we supply the same input G₁ (i.c., the synthetic images for the last task) to the current trainable model Mg and the stored (fixed) last model Ma-1- For training of Me, we then minimize the distance between the two sets of embeddings produced by those two
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Average Accuracy (%)
70
50
40
30
20
10
20
40
80
300
500
1000
# of iterations
(a) Average accuracy for the different number of iterations CIFAR- using our proposed method. The results indicate that the number of iterations does not have be very large.
(b) Forty eight generated synthetic images (32x32) for three different numher iterations: (i) iterations top images, (ii) iterations middle im- ages, and (iii) 1000 iterations is bottom images. A ResNet-18 18 is trained on CIFAR-10.
Figure 5: Synthetic images versus the number of iterations.
models. This way, the embedding space, the current model M2 will learn the knowledge of the embedding positions that had been learned by Ma-1 for the images G& of the last task k
To mathematically formulate the loss, let 7 [E],.... .... E Rox* denote the un-normalized embedding matrix produced in the current task time & by the trainable model M2 when the inputs are the synthetic images, GR. Similarly, Zi = [2]] ..... 2 E ÆpX= represents the un-normalized embedding matrix produced in the current task time k by the fixed last model Ma-1 when the inputs are the same synthetic images, GR- The vector 2 is the p-dimensional normommalized embedding vector obtained by model Mj when the imput is the jth synthetic image zz E Gk in a banih composed of images. The column vector x is defined in the same way, but by Ma-1. Our proposed regularization term is the element-wise MSE distance wetw the two embedding matrices, L mase-
[
11 2 1 E 2/
Alternatively, one might try to use different distance measures such dissimilarity losses. However, based our simulations, MSE exhibited the best performance. For the detailed simulation results, see Fig. in Section 4.4
absolute error (MAE) cosine
3.4.3 Intra-class and Inter-class Regularization Terms, intra and LDD
inter
In order to further mitigate the catastrophic forgetting, propose two additional loss terms, through which the past model M+-1 teaches M& how to not forget the knowledge of the past data in the embedding space,
as illustrated Fig. 6 Specifically, the intra-class loss and the inter-class loss are designed respectively by constructing intra-class and inter-class embedding scatters at the level of each mini-batch. Let Gi G denote the subset of G that contains the synthetic images of the 7th class only (in the last task), i I....,C. where C' is the number of classes in G& (i.e., the number of classes for the last task, k - 1). Letting (9i, [0A,v) E TR to represent the normalized
denote the number of images in GLA, we use Zi, = [= =,,K" embedding matrix produced by the current model Mj when the inputs are the synthetic images in Gi The vector <1,, represents the p-dimensional normalized embedding vector produced by Mj when the input is the 5th image of class i in Gi The class mean of the embedding vectors 2/,8 for class i is determined by: Σ) G..al == K We will construct scatter vectors the level of Aini-batches, each of which is of size
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jata
"D
|s um
Sk
interr
||
Sines
H
2,2
H.
Sinee
(a) Embedddngg produced (in the current task time k) by M using the synthetic images Gj for the three classes of the last task, - 1. Intra-class scatter matrices S s'intra and inter-class scatter matrices 1
(b) Embeddings produced (in the current task time k) by Mr using the synthetic images G3 for the three classes of the last task, k 1. Intra-class scatter matrices Sintra and inter-class are shown. To prevent forgetting the knowledge learned by MR-1, 1s we minimize the displacements from Skintra to Sintra, and from Sinter to Sinter, over two consecutive task times.
1.
are shown.
scatter matrices S,
Figure 6: Knowledge distillation through intra-class and inter-class losses.
n.. Recall that each mini-bac batch contains the synthetic images only for classes (not C). Then the mini-batch mean over e classes is given by μa = Si-1 Mi,k-
At the mini-batee batch level, we now define the inter-class scatter Sinter in the current task time k, which is constructed from the outputs of MR: for the synthetic images G5 of the classes in the last task k 1 as Sinter (pi, p ,,...,c.. C. In the same manner, Si S'inter is defined constructed in the current task time & from the outputs of M&-1, for the images G2 of the classes in the last task k- - 1. In order to transfer the knowledge from MR-1 (teacher) to Ms (student) about the embedding cluster distances among different classes learned in the last task h 1,1, 1, we design the inter-class regularization term Lib by penalizing the change from 5 g'inter to Sinter as follows:
the inter-class scatter, which is
i,k
i,
L Lintrr
Σ
Sinter S'inter ||. -5ik
(6)
KD
The second part of the information that we try to keep unchanged in learning the 1th task is the intra-class scatter denoted as gintra The Sintra constructed the current task time & from the outputs of Me. for the images Gk the classes in the last task h - S =
19.x| (2/, - M4,x), (,
Similarly, S'nttra is defined as the intra-class scatter, constructed in the current task time & from the outputs of Mg-1, for the images G₁ of the classes in the last task - 1. Our goal in the intra-class loss, denoted LKD is to penalize the change from S'intra to Sintre in order to transfer the knowledge (from M to M₂) about the embeddings within each class learned in the last task k 1-1. 1.
Tintra L
Σ
gintra S'intra i.k
KD
As shown in (1) the final training mini-batchh-wise loss L.M is the combination of the triplet loss, Ttri: inter-task confusion regularizer, LTCR, and the KD loss composed of the three proposed KD loss terms msee Li and inter as in (3)
4 Experiments
4.1
Experimental Setting
Datasets: The five most widely used datasets are selected. MNIST Deng (2012) and CIFAR-
10 Krizhevsky (2099) includes ten classes, which divided into five disjoint tasks, resulting in two classes
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per task. Mini-ImageNNet Vinyals et al.) (2016) is composed of 100 classes, and following Gu et al. 2022
we split 100 classes into ten disjoint tasks, including ten classes in each task. CIFAR-100 Krizhevsky (2009)
has 100 classes and two methods for splitting this dataset are used: (i) the entire dataset is divided into ten disjoint tasks, with 10 classes per task, (ii) half of the classes are used for the first task, and the remaining
half classes for the rest phases as in Zhu et al. (2021: 2022).
Image Le & Yang (2055) contains
200 classes and half of the classes are used for the first task as in ZZhu et al. (2021 2022).
Baselines: For performance comparison, we first consider a simple method of fine-tuning only the cur- rent model using the conventional triplet loss, which can be considered
performance lower bound. We also compare our method with the following state-of-the-arts (SOTAs): LWF Li & Hoiem (2018)
EWC++ Chaudhry et al. (2018a), AGEM Chaudhry et al. (2018b), ER Chaudhry et. al. (2019)
GSS Aljundi et al. (2019b), MIR Aljunni et al. (2019a), ASER / Shim et al. (2021), SCR Mai et al.
