Prospective Representation Learning for Non-Exemplar Class-Incremental Learning
Authors: Wuxuan Shi
Mang Ye
Venue: NeurIPS 2024 poster (2024)
Keywords: incremental learning
catastrophic forgetting
Primary area: machine_vision

Abstract: Non-exemplar class-incremental learning (NECIL) is a challenging task that requires recognizing both old and new classes without retaining any old class samples. Current works mainly deal with the conflicts between old and new classes retrospectively as a new task comes in. However, the lack of old task data makes balancing old and new classes difficult. Instead, we propose a Prospective Representation Learning (PRL) approach to prepare the model for handling conflicts in advance. In the base phase, we squeeze the embedding distribution of the current classes to reserve space for forward compatibility with future classes. In the incremental phase, we make the new class features away from the saved prototypes of old classes in a latent space while aligning the current embedding space with the latent space when updating the model. Thereby, the new class features are clustered in the reserved space to minimize the shock of the new classes on the former classes. Our approach can help existing NECIL baselines to balance old and new classes in a plug-and-play manner. Extensive experiments on several benchmarks demonstrate that our approach outperforms the state-of-the-art methods.

Prospective Representation Learning for Non-Exemplar Class- Learning
Wuxuan Shi', Mang Yel
SSchoo of Computer Science, Wuhan University, Wuhan, China
2 Taikang Center for Life and Medical Sciences, Wuhan University, Wuhan, China
{wuxuanshi, yemang) edu. https://github ctm/ http:/iuawb.co///hauuuaaaaaeeeee ShiiWuxuan//eeuTPP22244-
Abstract
Non-exemplar maassinncremenal learning (NECIL) is a challenging task that re- quires recognizing both old and new classes without retaining any old class samples. Current works mainly deal with the conflicts between old and new classes retrospec- tively as a new task comes in. However, the lack of old task data makes balancing old and new classes difficult. Instead, we propose Prospective Representation Learning (PRL) approach prepare the model for handling conflicts in advance. In the base phase, we squeeze the embedding distribution of the current classes to reserve space for forward compatibility with future classes. the incremental phase, we make the new class features away from the saved prototypes of old classes in latent space while aligning the current embedding space with the latent space when updating the model. Thereby, the new class features are clustered in the reserved space to minimize the shock of the new classes on the former classes. Our approach can help existing NECIL baselines to balance old and new classes in a plug-and -lay manner. Extensive experiments on several benchmarks demonstrate that our approach outperforms the ffute-of-the-ar methods.
Introduction
In recent years, deep neural networks (DNNs) have achieved great success in static scenarios. Research attention is increasingly turning to extending the learning capability of DNNs to open and dynamic environments. An important aspect is to enable the network to accumulate knowledge from new tasks as the input stream is updated (i.e., incremental learning [ 2 31).
Whenever new task arrives, is costly retrain the model with current and old data. Not to mention that the old data is not fully available. A typical alternative is to fine-tune the network with new data directly. However, this lead to drastic performance degradation on previously learned tasks, phenomenon known catastrophic forgetting 4 5]. While storing exemplars of each class is simple approach to mitigate forgetting, it relies on the quality of saved exemplars and faces challenges in storage and privacy, especially for sensitive domains such as medical imaging. Hence, this paper focuses on coping with catastrophic forgetting during incremental learning without storing any old samples, which is called non-exemplar dlass-incremental learning (NECIL. 6 77.
In NECIL, serious challenge is discriminate between old and classes without access to old data. Most methods usually start considering handling conflicts between old and new classes only when new tasks arrive. While some methods stored prototypes model the distribution of old classes g 6 2 10) others extend the network structure to accommodate new classes 7 IT] However, in the base phase (i.e,, training on the first task), traditional training allows different classes
"Corresponding Author: Mang Ye
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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to divide up all the embedding space, causing trouble for subsequent conflict resolution. As shown in Fig. in the incremental phase (i.e,, training on tasks after the first one), with the influx of new classes, there are overlaps of the old and new classes in the embedding space that are difficult to discriminate. Moreover, due to the unavailability of old class samples, handling this conflict with only new task data is intractable. Instead, we suggest addressing this issue by learning prospectively at the feature level, which requires a two-pronged effort in both the base and incremental phases.
Firstly, the model should make room advance for the incoming classes in the future. Thus, the space of past classes does not need to be drasti- cally squeezed when expanding new classes. To this end, during the base phase, we construct a preemp- tive embedding squeezing constraint to enforce intra-class concentration and inter-class reserved separation. Specifically, we push instances from the same class closer together and in- stances from different classes farther allows more
Traditional Training
Prospective Leannnng
Base Phase
Class
Reserved
Class
Reorvvl
Class
Incremental Phase
apart in a mini-batchi space to be reserved in the initial em- bedding space, thus making the model ready for future classes.
Class
overlap
Reserved
Rearvill
Class
Secondly, the model should minimize the shock and impact of the new classes on the past classes, i.e., em- bed the new classes into the reserved space as much as possible. However, achieving the desired embedding of new classes when the old class data is fully unavailable is difficult. Inspired
The traditional training paradigm in NECIL con- siders conflicts between old and new classes only when new classes arrive and is prone to overlap. We suggest prospective learning to reduce conflicts: (1) reserve space for unknown classes; (2) make the newly coming class embedded in the reserved space.
Figure 1:
by previous works 66: 10], we try to accomplish this using prototypes (typically the class mean in the deep feature space) saved for each old class. During the incremental phase, propose prototype-guided representation update mechanism. Concretely, we use the network learned from previous tasks extract features from new task samples and project these features and the saved prototypes into a latent space. In the latent space, the new class features are pushed away from the region hosting the old class and embedded as much as possible the reserved space with the help of prototypes. We guide the update of the current model representation through the latent space to reduce the shock of the new classes on the former classes.
In summary, combining the above two ideas, our Prospective Representation Learning (PRL. scheme makes the following main contributions:
We impose preemptive embedding squeezing constraint to reserve space for future classes by reinforcing intra-class concentration and inter-class reserved separation.
We propose prototype-guided representation update strategy that utilizes the saved proto- types to reduce the impact of expanding new classes on old ones.
Extensive experiments four benchmarks suggest the superior performance of our approach over the state-of-the- the-art. We also provide detailed analys of our method.
2 Related Work
2.1
Class-Ineremental Learning
Mainstream CIL. methods can be roughly divided into three categories: rehearsal-basee methods, regularization-base methods, and sructure-based methods.