(2021 , Gen. van de Ven et al. (2021), CF-IL Pourkeshavarzi et al. (2022). Semi Michel et al. (2022).
MGI Gu ct al. (2022), SDC Yu et al.)
(2020), Pass Zhu et al. (2021), and S-SRE Zhu et al. (2022) ES-
MER Sarfraz al. 2023). Reg Bhat al. 2024 CW-DPPER Chen el al. (2024) LODE Liang
& Li
2024).
As the trainable encoder, Ms. we use a ResNet-18 with the classifier part and the fully-connected layer removed as in Mai et al. (202)). Therefore, the embedding dimension p is equal to 512. All the baseline methods except the Gen. van de Ven et al. (202I) and CF-IL PPoureesaaarzii et al. )022) are evaluated with NCM. To comply with the majority of the baselines, Adamn is used as the optimizer with a learning rate 1e-6 and weight decay of 0.0001. The total number of epochs is 50 for each task. The mini-batch size b for constructing the triplet loss Leri and the inter-task confusion regularizer LTCr is b- = 64. The mini-batch size n for constructing the three KD losses is n 16. This means that, for constructing the total loss Lase in each batih, the total number of synthetic images is one-fourth of the current (new) actual images. Every individual mini-batch (whether from Dj or G2) is set to contain the samples only for e different classcs, where c = 2 for CIFAR-10 and MNIST. For CIFAR-100, Mini-ImageNNet, and Tia we set e = 4. This means that each mini-batch of size b- = 64 drawn from Ds contains 32 actual images for each class of both CIFAR-10 and MNIST, 16 actual images for each class of CIFAR- 100, Mini-ImageNet, and TinyImageNet. Also, cach mini-batch of size n 16 drawn from G₂ contains 8 synthetic images for each class of CIFAR-10 and MNIST, 4 synthetic images for each class of CIFAR-100, Mini-ImageNet, and TinyInageNet. Hyper-parameters in our method are: A 0.2, X2 = 0.8, À = 0.4, and A 10 for C0,,R-10, MNIST, and CIFAR-100. For Mini-ImageNet and ImaelnageNet we set A = 0.1, A2= = 0.3, A3- = 0.2, and A = 15 (see Appendix A.1 for the details).
Implementation details:
Learning of the initial task in II. non-incremental since there is nothing before it. Therefore, we use softmax loss only in the initial non-incremental step because softmax proved its power in static offline learning. For the non-incremental step, we use SGD with a learning rate of 0.001, momentum of 0.9, weight decay of 0.0005, and mini-batch&a size of 256 for all datasets. After completing the training of the initial non- incremental step, we remove the classifier part and use only the encoder part in the remaining incremental tasks. As a regularization method, we add some controlled noise to the triplets in the embedding space, akin to classical regularization methods, with the goal of reducing overfitting. We refer to this technique as 'noisy triplet loss' in our simulation results (see Appendix A.3 for the details).
4.2 Comparison Results
In terms of average accuracy Ak, our proposed method compared to all mentioned baselines in the class-IL setting. Table [ presents the experimental findings pertaining to equal splitting datasets, which means the number of classes is the same in all tasks. We used the repository to replicate the results for the bascline methods: LwF Li & Hoiem (2018), EWC++ Chaudhry el al.] (2018a). AGEM Chaudhry et al. (2018b), ER Chaudhry et al. (2019). GSS Aljundi et al. (2019b), MIR Aljundi et al. (2019a), ASER f Shim et al. (2021), and SCR Mai et al. (2021). within a controlled experimental framework. In all experiments, the data splits and the random seeds used for class selection were consistent across trials, with the reported results representing the average of 10 different seeds (lask orderings). Additionally, we reproduced the average
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accuracy shown in Table 1 for the methods ESMER Sarfraz et al. (2023] IMEX-Reg Bhat et al. (2024)
CW-DPPER Chen et al. [2024), and LODE Liang & I.i (2024) using the same data splits and task orderings However, for the methods Gen. van de Ven et al. (2021) J CFFIL PourKeshavarz et al. (2022), Semi Michel ct al. [002), andMGI Gu et al. 2022), we were unable to replicate the results based on the available source code; consequently, we extracted the results directly from the respective original papers. Symbol f indicates that the numerical results are directly copied from the original papers and 'x' denotes that the results are not available in those original papers. Whether each method stores any actual past data samples is denoted by I and o, where indicates that actual past data samples are stored and F represents the coreset replay-based methods. These results have been compared with the baselines that adopt the same data-splitting approach.
The results our proposed method were derived from ten independent runs with ten different class orderings. From the results, we can see that our proposed method outperforms all basclines by notable margins, achieving the stato-of-the-art (SOTA) performance. Even compared to Gen. van de Ven et al. (2021) which requires multiple models many the number of classes (e.g., 100 models for CIFAR-100), our melhod works better despite that we use only two models, (trainable) Mj and (stored and fixed) Mg-1, irrespective of the total number of classes. The memory requirements for each method are also provided to offer better insights.
Table 2 presents the findings regarding an increased number of tasks and the comparison with prior research that utilized half of the classes the initial task. Notably, results show that our proposed method outperforms previous approaches by a significant margin as the number of tasks increases. Although most Class-IL. studies average accuracy their primary metric, we also analyze final task accuracy, denoted as Atsst, in Table 3 for the samne number of classes in all tasks setting to provide additional insights. This comparison reveals that our method generally outperforms existing approaches in final task performance.
Table 1: Average accuracy, Ak (%). after finishing the final task. Our method considerably outperforms all methods, including the coresct replay-basod methods on all three datasets. The 'MS-10', 'MS-100', and 'MS-Mini' denote the memory size (MB) for CIFAR-10, CIFAR-100, Mini-ImageNet respectively.
Schemes
MNIST
CIFAR-10
CIFAR-
Mini- ImageNtt
MS-10
MS-100
MS-Mini
=
K 10
K =
Joint trainingo
98.1 1
83.9
74.3
72.1 22.2
Fine-tunco
18.2 18.2
16.9
5.420.9
4.320.9
42.6
42.6
42.6
LwFo
23.2=a.1
19.3+0.2
13.8+0.4
8,6+0.6
42.6
42.6
42.6
EWC+++
55.2
17.910.
5.7
4.2
140.4
140.6
140.6
AGEMt
64.7=0.5
27.8+1.