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reehearal--baser methods store a portion of seen data in a fixed-size memory buffer and replay it as new data arrives. Based on the stored data, some works use knowledge distillation techniques while others regularize the gradient to make more Additionally, several works design new strategies for memory management instead of simple random sampling. [19] 20 21 22 Although rehearsal-based methods effectively mitigate catastrophic forgetting, they are encumbered by privacy concerns and become impractical under stringent storage constraints.
to protect existing knowledge [12] 13
14
15
efficient use of the stored samples 16
17 18.
Regularization-baset methods estimate the importance of different parameters for past tasks and then limit the updating of these important parameters when learning new tasks 23 24 25 26]. In
incremental learning, the storage of importance weights becomes essential. However, these methods are encumbered by constraints on model parameters, consequently impeding knowledge transfer and leading to suboptimal performance, particularly in Long-sequence task streams.
Structure-based methods accommodate knowledge from new tasks by dynamically modifying the network structure. Some works extend the network by assigning new parameters of different forms to new tasks 127 28, 29 30). While this approach adeptly manages extended task sequences and sustains the performance of established classes, the linear growth of network parameters with the number of tasks and the necessity for reasoning across multiple forward propagations pose significant challenges. Parameter fusion [3]] and selecting partial parameters for expansion [3] mitigates this problem to some extent. An alternative is to mask part of the parameters that are highly correlated Their performance is
with the previous task at the parameter level or unit level B3 34 35
36
limited by the backhone obtained on the first task.
2.2 Mon-Exemplar Class-Incremental Learning
Recently, some works begin to focus on NECIL 8837 38 39 40 41: 42) 44 45 46), due to
where the algorithms have access to any past data. Li el al. (50] combine knowledge distillation with fine-tuning in a first attempt at incremental learning without a memory buffer. Zhu et al. [38 propose class augmentation and semantic augmentation to address the representation bias and classifier bias caused by the lack of old task data. Yin et al. (37) use model inversion technology to generate samples from previous tasks to alleviate forgetting. Based on (37. Gao et al. 39 introduce relation- relation-guided guided knowledge distillation to address the distributional gap between generated data and real data.
privacy and memory concerns 47 48 49
Zhu et al. 66] combat catastrophic forgetting for the first time by preserving prototypes and augmenting them. Yu et al. [ address the problem of prototype outdating in the current representation space by estimating the semantic drift of past tasks and compensating for it. Furthermore, Toldo el al. [9] subdivide the drift into feature drift and semantic drift and compensate for both, thereby achieving better results. Shi et al. [10) inject information about the current feature distribution into the prototype to model the distribution of past tasks. Wang et al. (5l) improve the prototype augmentation method based on density to make the model more focused on features of the old class with low density. Malepathirana et al. [52) use the domain information obtained from topological relations to optimize prototype augmentation to reduce inter-class overlap. However, previous works deal with conflicts between old and new classes only after the new data arrives and lack prospective consideration.
2.3 Embedding Space Regularization
Embedding space regularization has been extensively studied in literature 53
56
Chaudhry el al. (53) first propose learning tasks in different (low-rank) embedding subspaces that are kept orthogonal each other. They learn an isometric mapping by formulating network training as an optimization problem on the Stiefel manifold. Another idea is to implement orthogonality in the gradient space. Saha et al. (58) analyze network representations after learning each task with Singular Value Decomposition (SVD) to find the basis of the subspaces and store them in memory. Moreover, several methods promote forward compatibility through regularization in the initial phase. Zhou et al. [59] assign virtual prototypes to compress embeddings of known classes and reserve space for new classes. Shi et al. (00 encourage initial CIL learners to generate representations that are similar to those of models trained jointly on all classes. Compared to previous works, we target CIL. exemplar-fres scenarios (NECIL).. We consider how to resolve conflicts between new and old classes during the incremental phases, in addition to reserving space in the initial phase.
3

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3 Methodology
3.1 Problem Statement
The goal of NECIL is to continually train a unified model over a series of tasks to recognize all classes learned so far. The data stream can be defined as D {Do, Di.... Dr), where T is the number of incremental phases. At any phase i, the training set D, consists of the sample set X,(0 < < T) and the label set Y, In particular, the classes of all phases are disjoint, i.e. Yn = Ø Vi + j. It is notable that only Dr is available at current phase t. There are no old training sets (i.e, Do:t-1)
access save in memory. To facilitate analysis, model with two components: feature extractor F with parameters & and unified classifier G with parameters yo. For comprehensive evaluation of the model, the test set phase includes classes from all the seen label sets Yo U Y1 U... U At the time of testing, the model does not have access to the task ID, i.e., it does not know from which task the test sample come.
represent the
3.2 Baseline
We adapt the paradigm of existing NECIL works uses knowledge distillation and prototype rehearsal. Specifically, the base phase (i.e. = 0), the classification model is optimized under full supervision:
71 10 as our baseline, which primarily
argminG; = (fe, Pr; Di) (a.y)~D,
E Iv log (G (Fo.
(1)
Pe
where L, represents the overall loss function, Lee is the cross-entropy loss.
At the incremental phase (i.e., t > 0), standard fully supervised training seeks to minimize the following objective:
L Lce (0,, Pr: Do.c-1) + Lee (0z, (0; Di).
(2)
However, this especially challenging since previous training sets Do:-- are assumed to be unavailable in the NECIL setting. The absence of the first term in eq. (2) leads to a bias in favor of current classes in the feature extractor Fo, and the classifier G... To address this problem, existing
methods [38] 6 10) adopt knowledge distillation and prototype rehearsal to cope with the bias. Specifically, they take the frozen feature extractor Fe.-, from the previous phase
as teacher and the current one Fe, as a student. A distillation term is introduced to encourage the model to mimic the previous representation:
Lka(Oe; (0,,
Σ (z) Fo._, (z)122
ZEX;
where || ||2 denotes Fuclidean distance. Knowledge distillation helps maintain existing knowledge in Fe.. thus mitigating bias in the current feature extractor.
For the bias in the classifier, Specifically, after the training of - phase, we compute prototype p for each class e:
class class-representative prototypes (6] to balance the optimization.
pº = E
(Fe_.(()
c].
(a.1))-D-11
All prototypes of learned classes Po:-11 {ps, cloEYo. are stored in memory. In each training
iteration of current phase I, existing works [6, 38, 10 augment the memorized prototypes Po--1
to Po.-1 and train the classifier jointly with the current data D.. In particular, the prototypes are involved in the standard classification optimization with the following objective:
E ( Pott-) (pt.e)~Poos-1
log (9,, (+))).
(5)
Compared to exemplar rehearsal, prototype rehearsal is more memory efficient and privacy secure. In conclusion, the overall loss function of the baseline be expressed
(., D.) + CrpcooopPr Po.--1;; C. Lee (O., sPts D.) + on (n, 0,-1,
(6)
where an and (2 are the weights of the distillation loss and prototype loss, respectively. The specific implementation of prototype augmentation is not our focus. In this paper, we implement our approach based on the pipeline PRAKA [0]. Our method can be incorporated with different augmentations and plugged into other baselines, such PASS (6) and IL2A (38).

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Phase
Incremental Phase
festure
protatype
stored prototypes
CE Loss
+ *
Do
Fo
frozen old mode)
PES
Projector
Preemptive mbeeddig Squeezing
Laler--casss
reserved separation
Intre-class concentration
Space
Dt
latent space
aliem
current model
Constraints
Ft
curmnlspace
Figure 2: Overview of our Prospective Representation Learning (PRL) for NECIL. (A) During the base phase, we impose a preemptive embedding squeezing (PES) constraint to squeeze the space of the current class in preparation for accepting future new classes. (B) During the incremental phase, a prototype-guides away from old class prototypes in the latent space, which guides the update of the current model to mitigate the confusion of new classes with old classes.
representation update (PGRU) strategy is proposed to keep new class features
3.3 Prospective Representation Learning
An overview of our Prospective Representation Learning scheme is shown in Fig. 2 It consists of preemptive embedding squeezing constraint the base phase and a prototype-guide representation update strategy in the incremental phase. The specific implementation of the two components is described in the following.
Preemptive Embedding Squeezing, In the base phase (t = 0), a common training paradigm of NECIL is to optimize the empirical loss over the training set D, as eq. ( Without consideration of the future incremental learning, it overspreads the embedding space. As new classes come in, the embedding of old classes needs be squeezed to make room for new ones. However, striking balance in this process is challenging, especially without the old data. Therefore, we would like to be proactive and reserve space for future classes by squcezing the embedding of current classes in the base phase. Specifically, we impose preemptive embedding squeezing (PES) constraint to cluster features of the same class and make features of different classes separate from each other. To reduce complexity, the PES loss is computed over mini-batch data B = (x', y E D,, which can be formulated as:
Σ Ya' EBBB V/ y;
(Fo, ( Fo, (x))),
d = Σ
(8)
VaL V=r,*"EB
CrES(O; =1-::=1-110 + A (1+
where is the batch size, () denotes the cosine similarity operator. As LPES is minimized, the first term (1 s) facilitates intra-class concentration, and the second term (1 + d) aims to reinforce inter-class reserved separation, shown in Fig. 2 (A). Since s, d E 1-1, 1), both terms than zero. The hyper-parameter X controls the priority ratio of intra-class constraints and inter-class constraints. Since our PES is implemented in vectorized manner on the mini-batch, it does not incur excessive computational burden.
greater
With the preemptive embedding squeezing constraint, the optimization objective for the base phase training in eq. (I) can be rewritten as:
L: Loe Pi; D.) + 7 (Prs( D.).
(10)
where y is hyperparameter controlling the weights of loss.
5

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Algorithm 1 Proposed Method
input: Data streams D, Model ( (Fo, Gp), Factors À and 7, Projector Po.
1: for all phases & {0. 1,..,.7 T do
2: Get training set D:
3:
for minibatch B {at 1im De do
4:
i then
5:
Compute C. Lye + LPnS Update model (Fo,, 9pp
6:
7:
else
8:
Get prototypes set Po--1
9:
Compute C₁ Lee + aiLkd + agCyro + a3 PGCRGR Update model {Fe,, G and projector Po.
10:
end if
12: end for
13: Compute pd=
E
[Fo, (z) 1 =
(x Update prototypes set P0:01
14:
15:
end for
16: return Model {Fo, Gp.}
Prototype-Guided Representation Update. In the incremental phase (t >> 0), would like to embed the new class into the previously reserved space. The plain idea is to keep the new classes well clustered and distanced from the old ones. To this end, propose prototype-guide
representation update (PGRU) strategy, as shown in Fig. 2 (B), which employs prototypes as proxies for past classes to guide the embedding of new classes into the appropriate space. However, is not practical to establish relationship directly between the saved prototypes and the new class features extracted by the current model due to the continual updating of the current embedding space. To mitigate the mismatch between the old class prototype and the new class features, on the one hand, we use the frozen model from the previous phase / 1 extract the new class features, which has been implemented in the baseline as shown in eq. B on the other hand, the new classes features and the saved prototypes are projected into a unified latent space. Then, we construct orthogonal structures between the new class features and the old class prototypes in the latent space:
Lort
E (F),,
(11)
Ve'EB
Vp'EPor-1
where I denotes the absolute value operator, P is projector with parameters d. Similarly, Cort is also implemented in the mini-batch to reduce computational costs. Inspired by [61], we use simple undercomplete autoencoder the projector. It consists of a linear layer followed by ReLU activation that maps the features to a low-dimensional subspace and another linear layer followed by sigmoid activation that maps the features back high dimensions. When minimizing Cort, it will promote orthogonality between the new class features and the old class prototypes. By the above operations. we would like allow the new class of features be embedded in appropriate positions and keep clustering in the latent space.
Our ultimate goal is guide the update of the current model. Hence, align the current embedding space with the latent space as:
Latsgnn
LMSE(Poo (Fo., (e(())
(12)
TEX.
where LMSE is mean squared error (MSE) loss. In summary, the PGRU loss can be defined as:
LPGRU = Lort(de; D,, Pot-1) + Lutiign (0,, te; D2).
(13)
In the incremental phase, the optimization objective in eq. (6) can be rewritten as:
L, Lon Pr; D:) + on La D,)+
(14)
(ppp Po.-1) a3CpoRU (0c, QG De, Poa-1).
The main procedure is summarized in algorithm I

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4 Experiment
4.1 Experimental Setting
Dataset. We conduct comprchensive experiments on four public datasets: CIFAR-100 [62], Tinylm- ageNet [63] ImageNet-Subset and ImageNet-16 IK [64] CIFAR-100 consists of 100 classes, where each class contains 500 training images and 100 testing images with size 32x32. TinylmageNet has 200 classes in total, and the image size is 64x64. Each class in TinyImageNet contains 500 training images and 50 testing images. ImageNet- I is a large-scale dataset comprising about 1.28 million images for training and 50,000 for validation with 500 images per class. ImageNet-Subset is a 100-class subset randomly chosen (random seed 1993) from the original ImageNet-IK. KK. The image size of IeageNet-1 K much larger than the other two datasets, which poses test of sensitivity to large-scale data.
divide around half the classes for the base phase, and the rest are divided equally into all the incremental phases. For CIFAR- 100 and ImageNer-Subser. 1) 50 classes for base phase and 5 incremental phases of 10 classes; 2) 50 classes for base phase and 10 incremental phases of 5 classes; 3) 40 classes for base phase and 20 incremental phases of 3 classes. For TinylmageNee, we start by training the model with 100 classes in the base phase and distribute the remaining classes into three incremental settings: 1) 5 incremental phases of 20 classes; 2) 10 incremental phases of 100 classes; 3) 20 incremental phases of 5 classes
Protocol. Following the setting in 6
10. 7.7
Implementation details. Our method is implemented with PyCIL [65]. For a fair comparison with 16]. we adopt ResNet- 18 [66] as the backbone network. The batch size is set to 64 for CIFAR- 100 and TinyImageNet and 128 for ImageNet-Subser and ImageNet- IK. During training, the model is optimized by the Adam optimizer with 31 0.9, 83 0.999 and e le- (weight decay 2e-4). For ImageNet- K, the learning rate starts at 0.0005 for all phases. The learning rate decays to 1/10 of the previous value every 70 epochs (160 epochs in total) in the base phase and every 45 epochs (100 epochs in total) in each incremental phase. For other datasets, the learning rate starts from 0.001 and decays 1/10 of the previous value every 45 epochs (100 epochs in total) for all phases. We use = 0.5 and y = 0.1 for all datasets. Regarding the loss weights, for comprehensive performance considerations and with reference previous studies 6 5T], set 01 10, 022 10, and 0g for training. We conduct our experiments on an RTX4090 GPU,
Metric. We evaluate the methods in terms of average incremental accuracy. Average incremental accuracy Ar is computed as the average of the accuracy of all phases (including the base phase) and is a fair metric to compare the overall incremental performance of different methods:
1
AT
de:
(15)
T+1
where a, is the average accuracy over all seen classes phase l.
4.2
Comparison with SOTA
We compare our method with the state-of -hr- (SOTA) methods of NECIL (EWC 23 LwF MC
[67]. MUC [68], SDC [8), PASS (6) SSRE (7], SOPE [II, POLO [5I. PRAKA [10] and NAPA- VQ 52). "Fine-tuning" refers to continuously fine-tuning the network on the new task with only
cross-entropy loss. "Join!" means that when learning new task, all data from past tasks are available
to jointly train the model, which can be considered as an upper bound of the CIL model. The results reported for PASS are obtained with self-supervised learning.
The quantitative comparisons of average incremental accuracy are reported in Tab. I In comparison with the SOTA, our method improves by 1.4% and 6.0% on CIFAR-100 and Tiny ImageNet datasets, respectively. To further investigate the behavior of different methods on larger data, we also evalu- ated their performance on ImageNet-Subset Compared with suboptimal results, PRL achieves an average improvement of 3.6%. The outstanding performance on ImageNet- Subset demonstrates the reliability of our method. To provide a more nuanced view of the changes in performance of the different methods over the course of incremental learning, we show accuracy curves for CIFAR- 100, Tiny ImageNet and ImageNet-Subsee in Fig. 3 The accuracy of our method remains ahead as we continue to learn new tasks. By prospective learning, our approach demonstrates strengths early on that will be maintained and even enlarged over the course of continuously learning new tasks.
7

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Table 1: Quantitative comparisons of the average incremental accuracy (%) with other methods P represents the number of incremental phases. The best performance is shown in bold, and the sub-optimal performance is underlined. The relative improvement compared to the SOTA NECIL methods is shown in red.
CIFAR- 100, TinyImageNet and ImageNet-Subsee
CIFAR-100
Tiny ImageNet
SatageNet-Subset
Methods
P=5
P=10
P=20
P=5
P=10
P=20
P=5
P=10
P=20
Fine-tuning
23.15
12.96
7.93
18.64
10.68
5.75
23.43
13.12
7.96
Joint
76.72
76.72
76.72
63.08
63.08
63.08
78.94
78.94
78.94
EWC 23
24.48
21.20
15.89
18.80
15.77
12.39
20.40
LwF MC 67
45.93
27.43
20.07
29.12
23.10
17.43
31.18
MUC 68
49.42
30.19
21.27
32.58
26.61
21.95
35.07
SDC g
56.77
57.00
58.90
61.12
PASS 6
63.47
61.84
58.09
49.55
47.29
42.07
64.40
61.80
51.29
SSRE
65.88
65.04
61.70
50.39
48.93
48.17
67.69
SOPE
66.64
65.84
61.83
53.69
52.88
51.94
69.22
POLO 51
68.95
68.02
65.71
54.90
53.38
49.93
70.81
69.11
PRAKA 10
70.02
68.86
65.86
53.32
52.61
49.83
69.81
68.98
63.95
NAPA
12
70.44
69.04
67.42
52.77
51.78
49.51
69.15
68.83
63.09
PRL (Ours)
71.26
70.17
68.44
58.12
57.24
54.51
72.85
71.54
66.88
Improvement
+0.82
+1.13
+1.02
+3.22
+3.86
+2.57
+2.04
+2.32
+2.93
CIFAR-100 [5 phases]
phases)
phases)
80
PASS
S5RE
100-3 (co80)
70
70
60
50
60
SOPE
PRAKA
50
50
NAN-VQ
PRL (Ours]
100
Tinylmage/Net (5 phases]
NinylmageNet [10 phases)
TinylmageNet (20 phases)
ImageNet Subset (10 phases]
top 1Ac288)
50
60
60
40
30
100
120
240
260
200
140
160
200
120
540
250
180
200
number of dosses
numberr
number clssess
Figure 3: Detailed accuracy curves showing the top-1 accuracy of each incremental phase CIFAR- 100, TinylmageNer and ImageNet-Subbst..
4.3 Ablation Study
To analyze the impact of each component in our method, we perform several ablation studies on CIFAR-100 and TinyImageNet datasets. We use the prototype augmentation technique in [10] as
eq. (5) in our baseline. As shown in Tab. 2 The first line shows the performance of our baseline model. Our baseline strong due to using the prototype augmentation [10). Even on the strong baseline model, both preemptive embedding squeezing (PES) constraint and prototype-guided representation update (PGRU) strategy can bring considerable performance improvements. Furthermore, the table shows that PES plays more central role than PGRU. This is reasonable since the space reserved by PES for future classes the basis for the PGRU to guide new classes to embed in the representation space during the incremental phase.
4.4 Analysis
Visualization. analyze the impact of PRI. on representation learning, we visualize the embedding space of 2D feature vectors (IFAR-100 (5 phases) with t-SNE [69] in Fig. 4 Specifically, we (1)