14.3+0.3
11.7*0.0
108.9
108.9
199.4
ERI
67.1=1.1
47.1+0.9
27.6+1.1
20.8+1.2
46.9
48.4
57.4
GSSF
69.820.2
46.711.
26.810.4
21.021.1
95.1
95.1
104.2
MIRI
71.8+0.30
49.3+12
27.3+1.
21.8+1.0
95.1
108.9
198.4
ASER,
$
75.5=0.2
50.3+1.
29.3
22.1 20.1
62.1
62.1
152.6
SCR+
79.2
65.7+0.6
37.5+0.D
35.3
48.3
52.9
89.1
Gen.o
93.79
56.010.44 t
49.520.08
*
99.2
99.2
CF-ILo
95.3+0.15
75.34
59.2
Semit
92.340.10
57.9
38.9
96.8
102.3
MGI
90.8+0.3
52.112a
24.1+a.8
19.1=a.>
96.2
99.8
135.4
ESMERI 93.520.2
71.210.1
50.620.4
45.9
94.2
94.2
97.8
IMEX- Regt
95.7+0.10
74.7+a.1
49.9+o.3
46.1+o.9
98.9
98.9
102.5
CW- CW-DPPERi
91.820.2
67.810.s
49.610.
49.8
99.7
99.7
135.9
LODEI 95.520.9
76.5+a.
51.620.a
52.920.4
49.7
63.9
59.7
Our methodo
96.1
76.9
54.820.9
54.2
50.4
53.4
59.2
Evaluating forgetting O₃ serves as an additional measure to assess the extent to which model loses infor- mation after learning new knowledge. The lower forgetting values are the lesser forgetting concerning earlier tasks. The results of average accuracy and forgetting after each task are summarized in Table We can see a huge margin between fine-tuning and our method regarding forgetting values all three datasets.
To gain deeper insights into the model's performance on individual tasks, we generated confusion matrices for each task for CIFAR-10 with equal tasks. These matrices provide visual representation of the model's
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Table 2: Average accuracy, AK (%), after finishing the final task setting half of the classes for the first task.
Schemes
CIFAR-100
TinyImageNet
K = 5
K = 10
K 20
K = 5
K 10
K 20
Joint trainingo
74.32
74.32
74.32
66.81
66.81
66.81
SDC
Yu et al.
2020
56.77f
57.00f
58.90f
Pass
Zhu et al.
2022 1
63.47f
61.841
58.09f
49.55f
47.297
42.07f
S-SRE
Zhu et al.
2022
65.881
65.041
61.701
50.391
48.93.1f
48.17t
LODE
Liang & Li 2224
65.881
65.04f
61.70
50.391
48.93f
48.17f
Our methode
66.1520.10
65.8210.30
64.351o
55.3221.2
54.90
54.10
Table Final task accuracy, Alest (%).
Schemes
CIFAR-100
TinyImageNer
K = 5
K = 10
K = 20
K === 5
K 10
K 20
Joint. Trainingo
74.32
74.32
74.32
66.81
66.81
66.81
SCR
Mai et al. (2021)
31.22
28.65
26.10
29.15
27.45
23.11
ESMER
Sariraz et al. (2233 $
49.90f
48.77
47.35
48.85
47.30
48.40
IMEX-Rey
Bhat
2024
50.10
48.54
46.25
49.65
46.64
41.34
LODE
Liang & Li 2024
51.00
46.31
46.00
50.20
46.80
45.11
Our methodo
51.25
49.67
47.83
50.76
47.13
44.85
Table 4: Forgetting (%) and average accuracy (%) after cach task for method, LODE, and the lower bound (i.e., fine-tuning..
Method
Metric
CIFAR-10
k
2
3
4
Forgetting
9.5 12.2
15.7
28.6
Fine tuning
Accuracy
50.9 40.0
30.0
16.9
Forgetting
4.2 8.4
5.1
9.4
LODE Liang Li
2024
Accuracy
81.9
75.4
Forgetting
4.6 4.7
5.4
11.1
Our method
Accuracy
88.1
83.3
81.1
75.9
Method
Metric
CIFAR-100
2
Forgetting
3.8 12.1
7.0
7.9
10.2
11.4
5.9
4.3
4.0
Fine tuning
Accuracy
69.8
54.4
49.1
41.8
32.2
20.0
14.6
9.1
6.5
Forgetting
5.0 10.0
2.7
1.5
1.2
1.2
9.4
LODE Liang & Li
2024
Accuracy
86.3
74.1
67.3
64.7
62.8
61.1
60.4
58.4
51.5
Forgetting
5.3 8.6
2.9
2.6
2.2
1.0
1.7
Our method
Accuracy
82.2
71.8
69.5
66.7
63.4
60.2
59.6
57.5
54.5
Method
Metric
Mini
ImageNer
k
2
3
4
5
6
7
9
Forgetting
12.1 18.9
14.5
5.3
9.3
4.8
5.4
3.5
2.1
Fine tuning
Accuracy
51.5
32.1
20.0
18.9
11.0
9.8
6.1
5.5
5.2
Forgetting
8.7 9.7
4.8
3.4
3.0
3.1
2.0
9.7
9.1
LODE
Liang Li
2024
Accuracy
79.3 70.8
64.4
62.6
59.2
56.0
54.1
50.0
48.80
Forgetting
11.1 6.2
3.4
3.7
2.2
2.3
2.0
4.2
6.6
Our method
Accuracy
76.8 71.4
66.8
64.8
62.3
59.9
58.0
56.2
55.3
classification accuracy across different classes within each task. Fig. 7 shows the confusion matrices for all 5 tasks, where U presents the confusion matrix obtained from model M₁, which was trained on task k and then tested on classes for tasks 0 to j. j < By examining the confusion matrices, we can the patterns of misclassification arising from both catastrophic forgetting and task-confusion. iille fillustraas the order of
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classes for each task. From the visualization in Fig. 7 it is evident that the highest correct classification for Uj.8 occurs when & j. However, it is noteworthy that the worst classification is not necessarily associated with the imitial classes (i.e., j < k) suggesting the significance of the class ordering.
Table 5: The labels of classes associated with each task. Classes marked in bold represent the classes present at that task number. For instance, in task k = 2, the current classes are {0, 3), and previous classes are 24,2, 7,6)
Task# (k)
Categories
0
4
1
4
2
6
2
3
3
4
2
7
6
0
3
5
8
3
It can be clearly seen that controlling the position of embeddings in the embedding space through our proposed losses very effective for mitigating inter-task confusion and combating catastrophic forgetting, which leads superior performance to all those baselines. Furthermore, our results echo the claim of Mai et al. [2021 ; Yu et. al. (2020) that, in II, using metric learning with NCM classifiers could be better choice than softmax classifiers.
4.3 Ablation Study on Lase
In this subsection, more experiments are conducted to reveal the effect of each term of our loss LM, We present the results of ablation experiments for mnter-task confusion regularization, knowledge distillation (MSE, intra-class, and inter-class), and their collective impact four distinct datasets. With the exception of TinylmageNet, where allocate half of the total classes to the initial non-incremental task, all other datasets are configured with an equal distribution of classes in each task.
Effect of inter-task confusion regularization, Lren: To gauge the impact of Lren on the performance, we set A = The intention behind incorporating this term LTCR is to prevent overlap across the current classes and those classes that have been learned carlier, thereby mitigating the occurrence of inter-task confusion. The average accuracy is represented the third row of Table G Looking at Table 6 it becomes evident that climinating the inter-task confusion regularizer leads to a decline of no less than 1.1% across all datasets. Further insight into the impact of this term on individual intermediate tasks is provided in Fig. g (depicted by the yellow curve), illustrating a heightened prominence of the influence of LTCR the number of tasks increases.
Effect of the MSE loss, mase To assess how LKD affects the performance, we assign a value X2 = 0, (i.e., total loss T.M, Turi X1 Lren + >a Ab intre T.)D")). The objective of this term is to minimize the Euclidean distance between the embeddings of the current under-training model, denoted student), and the previously stored fixed model M₁-1 (the teacher) when the input comprises data generated from a prior task. This approach compels M& to acquire knowledge about past tasks from the teacher model Mę-1, thereby mitigating the phenomenon of catastrophic forgetting.
Me (the
The fourth row of Table t displays the performance after completing the final task across all datasets. Upon comparison with the outcomes of the LTCR, it becomes evident that the influence of this term is more pronouncod. Removing results in performance decrease of around 3%. Additionally, Fig. g a comparison is made between employing the MSE loss term and not using it (i.e., setting d2 0) for each incremental task. The significance of the MSE loss becomes evident in the outcomes the number of tasks incrcases.
Effeet of the intra- and inter-class losses, intra and Linder: We set X = O, to see the impact of our proposed intra- and inter-class losses on the average accuracy. The fifth row Table 0 displays the results of the performance evaluation following the completion of the final task. It is evident that intra- and inter-class losses play a pivotal role our suggested loss function. Its significance underscored by a reduction of up to 10% in the average accuracy upon its removal. This term embodies key strategy for
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992
2
2
2-
995
True label
17
854
34
95
0
6-
793
91
7.
2
7
Predicted label
Prodicted label
Predicted label
(a) Uo.o-
(b) U0.1-
(c) U1,1-
0
0
0
664
112
3
4
7
10
81
907
7
0
0
0
0
0
0
Tue label
irue label
0
0
34
772
73
76
40
10
27
836
31
88
0
0
744
6-
IB00
7-
Predicted label
Predicted label
Predicted label
(d) U0
(e) U1.2-
(I) U2.2.
/BB
54
2
2
35
2
0
758
True label
True bbee
27
842
0
5
6
6
7.
8
8:
6 Prodicted label
8
Predicted label
Predicted label
(g) Uo.3-
(h) U1.3
(I) U2.3-
8
0
0
0
0
0
2
True llbel
0
D
0
0
0
0
0
0
0
20
15
38
10
2
740
182
True
0
0
0
47
57
7.
0
0
17
5
91.0
0
2
3
4
8
6 Predicted label
8
9
3
8
9
Predicted label
Prodicted label
(i) U3.3-
(k) U0
U1.4-
12
40
10
0
1
2
52 2 17
53
23
23
45
0
0
0
TUR
7-
0
30 105
154202
0
1 2 3
3 6
8
2 3
4
5
6
7
8
Predicted label
Predicted label
Predicted label
(m) U2.4
(n) Us.4.
(o) U4.4.
Figure 7: Confusion matrix Uz.eJ = 0,...,,,k =,==0,00 O...., .,.,,,, using CIFAR-10
mitigating catastrophic forgetting, achieved through the innovative preservation of the positional relationship of previously learned classes within the embedding space. Moreover, looking at Fig. g the drop in the average
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Table 6: Average accuracy, As (%), after finishing the final task for ablation experiments. The mean and standard deviation (STD) reported from ten individual runs with ten different orderings of the classes.
Schemes
CIFAR-10 CIFAR-100 Mini-ImageNet
TinyImageNet
K =
== 10
K = 10
= 20
Fine-tune
24.7
37.2+1.
10.0
6,5
Our method when A 0
75.7
52.8
53.1
53.0
Our method when \ =
24.820.
49.520.85
51.0a1.0
51. 21.1
Our method when Às = 0
70.1+0.9
44.8+0.5
49.1+1.2
48 48.4+0.96
Our method
76.9
54.8+0.9
54.2 +
54.1+1.
CIFAR-10
CIFAR-100
Mini-ImageNel
TinylmageNe!
Average Accurary (96)
Averagee Accurasy (%6
Average Accuracy
Average Accurssy
Incremental Task
Incramental Task
Incremental Task
Incremental Task
Our method
Our method without MSE loss
=0)
- Finc tuning
Our method without task confusion regularizer 2, -0)
Our method without intra- and inter-class losses (2, -0)
Figure 8: Average accuracy, A& (%), for ablation experiments for all four datasets (best: viewed in color).
Only the incremental tasks (or states) are plotted.
accuracy is noticeable for each incremental task when Ag = O, which means the two losses play an essential role all datasets.
4.4 Ablation Study on MSE Loss, Linee
This section delves into the effects of various loss configurations on Mean Square Fuclidean (MSE) loss. To assess this, we substituted mcan absolute error (MAE) and cosine dissimilarity for MSE loss in our KD loss framework, evaluating their impact on CIFAR-100 and TinyImageNel with a total nunber of tasks K 10. Fig. g9 illustrate the outcomes, indicating that MSE consistently produces the optimal results. However, it is noteworthy that even with alternative configurations, our method surpasses most state-of-the-art. Thus, while our approach performs admirably across different loss setups, meticulously crafted configuration can lead to a notable performance enhancement as evidenced our ablation study.
4.5 Ablation Analysis of CF and ITC to Performance Degradation
In this subsection, we aim to analyze the extent of performance reduction caused by CF and ITC inde- pendently. CF refers to the phenomenon in continual learning where model, when trained sequentially on new lasks, experiences a significant decline in performance on previously learned tasks. This occurs as the parameters optimized for new tasks overwrite or interfere with the representations learned for earlier tasks. In contrast, ITC arises when the model struggles to differentiate between tasks, resulting in incorrect predictions that combine knowledge from multiple tasks. While CF primarily affects the retention of prior knowledge, ITC underscores difficulties in task discrimination. Thus, the proportion of ITC can be quantified using the following metric:
ITC (Accuracy given task-IDs) (Accuracy without task-IDs).