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Table 2: Ablation study (in average incremental accuracy) of method on CIFAR-100 and TinylmageNet datasets.
CIFAR-100
TinyImageNet
Methods
P=5
P=10
P=20
P=5
P=10
P=20
baseline 70.57
69.25
68.52
65.93
55.04
54.15
51.65
baseline w/ PES
69.64
67.58
57.08
55.84
53.58
baseline w/ PGRU
70.36
69.23
67.17
56.79
56.05
53.16
PRL
71.26
70.17
68.44
58.12
57.24
54.51
old coas
dass
Baseline
PRL
Baseline
PRL
Figure 4: Visualization of the impact of PRL on the feature representations. Dashed circles and arrows highlight observable differences between baseline and PRL. PRL visually concentrates the distribution of features within classes, disperses the distribution of features between classes, and mitigates inter-class confusion.
visualize the features of randomly selected subset of classes from Do (old class features) after the base phase, and (2) visualize the old class features along with subset of classes from Dr (new class features) after the last phase. As shown in the first row, once the training of the base phase (1 = 0) is complete, the model integrated with PRL has more tightly clustered intra-class distributions (blue circles) and more dispersed inter- distributions (-)). Thus, more space is reserved for learning new classes. The second row is visualized after the last phase
T 5). It can be observed that the overlap (red circles) in the baseline model increases, causing confusion between the old and new classes. In contrast, PRL reduces the overlap between classes, making them easier distinguish. Moreover, the new classes are farther away from the old ones (+) compared to the baseline.
Comparison of the confusion matrix. Figure 5 compares the confusion matrices obtained by fine- tuning, PASS (6) NAPA-VQ [52) and our PRL on CIFAR-100. The diagonal entries indicate correct classification, while the non-diagonal entries indicate misclassification. Due the forgetting of old classes, fine-tuning produces predictions that are biased toward the most recent classes, showing strong confusion on the last task. PASS clearly mitigates this confusion but still predicts more intensively on recent tasks. The predictions of NAPA-VQ are largely centered on the diagonal, but its predictions are more accurate for the initial classes that appear in the base phase (the red patches more localized in the first half of the diagonal). In contrast, there are more red patches visible along the diagonal and more evenly distributed in the confusion matrix of PRL, which explains the higher average accuracy of our method compared to NAPA-VQ and the absence of serious bias towards either new or old classes.
Fine-tuning
PASS
(c) NAPA-VQ
PRL(Ours)
20
20
20-
20-
0.8
Classes
40
0.6
60
60
0.4
30
30
80
50
02
300
20
40
50
20
100
130
20
40
60
100
100
20
66
86
100
300
20
40
50
80
100
0.0
Predicted Classes
Predicted Classes
Predicted Classes
Predicted Classes
Figure 5: The comparison of confusion matrix fine-tuning, PASS, NAPA-VO VQ and our method on CIFAR-10 100 (10 phases).

---

Plasticity and stability analysis. An incremental learner should acquire new knowledge of the current task for the sake of plasticity and also preserve knowledge from previous tasks for the
PRAKA
NAPA-VQ
PRL (Ours)
Old Tasks Average Accuracy
Current Task Accuracy
70
70
Accuracy (94)
sake of stability [T]. We present an
analysis of the plasticity and stability of the different methods in Fig. 6 First, observe gradual decline in aver-
50
age performance on past tasks during incremental learning. This is rational because experiencing more tasks also results in heavier catastrophic forget- ting. Nonetheless, our method exhibits better stability due to less degradation and consistently superior average per- formance old tasks. Then we turn our attention to the current task and also found a perfornance degradation as more and more tasks are learned. This corresponds to a gradual reduction in plasticity since tasks are sampled uniformly from the set of possible tasks, which is consistent with observations from
40
40
Phase
Phase
Figure 6: During incremental learning, our method shows less performance degradation on past tasks. Meanwhile, in contrast to other methods other methods whose performance on new tasks declines the number of tasks increases or remains poor, our method shows good plasticity in the performance of new tasks.
previous studies (72 73]. PRAKA [10] starts with good performance, but its plasticity degrades as more tasks are learned. NAPA-VQ consistently performs poorly on the current task, which is also in line with the results in Fig. [ Remarkably, PRL maintains a good performance on the current task
and has yet to show a visible decline. In general, our method achieves a better trade-off between
stability and plasticity.
5 Conclusion and Limitation
In this work, consider the conflict between old and new classes in NECIL from prospective view. In the base phase, we construct preemptive embedding squeezing constraint to reserve space for future classes by enforcing intra-class concentration and inter-class reserved separation. In the incremental phase, we propose a prototype-guided representation update (PGRU) strategy, which reduces the impact on the old class during model update by keeping the new class embedding away from the old class prototype. In cases where exemplars cannot be saved, waiting until the conflict arrives could exacerbate the problem, and we offer a novel solution. Through extensive experiments on four public benchmarks, our method exhibits excellent average performance and can provide good balance between stability and plasticity. However, since the number and distribution of unknown classes cannot be predicted, how to rationally allocate the space of base classes in prospective learning open to further discussion.
Acknowledgments
This work is partially supported by National Natural Science Foundation of China under Grant (62176188, 62361 166629, 62225113) and Key Research and Development Project of Hubei Province (2022BAD175). The numerical calculations in this paper have been done on the supercomputing system in the Supercomputing Center of Wuhan University.
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A Appendix supplemental material
A.1 Detailed Description of the Accuracy Curve
To facilitate comparison of future work with method, we provide detailed values of the accuracy curves in Tab. B] Tab. 4 and Tab.55 where 'A' represents the CIFAR-100 dataset, 'B' represents the TinyImageNet dataset and 'C' represents the ImageNet-Subset dataset, respectively.
Table 3: Detailed values of accuracy under the setting of 5 phases.
Phase
Dataset
5
A 82.80
75.65
72.10
68.26
65.52
63.44
66.58
60.58
59.04
57.14
54.10
52.13
C
84.52
77.90
72.32
69.72
67.16
65.44
Table 4: Detailed values of accuracy under the setting of 10 phases.
Phase
Datasets
0
3
5
8
10
82.80
78.76
74.90
73.18
70.71
69.53
67.35
65.36
64.90
63.24
61.71
B
66.58
62.75
61.02
58.83
58.57
56.73
56.34
54.79
53.18
51.64
50,25
C 84.52
80.69
76.37
73.57
71.89
70.51
68.6
67.13
65.53
63.68
64.10
Table 5: Detailed values of accuracy under the setting of 20 phases.
Phase
Datasets
0
2
3
5
8
A
83.45
79.81
78.85
76,80
76.06
74.64
72.64
70.52
68.27
67.84
B
66.38
63.26
62.22
61.19
60.07
58,85
57.68
57.46
56.45
55.31
C
84.75
80.84
77.91
78.08
75.27
74.55
73.31
69.38
67.75
65.85
Phase
Datasets
10
12
13
14
15
16
17
18
19
20
66.80
66.36
66.37
64.06
62.84
61.46
61.61
60.77
58.98
58.94
57.74
B
54.34
53.61
53.51
52.41
51.69
50.23
49.06
48.05
47.58
47.63
45.58
C
63.66
62.36
62.18
60.86
60.22
60.85
57.73
57.91
57.30
57.32
56.52
Evaluation Large Datasets and Robustness. To further demonstrate the effectiveness of our method, we evaluated it on a large-scale dataset - ImmageNetIIK For ImageNet-IK, we allocate 500 classes for the base phase and 50 classes for each of the 10 incremental phases. As shown in Table o our method shows an improvement of 1.9% compared to the suboptimal results. The results of our method obtained by averaging three replicate experiments, and we different random seed for each run. To illustrate the stability of our method, we report the standard deviation of these three results. As shown in Tab. 6. the random seed has little impact the results of our approach.
Table 6: The number after + in the last line represents the standard deviation of three different runs.
CIFAR- 100
TinyImageNet
Methods
P=5
P=10
P=20
P=5
P=10
P=20
SOPE 11
66.64
65.84
61.83
53.69
52.88
51.94
POLO
51
68.95
68.02
65.71
54.90
53.38
49.93
NAPA [22
70.44
69.04
67.42
52.77
51.78
49.51
PRL (Ours)
11.26-00.19 19
70.1740.31
68.44
58.12-10.48
57.24+0.41
54.51
ImageNet-Subset
ImageNet-IK
Methods
P=5
P=10
P=20
P=10
SOPE 11
69.22
60.20
POLO
51
70.81
69.11
61.53
NAPA 52
69.15
68.83
63.09
54.21
PRL (Ours)
22.85-400.55
71.54:10.27
66.88-L0.37
62.74-10.34
15