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60
50
SCOuSry 1N0
30
30
10
10
MAE
Costne Dissmilarty
MSE
MAE
Cosine Dissinlianty
MSE
(a) The impact of different configurations of the Linae on the final average accuracy Ag %, for the CIFAR-100 dataset.
(b) The impact of different configurations of the Linae the final average accuracy Ag %,, for the Tinylma- geNet. dataset.
Figure 9: The effects of various loss configurations on MSE loss.
Fig. 10 illustrates the performance degradation caused by CF and ITC for our method, compared to fine- tuning and two recent approaches. As shown, our method effectively mitigates both ITC (indicated by the red values next to the red arrows) and CF (indicated by the black values next to the black arrows) more efficiently than the compared methods.
OF and ITC for CIAAR 10
CF aFand ITC Thylmageeiit
80
140
14.
33.5
A.U
10.8
6.8
70
37.3
6cCuracy
18.0
Upper bound
Time turing (e tesl-DD)
00
Hine turing twno Lack Uso
30
29.8
(Maungan (20222) taak
CH-IL
eng (20242) SasR-E3s
LOOE
(2004)) tank-itDe)
Our mithrdd tase-llst
Our methert (win taxs-1Dss
Fine
CH-II
LoDe
methhoo
0
tuning
CP-B [Machgan (2022))
1GDe (Liang (20241)
metrod
[Mothgga (20021)
(Liang (2024))
(a) The values CF ITC on the final average accuracy A2, for the CIFAR-10 dataset.
(b) The values CF ITC on the final average accuracy Ag, for the TinylmageNet dataset.
Figure 10: Analysis of CF and ITC to Performance Degradation (legend provided in (a)).
4.6 Ablation Study on Architectures
For further experimental results, we investigated additional network architectures, as shown in Table From the table, is evident that as the size of the network increases, the average accuracy improves. However, the improvement observed for CIFAR-100 is less pronounced compared TinylmageNet.
4.7 Ablation Study on Memory-Agnostic Measure
In this subscction, we present results for memory-agnostic measure proposod by Zhou et al. (2024) and Zhou et al. (2023). This metric calculates the area under the performance-memon curve (AUC). To evaluate this metric, computed the average accuracy of various methods across range of memory sizes, from small
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Table Average accuracy, Ax (%) for different networks.
Architecture CIFAR-100 TinyImageNes
K = 10
K = 20
ResNet-18
65.82
54.10
ResNet-34
66,10+a.2
54.85+0.75
ResNet-50
20.25
20.52
to large, by adjusting the exemplar size for all methods while using single benchmark backbone, in Mai ct al. (2021). Fig, 11 illustrates the performance-memory curve for CIFAR-100, while Table S provides the (AUC-A). Both Fig. 11 and Table reveal that beyond a memory size of 44 MB (when the number of generated images exceeds 1k), the performance of our met hod stabilizes. This demonstrates that our method more scalable and extendable compared to other evaluated.
AUC values for average performance-
CIFAR-100
R400 agee accuraey (5))
SCR
LODE
Our mathod
Memory Size (MB)
Figure 11: The average accuracy of various methods is evaluated over range of memory sizes, from small to large. All three compared exemplar-based methods utilize benchmark backbone, as in Mai et al. (2021). To ensure fair comparison, memory costs are aligned by adding exemplars to the compared methods. For our method, the number of generated images is adjusted to match different memory size requirements.
Table 8: Memory-agnostic performance measures (AUC-A)
Schemes
CIFAR-100
K 10
ASER, g
Shim al. 2021
311.9
SCR
Mai al. [2021
453.9
LODE
Liang & Li (2024
698.5
Our method
760.3
5 Conclusion
In this paper, ventured into the realm of caassinncemmenal learning (class-IL), utilizing the potent tool of metric learning. Instead of storing any actual past data samples, we stored and re-used single past-trained encoder in a recursive manner to generale the past synthetic images. Leveraging these hesized images, we introduced three novel rules, or metric KD regularizers, designed to mitigate the issue of catastrophic forgetting, where previous knowledge lost when learning new classos. Additionally, we incorporated an inter-task confusion regularizer to alleviate the overlap among distinct classes within the embedding space. Experimental results showed the superior performance of our approach compared to many recent approaches.
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A Appendix
A.1 Choosing Hyper-paramen parrreearrmersss
In this subsection, we examine the choice of the number of synthetic images and the values for the loss term coefficients equations (T) and (3) across different simulation setups. Fig. 12 shows the final accuracy of our method on CIFAR-10U using various amounts synthetic images. is evident that beyond one-fourth of the real datasct, performance improvement becomes negligible. Therefore, we set the number of synthetic images to one-fourth of the real data for each lask across all simulation settings.
CIFAR-100
60
Average accuracy (96
50
40
30
12.5%
25%
50%
100%
Percentage synthetic images
Figure 12: The effect of different numbers of synthetic images on the final average for the CIFAR-100 dataset.
Table 9 presents the results of performance evaluations across varions loss term coefficient values in (1 and The determination of final coefficients follows a specific approach. Through empirical observations, it was identified that employing siguificantly distinct values for A and A25 or setting A = X2 with \ > Aa results in poor accuracy. Conversely, opting for \₁ A2 and selecting A3 > λι yields improved performance, and the specific value assigned A1 has minimal impact on the ultimate classification accuracy, long it satisfics the constraint d < 1.
Table 9: Impact of hyper- hyper-parametenn in and
3 on average accuracy, Ag (%).
Schemes
Tiny ImnylmaeeNet
CIFAR-
A1
d2
As
Ax
A1
X2
Às
Ak
0.1
0.1
0.2
52.88
0.1
0.1
0.2
64.00
0.2
0.2
0.3
54.20
0.2
0.2
0.3
64.65
0.3
0.3
0.4
54.00
0.3
0.3
0.4
64.28
0.4
0.4
0.5
53.72
0.4
0.4
0.5
64.20
0.2
0.2
0.5
54.55
0.2
0.2
0.5
64.96
Our method
0.2
0.2
0.6
54.40
0.2
0.2
0.6
65.14
0.2
0.2
0.4
54.92
0.2
0.2
0.7
65.60
0.2
54.15
0.2
65.85
0.1
0.1
0.4
53.91
0.2
0.2
0.9
65.52
0.1
0.1
0.5
53.25
0.1
0.1
64.83
The hyper-parameter A in equation
controls the weight of the feature distribution regularization term in DeepInversion. A well-balanced setting ensures effective alignment of feature statistics without excessive
3
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regularization, thereby enhancing generalization and improving model performance. To identify the proper value of λs, conducted experiments varying it across the range [5, 10, 15, 20, 50). The results, summarized in Table [0] demonstrate that higher-resolution datasets typically require larger values of ) for better performance.
Table 10: The effect of As on Average accuracy, Ak (%)
CIFAR-100 TinyImageNet
K = 10
K = 20
A = 5
54.6103
53.921.1
AS = 10
54.8=0.9
53.8+0.9
A - 15
54.520.6
54.1
A = 20
54.1+0.7
53.9+1.2
A 50
53.620.6
53.3214
A.2 Computation Efficiency Analysis
The additional component of our method, compared to baseline approaches without data generation (e.g., fino-tuning, LwF, and E.C)), the generation of synthetic samples during training. Hence, evaluate the computational efficiency of our approach, we measured the time required to generate batch of 16 images across different image sizes using single NVIDIA V100 GPU. The experiments were conducted over 10 independent trials, with each trial running 100 iterations. The average time per batch was recorded using the Python time module, and the results are summarized in Table 11 Even for high-rosolution images x224 x3), the generation process demonstrated acceptable compulational efficiency, requiring only 3.38 seconds per batch. This indicates that the training complexity, even for large image sizes, is not a significant issue in practice.
Table 11: Computation efficiency for generating batch of 16 images with 100 iterations on single NVIDIA V100 GPU.
Image Size
Mean Time per Batch (seconds)
32x32x3
2.06
64x64x3
2.11
84x84x3
2.34
224x224x3
3.38
A.3 Noisy Triplet Loss
The term Lori in !I is a triplet loss used to learn the current task. In this paper, we use a very simple, yet effective way to construct the triplet loss for mitigating over-fitting while learning the current task. general, when the model learns how make the distances between anchor-positioe pairs smaller than those of anchor-negative pairs, the learning process will stop; however, this does not necessarily prevent the model from being over-fitted. In proposed scheme, a regularization method, add noise to some of the enbeddings in order to alleviate over-fitting. To be more precise, let H₃ [h!...., h&l E Roxb denote the un-normalized embedding matrix produced by M2 and let H₁ = [h], .... Ag] Rpxb denote its normalized
version with A Rg where ||-I| denotes la norm. We add noise to some normalized embeddings hig that |ل
the pairwise distances for triplets become randomly different in each mini-batch. Specifically, we randomly select a subset of the normalized embeddings in each mini-batch. Then we add Gaussian noise to the selected 1e followed by creating triplets. This helps the network to learn the features with a lower risk of over-fitting while fulfilling the triplet loss inequality.
For generating noisy triplets, as the added noise, we choose zero-mean Gaussian noise w with variance o², i.e. w ((000²). The noise variance, x2, is essential hyper-parameter. Based our experiments, we
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100
- Fine tuning standard triplat loss (no noise)
90
Fine tuning nndisy triplet (10%)
tuning noisy triplet (25%)
80
Fine tuning + noisy triplet (50%)
tuning nolsy triplet (75%)
Average Accuracy (%)
70
Fine tuning noisy triplet (100%)
60
30
20
0
Incremental Task
Figure 13: Average accuracy obtained by fine-tuning ResNet-18 using the classical triplet loss and noisy triplet loss with five different portions of noisy triplets in each mini-batch. The model is trained on CIFAR- 100 (best viewed in color). NCM is used in the test time, the results indicate a significant improvement in the final task (about 30%) using noisy triplet loss.
find that it should be less than 0.01 for all datasets. In the simulations, set 0² 0.005 for CIFAR-10 and x² 0.01 for all three CIFAR-100, Mini-ImageNet, and TinylmageNet.
One interesting (and important) question is whether the noisy triplet loss is still effective for general IL (i.e., other than our proposed IL method). To answer the question, we compare the noisy triplet loss and the standard (traditional) triplet loss in the baseline IL setting which vanilla fine-tuning used in each task. In the simulation, we train a single encoder, ResNet-18, on CIFAR-100. The squared Euclidean distance utilized the distance metric in the triplet. loss. The performance of the traditional triplet loss and noisy triplet loss is compared in Fig. 13 in which the average accuracy is plotted for the case of no noise and for the case of adding noise to 10% of embeddings, 25% of embeddings, 50% of embeddings. 75% of embeddings, and 100% of embeddings. The effectiveness of noisy triplet loss is clear from Fig. 13 and the best performance is achieved when the noise added to 25% of the embeddings. The accuracy improvement is about 30% at the end of the training (i.e., at the incremental task of 9).