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Table We report the performance gain of average incremental accuracy by applying PRL other NECIL baselines. Absolute gains are marked in (red).
CIFAR-100
Methods
P=5
P=10
P=20
IL2A [38
67.35
61.03
60.67
+PRL
69.53 (+2.18)
62.49 (+1.46)
62.36(+1.69)
PASS [6]
63.47
61.84
58.09
+PRL
66.22 (+2.75)
62.85 (+1.01)
58.85 (+0.76)
Plug-and-play with other NECIL methods. Existing NECIL methods mainly focus on backward- looking means of resolving conflicts between old and new classes, which does not contradict our prospective learning. Therefore, integrate PRL into the existing NECIL methods. Tab, Tab..7illa illlustrates the performance gains achieved by incorporating PRL these methods. In the setting of the CIFAR dataset with three different lengths of task sequences, PRL improved accuracy by average of 2.7% for IL2A 38 and 2.3% for PASS (6, which demonstrates the good compatibility of our method.
A.2 Impact of the hyper-parameter
To investigate the sensitivity of our method to the pyper-parameters À and 7, we performed ablation experiments on three settings (5 phases, 10 phases and 20 phases) of the CIFAR-100 dataset. In Fig. we show the impact of A, which controls the priority ratio of intra-class constraints and inter-class constraints. A smaller À means that the preemptive embedding squeezing (PES) is more concerned with intra-class concentration. Conversely, for a larger more emphasis placed on inter-class separation. When the value of À is either too large too small, the performance of our method degrades, indicating that there is need to maintain a certain balance between the intra-class constraint and the inter-class constraint. The best performance is achieved when À ís equal to 0.5, suggesting that for prospective learning NECIL, intra-class concentration could more important than inter-class separation.
We also provide an analysis of the impact of the hyper-parameters 7 in Fig. The performance of our method is stable on the 5 phase setting. The performance of the model gradually increases as increases on the 10-phase and 20-phase settings, peaking at ạ 0.1. However, continued increase in the values of leads to a decline in model performance. We argue that too large loss weights cause PES to interfere with the optimization of cross-entropy for classification performance. In addition, our method is more sensitive to the values of À and when there are more tasks (20 phases) to learn.
For the hyperparameter of loss weight, a sensitivity analysis is performed on one of the hyperparameters, default settings are used for the remaining hyperparameters. As shown Fig. [ the left column shows the effect of changing the value of each hyperparameter on the average incremental accuracy of our method, and the right
(r) 10, 02 10, and 03 by default. When
72
71.01
71008
71.17
71.32
71.18
70.56
average accuracy (96)
72
71.14
71.16
70.1
70
70.10
70.17
70
68.67
70.17
68
67.93
67.72
67.48
67.52
57.78
67.81
67.49
67.14
66
5 phoses
10 phoses
20 phases
64
64
62
0.25
0.75
0.02
value of
value
Figure 7: Impact of the preemptive embedding squeezing, which con- trols the priority ratio of intra-class constraints and inter-class constraints. Larger values of À represent a stronger inter-class separation.
À in our
Figure 8: Impact of the hyper-paramen which controls for the weight of the PES loss. Larger values of X represent that the PES loss exerts greater influence in the base phase of training compared to the cross-entropy loss.
16

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Impact of hyperprrameeerr on overall performance
Impact hyperparameters on the new and old tasks
[a]
(d)
80
incremental acuuracy [84
72
70.48
72.50
71.6
71.19
dasses
classss
$8.69
(%6) aacunnee
70
1A.10
07.12
65.68
60
64
-ijeo Pu5
P+30
P-20
50
3
10
15
20
value of (
value dq
(b)
(e)
80
average intremental accurasy [8)
11:21
71:17
71:24
71:20
70.56
- new disses
145 chrses
70.55
70
70
93.93
70.09
70.17
00.01
68.00 20
GLM
08.15
60
PrS
Ph
P-20
50
61
10
20
3
10
20
value ifg
volue (1)
(c)
(f)
avange incrementii accuracy (8)
70
70:88
71.35
71.26
71.04
70.79
inder new dasses
-d clases
655
00.72
70.09
70.17
70.25
70.22
accuracy
60
65.32
08.44
18:20
68.11
68.06
67.54
55
P-10
50
0.5
1
10
value of 0g
value R3
Figure 9: The figures in the left column show the effect of changing the value of each hyperparameter on the average incremental accuracy of our method on CIFAR-100 dataset, where 'P' denotes the number of incremental phases. The figures in the right column show the effect of changing the value of each hyperparameter in the last phase on the accuracy on the new and old tasks on CIFAR- -10AR-100 dataset (P=10), respectively.
column shows the effect of changing the value of each hyperparameter in the last phase on the accuracy on the new and old tasks, respectively.
Among the three byperparameters in eq. (4). an and ar are common in previous NECIL methods and represent the weights of distillation loss and prototype loss, respectively. The main role of these two loss functions is to maintain the pre-existing knowledge of the model. Therefore, as shown in Fig. (d) and Fig. (e), as on and 02 get larger, the optimization of the model will biased towards maintaining stability at the expense of plasticity, resulting in the model performing better on the old task and worse on the new task. can be seen that as the value of a1 and 02 increases to a certain level its performance improvement on old tasks slows down. Excessively large values of and will bring much less gain on the old task than they will hurt performance on the new task. For the consideration of comprehensive performance and with reference to previous works 6 51, we set
01 = 10 and 22 = 10 for our method.
Then controls the loss of the Prototype- Guided Representation Update (PGRU) proposed in this paper. In Fig. (c), as 0g increases PGRU comes into play. The effect of increasing ag on the overall performance of the algorithm fluctuates, which may be caused by overly strict constraints on the learning of new class representations. Overall, our algorithm robust to the hyperparameters.
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24


Reviews:
[{"review_id": "KBHa8gKkyP", "reviewer": "Reviewer_KX3q", "summary": "The paper proposes a method to deal with incremental classification task in which no exemplars from the previously seen classes can be saved for usage during training on the newly arriving classes. The proposed method squeezes the embedding distribution of the current classes to reserve space for forward compatibility with future classes and reduces the impact of introducing new classes by trying to restrict the embeddings of the new classes in the regions not occupied by the previously seen classes. The method uses the class prototype of the previously seen classes but does not use any exemplars. The method uses Preemptive Embedding Squeezing and Prototype-Guided Representation Update to achieve the above goals.", "questions": "The paper should include a separate section to discuss the difference between this method and other methods that employ feature space compression for incremental learning.\nThe standard deviation in the results between different runs is not mentioned.\nApart from accuracy improvement, does the proposed method involve fewer/more parameters as compared to the other compared methods? Is there any difference in training or testing time for the proposed method as compared to the others.", "limitations": "The paper mentions a limitation in that it is not able to rationally allocate the space of base classes since the number and distribution of unknown classes cannot be predicted. However, the authors did not experimentally demonstrate any such issue, which can be possibly done by changing the order of the classes between multiple runs.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The proposed method is based on the premise of compressing the feature space occupied by the previously seen classes to ensure less interference between old and new classes, which sounds logical. \nThe method seems to be clearly written.\nThe proposed method performs well on all the compared datasets.", "weaknesses": "The paper should include a separate section to discuss the difference between this method and other methods that employ feature space compression for incremental learning.\nThe standard deviation in the results between different runs is not mentioned.\nApart from accuracy improvement, does the proposed method involve fewer/more parameters as compared to the other compared methods? Is there any difference in training or testing time for the proposed method as compared to the others.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your positive response! We are delighted that the reviewer has found our method clear and sound. We have addressed the main points and questions below.\n\n---\n\n**Q1：Lack of discussion with other methods that employ feature space compression for incremental learning.**\n\n**A1**: Thanks to your suggestion, we will add a separate subsection to the Related Work section to discuss methods on feature space compression in incremental learning.\n\n---\n\n**Q2: The standard deviation of the results between different runs that change the order of the classes.**\n\n**A2**: We perform three runs and use a different random seed to set the class order for each run. The table below shows the standard deviation of the three runs, where 'P' denotes the number of incremental phases and 'Tiny' denotes the TinyImageNet dataset. The experiments show that our method is robust to different class orders.\n\n|     | &nbsp; CIFAR100 (P=5) &nbsp; | &nbsp; CIFAR100 (P=10) &nbsp; | &nbsp; CIFAR100 (P=20) &nbsp; | &ensp; Tiny (P=5) &ensp; | &ensp; Tiny (P=10) &ensp; | &ensp; Tiny (P=20) &ensp; |\n| --- | :---: | :---: | :---: | :---: | :---: | :---: |\n| PRAKA | 68.95 | 69.02 | 65.71 | 54.90 | 53.38 | 49.93 |\n| NAPA-VQ | 70.44 | 69.04 | 67.42 | 52.77 | 51.78 | 49.51 |\n| PRL (Ours) &nbsp; | **71.26**$\\pm$0.19 | **70.17**$\\pm$0.31 | **68.44**$\\pm$0.24 | **58.12**$\\pm$0.48 | **57.24**$\\pm$0.41 | **54.51**$\\pm$0.36 |\n\n---\n\n**Q3: Comparison on the number of model parameters, training time and testing time.**\n\n**A3**: The introduction of a projector in our method introduces additional parameters, but the number of parameters added is minimal compared to the network as a whole. And the forward propagation does not need to go through the projector during the test. The following table shows the model parameters of our method, the training time for one epoch in the last incremental phase and the testing time (on all classes) on **CIFAR-100**. The experimental results are performed with in the same environment.\n\n**Model parameters：**\n\n|     | &nbsp; PASS &nbsp; | &nbsp; PRAKA &nbsp; | &nbsp; NAPA-VQ &nbsp; | &nbsp; PRL (Ours) &nbsp; |\n| :---: | :---: | :---: | :---: | :---: |\n| Parameters &nbsp; | 10.93M | 11.02M | 11.18M | 11.30M |\n\n**Testing time:**\n\n|     | &nbsp; PASS &nbsp; | &nbsp; PRAKA &nbsp; | &nbsp; NAPA-VQ &nbsp; | &nbsp; PRL (Ours) &nbsp; |\n| :---: | :---: | :---: | :---: | :---: |\n| Test time &nbsp; | 1.82s | 2.38s | 4.31s | 1.74s |\n\n**Training time for one epoch:**\n\n|     | &emsp; P=5 &emsp; | &emsp; P=10 &emsp; | &emsp; P=20 &emsp; |\n| :---: | :---: | :---: | :---: |\n| PASS &nbsp; | 10.09s | 5.92s | 4.81s |\n| PRAKA &nbsp; | 7.62s | 4.27s | 3.57s |\n| NAPA-VQ &nbsp; | 20.06s | 10.62s | 6.54s |\n| PRL (Ours) &nbsp; | 7.97s | 4.54s | 3.55s |\n\nWe are looking forward to answering any follow up questions during the discussion period.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Shxbdk3eeW", "reviewer": "Reviewer_FnFn", "summary": "This paper focuses on non-exemplar class-incremental learning, specifically addressing the challenge of balancing old and new classes. The author introduces Prospective Representation Learning (PRL), which involves constructing a preemptive embedding squeezing constraint to allocate space for future classes. Additionally, the author proposes a prototype-guided representation update strategy.", "questions": "1.Many previous works have studied mapping class centers to different subspaces (orthogonal). The paper should compare similar works to highlight the differences and advantages of the proposed method. As indicated by the following references: 1, 2.\n2.The PASS paper also uses prototype augmentation (and proposes other methods), but your baseline is higher than PASS, especially in TinyImageNet P=20, by almost 10%. The author should explain the advantages of using prototype augmentation in the baseline or provide experimental results without prototype augmentation.", "limitations": "Yes", "rating": 5, "confidence": 5, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "1.The Preemptive Embedding Squeezing (PES) constrains the current class space to prepare for accommodating future new classes.\n\n2.The Prototype-Guided Representation Update (PGRU) strategy ensures that features of new classes remain distinct from prototypes of old classes in the latent space.\n\n3.The writing is clear.\n\n4.The paper includes extensive experiments.", "weaknesses": "1.What is the meaning of IIC in equation 9? The paper does not explain its meaning; I guess it stands for PES.\n2.Many previous works have studied mapping class centers to different subspaces (orthogonal). The paper should compare similar works to highlight the differences and advantages of the proposed method. As indicated by the following references: [1,2,3].\n3.The PASS paper also uses prototype augmentation (and proposes other methods), but your baseline is higher than PASS, especially in TinyImageNet P=20, by almost 10%. The author should explain the advantages of using prototype augmentation in the baseline or provide experimental results without prototype augmentation.\n4.In equation 14, there are many hyperparameters, /alpha1,2,3. The author should provide more sensitivity analysis of the hyperparameters to make the experiments more thorough.\n\n[1] Chaudhry A, Khan N, Dokania P, et al. Continual learning in low-rank orthogonal subspaces[J]. Advances in Neural Information Processing Systems, 2020, 33: 9900-9911.\n[2] Guo Y, Hu W, Zhao D, et al. Adaptive orthogonal projection for batch and online continual learning[C]//Proceedings of the AAAI Conference on Artificial Intelligence. 2022, 36(6): 6783-6791.\n[3] French R M. Dynamically constraining connectionist networks to produce distributed, orthogonal representations to reduce catastrophic interference[C]//Proceedings of the sixteenth annual conference of the cognitive science society. Routledge, 2019: 335-340.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your thoughtful questions! We are glad that you found the paper easy to read and affirm our experiment. We hope that our response below will address your\nconcerns.\n\n---\n\n**W1: What is the meaning of IIC in equation 9? Is it a writing error?**\n\n**A1**: We are sorry for our writing error. It should be $\\mathcal{L}_{PES}$ in Eq. 9. We will carefully check and ensure such errors are eliminated in the final version of the paper.\n\n---\n\n**W2 & Q1: Discussion of the differences and advantages of the method proposed in this paper over previous studies on mapping class centers to different subspaces.**\n\n**A2:** First, unlike previous works, PRL targets CIL in exemplar-free scenarios (NECIL). PRL does not need to store exemplars of past tasks to promote subspace orthogonality.\n\nSecond, previous works start to deal with the conflict between old and new tasks only when a new task arrives. However, due to the lack of samples from old tasks in NECIL, it is intractable to deal with this conflict using only the new task data. Instead, we consider reserving space for unknown new classes in the initial phase to prepare for conflict resolution in advance.\n\nThe references you provided is enlightening to our research. We will include a discussion of the above methods in the Related Work section.\n\n---\n\n**W3 & Q2: Explain the advantages of using prototype augmentation in the baseline compared to PASS.**\n\n**A3:** Since only one prototype is saved for each class, using one prototype to represent the old class distribution would lack diversity. Prototype augmentation helps to maintain the discrimination between old and new classes and prevents the decision boundary from being biased in favor of the new classes. From the perspective of our paper, both prototype augmentation and the knowledge distillation technique commonly used in NECIL are prompting the model to achieve backward compatibility, *i.e.*, to make the updated model compatible with classes that have already been learned. The PRL proposed in this paper, on the other hand, is prompting the model to achieve forward compatibility, i.e., enhancing the ability of the model to be compatible with unseen classes. Therefore, better performance can be achieved when both forward and backward compatibility of the model are improved.\n\nAfter PASS [1], many other prototype augmentation strategies have been proposed, such as [2, 3]. We adopt the prototype augmentation method called Prototype Reminiscence (PR) from [2] as our baseline, which is described in Section 3.2 (line 162).\n\nThe experiments in the Appendix (Table 6) also demonstrate that our PRL can be combined with PASS or other methods in a plug-and-play manner and enhance its performance. We complement the performance of PASS combined with PRL on the **TinyImageNet** dataset in the following table, where 'P' denotes the number of incremental phases. It can be seen that the PRL brings a significant boost to PASS as well.\n\n|     | &ensp; P=5 &ensp;  | &ensp;  P=10 &ensp;  | &ensp;  P=20 &ensp; |\n| :---: | :---: | :---: | :---: |\n| PASS &ensp;| 49.55 | 47.29 | 42.07 |\n| PASS+PRL &ensp; | 52.19 | 50.38 | 42.63 |\n\n---\n\n**W4: More sensitivity analysis of the hyperparameters.**\n\n**A4:** We set $\\alpha_1=10$, $\\alpha_2=10 $, and $\\alpha_3=2$ by default. When a sensitivity analysis is performed on one of the hyperparameters, default settings are used for the remaining hyperparameters. Due to rebuttal limitations, the experiment results are shown in the **pdf file** attached to the Author Rebuttal. The figures in the left column show the effect of changing the value of each hyperparameter on the average incremental accuracy of our method. The figures in the right column show the effect of changing the value of each hyperparameter in the last phase on the accuracy on the new and old tasks, respectively.\n\nAmong the three hyperparameters in Eq. 14, $\\alpha_1$ and $\\alpha_2$ are common in previous NECIL methods and represent the weights of distillation loss and prototype loss, respectively. The main role of these two loss functions is to maintain the pre-existing knowledge of the model. Therefore, as shown in Figure (d) and Figure (e), as $\\alpha_1$ and $\\alpha_2$ get larger, the optimization of the model will be biased towards maintaining stability at the expense of plasticity, resulting in the model performing better on the old task and worse on the new task. It can be seen that as the value of $\\alpha_1$ and $\\alpha_2$ increases to a certain level its performance improvement on old tasks slows down. Excessively large values of $\\alpha_1$ and $\\alpha_2$ will bring much less gain on the old task than they will hurt performance on the new task. For the consideration of comprehensive performance and with reference to previous works [1, 3], we set $\\alpha_1 = 10$ and $\\alpha_2=10$ for our method.