25


Reviews:
[{"review_id": "9r8QqtFwp8", "reviewer": "Reviewer_jbP3", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths:**\n- Overall, the paper is basically well written with clear technical contribution. The technique is well explained and is technically sound. \n\n**Weakness:**\n- MNIST is also a widely used dataset, often used alongside CIFAR-10/CIFAR-100/etc. for incremental learning algorithms validation. So it is necessary to include the results of all methods on this dataset in the experiments.\n- Although Fine-tune is considered as a performance lower bound in the baselines, the experimental results do not include performance upper bound (e.g., learning all the tasks jointly), in the comparison.\n- Table 3 just shows the results in two IL scenarios, and the proposed method performs best in only one case. Personally, it is inappropriate for the authors to claim that their method generally outperforms existing approaches in final task performance. Moreover, why are results only shown for the two IL scenarios? Is it because the proposed method does not perform well on other scenarios such as CIFAR-100 ($K=5, K=20$) and TinyImageNet ($K=5, K=10$)?\n- In Table 4, it is not convincing to illustrate the superiority of the proposed method in alleviating forgetting by only comparing with the lower bound method Fine-tune. At the very least, a comparison should be made with existing SOTA methods, such as LODE, which performs well among the baseline methods.\n- A quantitative analysis of computational efficiency is not available in the current manuscript.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "The authors present a method for class-incremental learning which focus on tackling two fundamental issues: the inter-task confusion and the catastrophic forgetting. The main contribution of this paper is to propose to treat the above two issues separately, i.e., the authors 1) use the centroids of previously learned classes as negative samples to design a regularization term customized to overcome inter-task confusion; 2) propose a KD method utilizing inter-class clusters, intra-class clusters and mean square distances in the embedding space to combat catastrophic forgetting. Extensive experiments performed on several classical classification tasks demonstrate that the proposed method achieves the state-of-the-art performance in the setting of class-IL.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "- Add the results of all methods on dataset MNIST in the experiments.\n- Include performance upper bound such as learning all the tasks jointly, in the experimental comparison (i.e., Table 1).\n- Add in Table 3 the performance results of each method on the final task in several other cases, for example CIFAR-100 ($K=5, K=20$) and TinyImageNet ($K=5, K=10$). At the same time, rephrase the related analysis in the main text.\n- Add in Table 4 the results of the evaluation of existing SOTA methods (e.g., LODE) in alleviating forgetting.\n- Computation efficiency analysis.\n\n**Typos:**\n- The caption of Figure 4 is the same as that of Figure 3, which should be corrected.\n- In Section 3.3 (Eq. (2)), $v\\prime$ and $v’$ are not consistent. According to my understanding, $v’$ should be corrected to $v\\prime$.", "broader_impact_concerns": "No major concerns.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "oAeWQ3ajA2", "reviewer": "Reviewer_KcYV", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n\n1. The writing is basically clear. I believe readers can easily touch the core idea of this work due to the clear writing.\n2. The experiments are extensive. The authors have conducted experiments on four common datasets and compared their method to many SOTA baselines, including three works published in 2024. The experimental setting is comprehensive to validate the effectiveness.\n\nWeaknesses:\n\n1. The KD regularization is not novel in class-Incremental learning. In the past work [1], they have proposed a KD method for the problem of class-incremental learning, so I believe this has been an old-fashion idea in this community. Although the authors use a KD method in the embedding level, but it is also not new in the area of KD. Therefore, I am not convinced by the novelty of this method due to the KD part.\n2. The proposed method is complicated. In the proposed loss function, there are *five* terms with *three* hyperparameters, which are too complicated to implement in practice. Besides, the authors even add a data generation part in the method, which I believe is expensive in real world and introduce an extra hyperparameter. In my view, it would be challenging to tune the four hyperparameters in the loss function and data generation process.\n3. The computational efficiency should be compared in the experiments. Due to the complexity of the proposed method, it would be better if the authors can add an experiment to compare the time-consuming of the proposed method with baselines. \n\n[1] Kang, Minsoo, Jaeyoo Park, and Bohyung Han. \"Class-incremental learning by knowledge distillation with adaptive feature consolidation.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2022.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "In this paper, the authors focus on the problem of class-incremental learning, where the model learns from sequential input data without accessing all past data. To this end, they aim to address the two challenges of class-incremental learning: inter-task confusion and catastrophic forgetting. In their method, they propose two regularizers in the new loss functions to combat inter-task confusion and Catastrophic Forgetting, respectively. For inter-task confusion, they propose a margin loss by using the centroids of previously learned classes as negative sample. For Catastrophic Forgetting, they use KD method in the embedding space and synthesizing past data samples by storing and re-using a past trained model. Experiments on CIFAR-10/100 and Mini-ImageNet, TinyImageNet are conducted to show the effectiveness of the proposed method.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "No", "audience_explanation": "", "requested_changes": "1. Parameter sensitivity analysis of $\\lambda_b$. The authors should provide an analysis to show how the hyperparameter $lambda_b$ affects the data generation and the final accuracy.\n2. Add a comparison of computational efficiency. See Weaknesses.\n3. The authors may need to clarify the novelty of the KD regularization in the problem of class-incremental learning.", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "SncCn602L2", "reviewer": "Reviewer_rxXC", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "# Strengths\n- The paper tackles an important and challenging real-world problem.\n- The paper is written well and is easy to follow. I particularly like the illustration presented in Figure 2 as it explains the core intuition behind the proposed loss function. \n- This work is compared against several baselines in Table 1 across several small and mid-sized datasets.\n- The work analyzes the effect of different loss terms through their ablation study, which shows the significance of each loss term. \n\n# Questions and Comments\n1. **Claim regarding inter-task confusion** [Motivation]\n\n    I find the distinction between inter-task confusion and catastrophic forgetting somewhat unclear. Authors have stated (page 2 1st para last line) - \"Although these two concepts often have not been clearly distinguished in the literature, the inter-task confusion and the catastrophic forgetting should be treated separately because the former refers to the confusion between the current and past tasks, whereas the latter refers to forgetting the past tasks.\" As per my understanding, Catastrophic Forgetting occurs due to the new task overwriting some of the information learned previously. In class incremental learning, since the task split is based on classes, learning new classes can inadvertently overwrite information about old classes. This implies that class confusion is the major contributing reason for catastrophic forgetting. Many existing CIL methods mentioned by the authors, such as data replay, regularization, parameter isolation, and hybrid approaches, effectively address catastrophic forgetting by primarily focusing on mitigating inter-task (class) confusion. For instance, naive data replay, which stores samples from past tasks, combats catastrophic forgetting by allowing the model to learn from past data. This simultaneously helps the model distinguish between past and current classes, thereby alleviating the challenge of class confusion.\n \n2. **Generation of only 1 task** [Method]\n    \n    Authors use the model trained on $(k-1)^{th}$ task to generate the images only for the previous task. Only these images are used for KL divergence-based loss terms. In my understanding, this should affect the algorithm's ability when the number of tasks is large. Or the task split is designed in a way that the confusing classes are kept far apart. \n\n3. **Accuracy Comparisons against several works** [Evaluation]\n\n    Authors state that the ordering of the classes in crucial for Class Incremental learning (on Page 13). In my experience the final converged model is also sensitive to the initialization, the training setup and the hyperparameters. The authors have made efforts to add several comparison points in Table 1. I believe the authors report the numbers from the original paper for many of the work and this makes the comparison unfair as the different papers would have different task splits and training setups. \n\n4. **Budget normalised comparisons** [Evaluation]\n    \n    It might be unfair to compare the performance of the methods as these methods might have different computing and memory requirements. The authors should consider adding a discussion on the budget requirement of different methods.