\n\nThen $\\alpha_3$ controls the loss of the Prototype-Guided Representation Update (PGRU) proposed in this paper. In Figure (c), as $\\alpha_3$ increases PGRU comes into play. The effect of growing $\\alpha_3$ on the overall performance of the algorithm fluctuates, which may be caused by overly strict constraints on the learning of new class representations. Overall, our algorithm is relatively robust to the choice of hyperparameters.\n\nWe will add a clarification on hyperparameters in the final version.\n\n---\n\n**Reference:**\n\n[1] Zhu F et al. Prototype augmentation and self-supervision for incremental learning. CVPR 2021.\n\n[2] Shi W et al. Prototype reminiscence and augmented asymmetric knowledge aggregation for non-exemplar class-incremental learning. ICCV 2023.\n\n[3] Wang S et al. Non-Exemplar Class-Incremental Learning via Adaptive Old Class Reconstruction. ACM MM 2023.\n\n---\n\nWe are looking forward to answering any follow up questions during the discussion period.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "MQDspDFGeE", "reviewer": "Reviewer_SYbV", "summary": "This work introduces a Prospective Representation Learning (PRL) scheme to prepare the model for handling conflicts of the balance between the old and new classes in Non-exemplar class-incremental learning (NECIL). The author proposes to squeeze the embedding distribution of the current classes in the base phase and make the new class features away from the saved prototypes of old classes in the incremental phase, improving the balance of old and new classes in the existing NECIL baselines.", "questions": "1. Why not perform Preemptive Embedding Squeezing (PES) on new classes during the incremental phase? Will this not cause overlap in the feature space of the new classes?\n2. What does the $L_{IIC}$ of Formula 9 indicate? I do not find the corresponding explanation. (ps: I guess the author may have mistakenly wrote $L_{PES}$ as $L_{IIC}$)\n3. What do the old class prototypes of formula 11 and the potential spatial features of formula 12 specifically refer to, and is there a relationship between them?", "limitations": "None", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. This work proposes the Prospective Representation Learning (PRL) scheme to solve the balance problem between old and new classes in NECIL tasks.\n2. The proposed PRL scheme is plug and play, making it convenient to combine with other models.", "weaknesses": "1.  Few analysis was conducted on the loss weight α in formula 14.\n2.  There are some grammar or writing errors in the text, such as the repeated appearance of the \"propose\" on line 111.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you so much for the insightful questions! We will revise our manuscript accordingly and address your questions below.\n\n---\n**W1: Few analysis was conducted on the loss weight α in formula 14.**\n\n**A1:** We set $\\alpha_1=10$, $\\alpha_2=10$ , and $\\alpha_3=2$ by default. Due to rebuttal limitations, the experimental results are shown in the **pdf file** attached to the Author Rebuttal. In Eq.14, $\\alpha_1$ and $\\alpha_2$ are common in previous NECIL methods and represent the weights of distillation loss and prototype loss, respectively. The main role of these two loss functions is to maintain the pre-existing knowledge of the model. Therefore, as shown in Fig.(d) and Fig.(e), as $\\alpha_1$ and $\\alpha_2$ get larger, the optimization of the model will be biased towards maintaining stability, resulting in the model performing better on the old task and worse on the new task. For the consideration of comprehensive performance, we set $\\alpha_1 = 10$ and $\\alpha_2=10$ for PRL.\n\nThen $\\alpha_3$ controls the loss of the Prototype-Guided Representation Update (PGRU) proposed in this paper. In Figure (c), as $\\alpha_3$ increases PGRU comes into play. The effect of growing $\\alpha_3$ on the overall performance fluctuates, which may be caused by overly strict constraints on the learning of new class representations. Overall, our algorithm is relatively robust to the choice of hyperparameters.\n\n---\n**W2 & Q2: Some grammar or writing errors.**\n\n**A2:** Thank you for pointing out our error. As you guessed, $\\mathcal{L}_ {IIC}$ was a writing error, and should actually be $\\mathcal{L}_ {PES}$. We will carefully scrutinize the main text and the appendix, and ensure such errors are eliminated in the final version of the paper.\n\n---\n**Q1: Why not perform Preemptive Embedding Squeezing (PES) on new classes during the incremental phase? Will this not cause overlap in the feature space of the new classes?**\n\n**A3:** First, going into the incremental phase, the main problem faced by the model shifts from adjusting the relationship between new classes to dealing with the overlap between the new classes and the old ones, especially in the absence of samples from the old classes. We therefore propose Prototype-Guided Representation Update (PGRU) to alleviate this problem. Due to the shift of the main problem, the improvement from performing PES in the incremental phase is not obvious.\n\nWe further reflect on this issue. This could be caused by the fact that as incremental learning goes on and on, the number of new classes is relatively small compared to the old ones. Therefore we try to increase the number of classes in the incremental phase for our experiments on CIFAR-100. In the following table, we performed only one incremental phase and set the number of classes $C$ in the incremental phase to 5, 10, 20, and 50, respectively. It can be seen that the effect of PES is gradually apparent when the number of new classes increases.\n\n| |C=5|C=10|C=20|C=50|\n|---|:---:|:---:|:---:|:---:|\n|w/ PES|80.97|79.10|77.78|73.96|\n|w/o PES|80.84|79.05|77.34|73.37|\n\nCertainly, the ratio of the number of new classes to the number of old classes naturally decreases as the tasks learned by the model accumulate, so we only employ PES in the initial phase. Previous work [1] that considered forward compatibility also optimized the learning of the model only in the initial phase.\n\nSecond, in the incremental phase, due to the sufficient number of samples in the new classes, the cross-entropy loss also makes the features of the new classes distinguish from each other and reduce the overlap of the new classes.\n\n---\n**Q3: What do the old class prototypes of formula 11 and the potential spatial features of formula 12 specifically refer to, and is there a relationship between them?**\n\n**A4:** We have described the old class prototypes and the features in the potential space in Sections 3.2 (line154-158) and Section 3.3 (line195-200), respectively. At the end of each phase, a prototype is computed and saved for each class of the current task. As shown in Eq.4, the prototype is usually the average of all the features of the class. This is widely used in existing NECIL methods [2, 3]. The potential spatial features refer to features $\\mathcal{P}_ {\\phi_ t}(\\mathcal{F}_ {\\theta_ {t-1}}(x^i))$ that have been projected, where $x^i$ denotes the sample of the current class, $\\mathcal{F}_ {\\theta_ {t-1}}(x^i)$ is the feature extracted by the teacher model (the model trained from the previous phase).\n\nOld class prototypes cannot be updated after saving due to the absence of old class data. Since the teacher model $\\mathcal{F}_ {\\theta_ {t-1}}$ is frozen, $\\mathcal{F}_ {\\theta_ {t-1}}(x^i)$ also does not change in the current phase of training. Therefore, we introduce a projector $\\mathcal{P}_ {\\phi_t}$ to project the prototypes $\\boldsymbol{p}^c$ and $\\mathcal{F}_ {\\theta_ {t-1}}(x^i)$ into a potential space. Optimizing the projector via Eq.11 can change the relationship between $\\boldsymbol{p}^c$ and $\\mathcal{F}_ {\\theta_ {t-1}}(x^i)$ in the potential space thus avoiding the new class features to be too close to the region where the old class prototype is located. Eq.12 is to align the features $\\mathcal{F}_ {\\theta_ {t}}(x^i)$ extracted by the current updated model $\\mathcal{F}_ {\\theta_ {t}}$ with the potential spatial features $\\mathcal{P}_ {\\phi_ t}(\\mathcal{F}_ {\\theta_ {t-1}}(x^i))$ that have been adjusted by the projector. \n\nWe will optimize the expression to make this clearer in the final version.\n\n---\n**Reference:**\n\n[1] Shi et al. Mimicking the Oracle: An Initial Phase Decorrelation Approach for Class Incremental Learning.\n\n[2] Zhu et al. Prototype augmentation and self-supervision for incremental learning.\n\n[3] Shi et al. Prototype reminiscence and augmented asymmetric knowledge aggregation for non-exemplar class-incremental learning.\n\n---\nWe are looking forward to answering any follow up questions during the discussion period.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "aPDqLuHHpO", "reviewer": "Reviewer_nQN3", "summary": "This paper aims to solve the catastrophic forgetting in non-exemplar class-incremental learning. The authors propose Prospective Representation Learning (PRL) to prepare representation space for classes in later tasks in advance. Such forward compatible method first squeezes the embedding distribution of the current classes to reserve space for forward compatibility with future classes, then makes the new class features away from the saved prototypes of old classes. Extensive experiments are performed to demonstrate that the method is effective.", "questions": "1. What are the advantages of PRL over other forward-compatible methods?\n2. Can you provide the evaluation results on large datasets?", "limitations": "The paper has a section of limitation.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The paper is easy to understand and follow.\n2. The reported performance of the proposed method seems good, especially in TinyImageNet.\n3. The illustration of the method is clear.", "weaknesses": "1. The novelty of the method could be one of the concerns. There are previous works considering forward-compatible incremental learning [1,2]. The embedding space reservation is not a new concept, which has been proposed in [2]. This paper lacks related works and discussion on the advantages over other forward compatible methods and comparison with them.\n2. Lack of evaluation on large datasets like Imagenet1000.\n\n[1] Shi et al. Mimicking the Oracle: An Initial Phase Decorrelation Approach for Class Incremental Learning.\n\n[2] Zhou et al. Forward Compatible Few-shot Class-Incremental Learning.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive feedback! We hope the following responses can address your concerns.\n\n---\n\n**W1 & Q1: What are the advantages of PRL over other forward-compatible methods?**\n\n**A1:** First, unlike previous works, PRL targets CIL in exemplar-free scenarios (NECIL). NECIL requires the algorithm to learn a unified model without access to any data from previous tasks, which means that the commonly used memory buffers are not available thus more challenging.\n\nSecond, compared to previous works, PRL considers how to resolve conflicts between new and old classes during the incremental phases, in addition to reserving space in the initial phase. Zhou et al [2] also mentioned that such conflicts need to be taken into account when it transforms into a CIL problem (*i.e.*, there are enough instances of the new classes). Compared to the work of Zhou et al [2], which presupposes unseen classes by mixing instances from the initial task, our approach improves the forward compatibility of the model without interfering with the learning of the initial task itself.\n\nThe reference works you provided are inspiring to our research. We will add a discussion of the works on forward-compatible incremental learning in the final version of our paper.\n\n---\n\n**W2 & Q2: Lack of evaluation on large datasets like Imagenet1000.**\n\n**A2:** The following table compares the average incremental accuracies of the different methods for the 10 phases setting on ImageNet-1k. We will provide more experimental results on ImageNet-1k in the final version of the paper.\n\n|  | &ensp; PASS &ensp; | &ensp; SSRE &ensp; |  &ensp; SOPE &ensp; | &ensp; POLO &ensp; | &ensp; NAPA-VQ &ensp; | &ensp; PRL (Ours) &ensp; |\n| --- | :---: | :---: | :---: | :---: | :---: | :---: |\n| Accuracy (%) | 55.90 | 58.12 | 60.20 | 61.53 | 54.21 | **62.74** |\n\nWe are looking forward to answering any follow up questions during the discussion period.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We thank all reviewers for their positive view of our work and valuable feedback. We responded to reviewers' comments in individual replies to each reviewer with references to weakness (**W**) and questions (**Q**).