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "No", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This work leverages several techniques like Generative Data Replay and Knowledge Distillation to tackle the challenges of class Incremental learning within the metric learning framework. The work claims to tackle two key challenges: inter-task confusion and catastrophic forgetting. To mitigate these issues, they introduce a novel loss function, $\\mathcal{L}_{M_k}$ (Equation 1), comprising three components given below\n\n- **$\\mathcal{L}_{tri}$** loss s Schroff et al. (2015), is used to train the $k^{th}$ task as it is superior in the IL context Yu et al. (2020).\n- **$\\mathcal{L}_{TCR}$**  (Equation 2), the inter-task confusion regularizer, specifically aims to prevent confusion between the current task and previously learned tasks.\n- The authors propose storing the model trained on the preceding k−1 tasks to combat catastrophic forgetting. This stored model is then used to generate synthetic images of the $(k−1)^{th}$ task. These synthetic images are incorporated during the training of the $k^{th}$ task, ensuring the preservation of the embedding space for previous tasks while simultaneously learning new embeddings (facilitated by the knowledge distillation loss, **$\\mathcal{L}_{KD}$** (Equation 3).\n\nThe authors claim that their approach is effective by outperforming several baseline methods. Furthermore, they conduct ablation studies to analyze the contributions of each proposed loss term.", "claims_and_evidence_yn": "No", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "# Requested changes based on the questions and comments above:\n1. **Claim regarding inter-task confusion** [Motivation]\n    - Authors state (Page 2, para 2 first line) \"many researchers have proposed various approaches to tackle catastrophic forgetting while very few have tackled inter-task confusion explicitly.\" I would request the reviewers to add citations to a few works that tackle 'inter-task confusion' explicitly. \n    - As the authors admit that the concepts of catastrophic forgetting and inter-task confusion have not been well distinguished in literature, I request the authors to add clear definitions that can lead to some measurable metric to test what fraction of performance drop is caused due to each of these concepts. \n    - I recommend the authors use these definitions to quantitatively assign what portion of performance improvement is alleviating catastrophic forgetting and inter-task confusion for at least a few of the methods in Table 1. \n    \n2. **Generation of only 1 task** [Method]\n    \n    - Authors should consider clearly stating that they **only generate sample for 1 previous task**, where the claims regarding the use of generative replay are made. I was under the impression that author were generating the samples for each task until I reached the Section 3.4 (on pg 7).\n        - the abstract - \"we also propose that the past trained model is stored and re-used for generating past data samples. \", \n        -  the introduction - \"We first use Mk−1 to synthesize past data samples Gk, which will be used for training Mk.\" and \n        - contribution - \"To this end, we also propose a method for synthesizing past data samples by storing and re-using a past trained model Mk−1.\"\n    - **Task scalability**- It would be interesting to see how this algorithm behaves when there are large number of tasks, for example Cifar100 with 20-25 task splits. Will this method be effective against the data replay baselines as this algorithm only generates data for past 1 task? \n    - Additionally, authors can consider demonstrating how the embeddings for the first task change with incremental learning. \n\n3. **Comparisons against several works** [Evaluation]\n    - I would strongly recommend the authors reimplement a few of the recent baselines for a controlled experiment. Where each of the algorithms gets the same task split and all the algorithms have the same initialization after the first task (as the incremental nature of the algorithm is only apparent from task2). Alternatively ( and probably more simpler approach), the authors can report the number from some other papers containing several methods like [1], provided they able to (a) test the reproducibility of the results reported in the paper and (b) are able to port their method into these repositories and get the numbers corresponding to their method.\n    - I would recommend the authors to add a few more architectures in the comparison. \n    - I request the authors to add data entry for vanilla training of the network on the entire dataset as the upper bound in all the tables to show how much performance gap comes from the incremental nature of the task.   \n    - Authors primarily use Average Accuracy to compare several algorithms. The authors should also consider adding several other metrics such as Last model accuracy and backward transfer [2]. \n\n4. **Budget normalised comparisons** [Evaluation]\n    - The author should report the memory and compute requirements of each of the methods in the Table. \n    - Additionally, the authors can use the metrics AUC-L  and AUC-A to compare memory agnostic measures proposed in [1]. \n    - It can be a good contribution if authors can come up with a compute agnostic measure as the proposed method might requires additional compute to generate the images. (May be this compute is negligible in comparison to other methods, in which case the proposed algorithm would show impressive numbers.)\n\n\n\n# Reference\n[1] Zhou, Da-Wei, et al. \"Class-incremental learning: A survey.\" IEEE Transactions on Pattern Analysis and Machine Intelligence (2024).\n\n[2] Saha, Gobinda, and Kaushik Roy. \"Continual learning with scaled gradient projection.\" Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 37. No. 8. 2023.", "broader_impact_concerns": "None", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "PFw2ndSwUn", "reviewer": "Reviewer_RT7T", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "**Strengths**\n\n1- The authors mention some exciting findings. For example, the best synthetic data for task i can be generated by the model trained on task i. So, it is better to train the generative model, generate the synthetic data, and use them for future training.\n\n2- The authors show superior performance comparing the prior works.\n\n3- The ablation study is comprehensive.\n\n**Weakness**\n\n1- The paper is tough to follow and lacks organization. Many parameters are employed in different components of the algorithms, but some of the methods are not properly referenced or defined. Also, a diagram or algorithm block could help the reader understand each part and the overall algorithm.\n\n2- The authors' novelty is not very clear.\n\n3- Please check out the requested changes.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "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": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper proposes a new algorithm to alleviate catastrophic forgetting in Class-IL.The authors first explain that there are multiple sources for the poor performance of the models in incremental learning. First, the training data of prior tasks are not available during the training of the future tasks; second, the model has not learned to distinguish between classes from different tasks.\n\nThey propose a combination of loss terms to train the model with two goals in mind. First, remind the model of the past task and help it to identify classes from different tasks.", "claims_and_evidence_yn": "Yes", "claims_explanation": "", "audience_yn": "Yes", "audience_explanation": "", "requested_changes": "* Some methods and losses are mentioned very early and never discussed properly or introduced very late. For example, metric learning is briefly mentioned in section 2.2, and it plays an essential role in the final algorithm but is not adequately explained. The same goes for *l*$^{mse}$, defined two pages after introducing it. Another example is $h_k$, shown in a figure on page 2 and used on page 4 without any description. \n\n* In section 3.1, only average accuracy is mentioned as the evaluation metric, and the forgetting is missing. \n\n* Can you explain the eq 2 (L$_{TCR}$)? What is positive input ($x_p$)? Are the inputs in embedding space? What is the learnable parameter here? \n\n* The author's contributions are not very clear. It would be helpful to point out the terms directly brought from previous literature in continual learning versus the losses that the authors propose. For example, is $l_{mse}$ a new loss? It looks pretty similar to equation 12 in [1].\n\n\n[1] Smith, James, et al. \"Always be dreaming: A new approach for data-free class-incremental learning.\" Proceedings of the IEEE/CVF international conference on computer vision. 2021.", "broader_impact_concerns": "NA", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: Please include the requests from reviewers and additional experiments that have been performed.
Decision: Accept (poster)