In response to the question of Reviewer FnFn and Reviewer SYbV about the analysis of the hyperparameters $\alpha$ in Eq. 14, we have attached a pdf file showing the experiment results. In the pdf file, the figures in the left column show the effect of changing the value of each hyperparameter on the average incremental accuracy of our method; the figures in the right column show the effect of changing the value of each hyperparameter in the last phase on the accuracy on the new and old tasks, respectively.

Please let us know if there are additional items or further clarifications/discussions we could address. We will incorporate clarifications and additions, as we specified in our replies, in the final version of our work.

Meta-review: This paper introduces a Prospective Representation Learning (PRL) scheme designed to manage conflicts between old and new classes in non-exemplar class-incremental learning. The proposed approach includes strategies for both the base and incremental stages, effectively reserving space in the learned representation and maintaining its structure as new classes are introduced. Experimental results demonstrate the effectiveness of PRL.

The paper has received mixed reviews, with one reviewer increasing their score after the rebuttal, while others did not respond to the updated results provided by the authors. The final scores after the rebuttal phase are (6, 5, 5, 4).

After a careful review, the AC finds that the paper does introduce a degree of novelty and the results validate its effectiveness. Given the significance of this approach to the field of class-incremental learning (CIL) and its potential to inspire future research, the AC suggests this paper as a borderline accept.

If the paper is accepted, the authors should carefully address the concerns raised by the reviewers, particularly the need for more detailed comparisons and in-depth analysis with baselines using CE losses, as well as further discussions of the related works mentioned by the reviewers.
Decision: Accept (poster)