IDER: IDempotent Experience Replay for Reliable Continual Learning
Authors: Zhanwang Liu
Yuting Li
Haoyuan Gao
Yexin Li
Linghe Kong
Lichao Sun
Weiran Huang
Venue: ICLR 2026 Poster (2026)
Keywords: continual learning
reliable
idempotence
Primary area: transfer learning, meta learning, and lifelong learning

Abstract: Catastrophic forgetting, the tendency of neural networks to forget previously learned knowledge when learning new tasks, has been a major challenge in continual learning (CL). To tackle this challenge, CL methods have been proposed and shown to reduce forgetting. Furthermore, CL models deployed in mission-critical settings can benefit from uncertainty awareness by calibrating their predictions to reliably assess their confidences. However, existing uncertainty-aware continual learning methods suffer from high computational overhead and incompatibility
with mainstream replay methods. To address this, we propose idempotent experience replay (IDER), a novel approach based on the idempotent property where repeated function applications yield the same output. Specifically, we first adapt the training loss to make model idempotent on current data streams. In addition, we introduce an idempotence distillation loss. We feed the output of the current model back into the old checkpoint and then minimize the distance between this reprocessed output and the original output of the current model. This yields a simple and effective new baseline for building reliable continual learners, which can be seamlessly integrated with other CL approaches. Extensive experiments on different CL benchmarks demonstrate that IDER consistently improves prediction reliability while simultaneously boosting accuracy and reducing forgetting. Our results suggest the potential of idempotence as a promising principle for deploying efficient and trustworthy continual learning systems in real-world applications. Our code is available at https://github.com/YutingLi0606/Idempotent-Continual-Learning.

Published as conference paper at ICLR 2026
MIFA LAB
IDER: IDEMPOTENT EXPERIENCE REPLAY FOR RELI- ABLE CONTINUAL LEARNING
Zhanwang Liu
Yuting Li
Haoyuan Gao
Yexin Li
Linghe Kong!
Lichao Sun
Weiran Huang
1 School of Computer Science, Shanghai Jiao Tong University
Shanghai Innovation Institute State Key Laboratory General Artificial Intelligence, BIGAI
Lehigh University
ABSTRACT
Catastrophic forgetting, the tendency of neural networks to forget previously learned knowledge when learning tasks, has been major challenge in contin- ual learning (CL). To tackle this challenge, CL. methods have been proposed and shown reduce forgetting. Furthermore, CL models deployed in mission-critical settings can benefit from uncertainty awareness by calibrating their predictions to reliably assess their confidences. However, existing uncertainty-aware continual learning methods suffer from high computational overhead and incompatibility with mainstream replay methods. To address this, we propose idempotent expe- rience replay (IDER), a novel approach based on the idempotent property where repeated function applications yield the same output. Specifically, we first adapt the training loss to make model idempotent we introduce an idempotence distillation loss. We feed the output of the current model back into the old checkpoint and then minimize the distance between this reprocessed output and the original output of the current model. This yields a simple and effective new baseline for building reliable continual learners, which can be seamlessly integrated with other CL approaches. Extensive experiments different CL benchmarks demonstrate that IDER consistently improves predic- tion reliability while simultaneously boosting accuracy and reducing forgetting. promising principle for deploying efficient and trustworthy continual learning systems in real-world appli- cations. Our code available at https: /ttg//gttttbbttt com/ Wtttiiniii0000 Idempotent-Come inual Learning.
current data streams. In addition,
Our results suggest the potential of idempotence
INTRODUCTION
Deep learning has achieved impressive success across various domains. However, static batch setting where the training data of all classes can he accessed at the same time is essential for attaining good performance (Le & Yang, 2015; Rebuffi al., 2017). In many real-world deployments, data arrive sequentially and previously seen samples cannot be fully retained due to storage or privacy constraints. This makes it major challenge because neural networks tend rapidly forget previously learned knowledge when trained on new tasks, which is phenomenon known as catastrophic forgetting (McCloskey & Cohen, 1989).
To address this challenge, continual learning (CL) is proposed to enable models to accumulate knowledge as data streams arrive sequentially. Among valid CL strategies. rehearsal- approaches are popular as they are simple and efficient. They (Boschini et al., 2022; Buzzega et al., 2020; Caccia al., 2021; Chaudhry et al., 2019; Wu et al., 2019) address this by storing a small, fixed- capacity buffer of exemplars from previous tasks and replaying them when training new task, thereby regularizing parameter updates and mitigating catastrophic forgetting. Despite strong average accuracy, CL methods are often poorly calibrated and over-confident, problem exacerbated by
"Equal contribution. This work was conducted at MIFA Lab (members from SJTU & SII).
Correspondence to Weiran Huang huang @ outlook.comm

---

Published as conference paper at ICLR 2026
help preserve model distribution, thereby mitigating MIFA LAB
Expected Calibration Error
Final Average Accuracy
Number of Parameters (M)
0.300
25
0.275
47.5
0.20
0.22
15
0.000
0.175
37.5
0.150
5-
0.129
0.100
DER
NPCL
IDER (Ours)
DER
NPCL
IDER (Ours)
DER
NPCL
IDER (Ours)
Figure 1: We propose the IDER method, which can be directly applied to many recent rehearsal -easeddsal-base continual learning methods, resulting in less calibration error and significant improvements in FAA with less parameter growth compared with NPCI..
recency bias toward new tasks (Arani et al., 2022). Thus, this undermines the broader deployment of CL models in real-world settings (Li et al., 2024b), especially in safety-critical domains (healthcare, transport, etc.) (LeCun, 2022). CL models deployed in these domains can benefit from uncertainty awareness by calibrating their predictions to reliably assess their confidences (Jha et al., 2024). To tackle this issue, Jha al. (2023) propose neural processes based CL method (NPCL). However, it causes non-negligible parameter growth and exhibits incompatibility with logits-based replay methods due to the stochasticity in the posterior induced by Monte Carlo sampling. Motivated by these limitations, we aim for lightweight and compatible principle for reliable CL methods.
We draw inspiration from idempotence, a mathematical property that arises in algebra. An operator is idempotent if applying it multiple times yields the same result applying it once, formally expressed as [((())) = (x). ). It can be used in deep learning by recursively feeding the model's predictions back imputs, allowing the model to refine its outputs (Durasov et al., 2024a; Shocher et al., 2023). Durasov et al. (2024b) empirically demonstrate that a deep network f takes as input a vector and second auxiliary variable that can either be the ground truth label y corresponding a neutral uninformative signal () and is trained so that f(r, 0) = f(x:, y) = then the distance [a, (a, 0)) - f(x, 0)]l correlates strongly with the prediction error. What if we actively minimize this distance of buffer data when we learn new tasks in CL settings? Could we project outputs into the stable manifold where instances are mapped to themselves to prevent predictive distribution drift?
Thus, we propose an Idempotent Experience Replay (IDER) inspired by Idempotence, a simple and effective method that enforees idempotence for CL models when learning new tasks. We demonstrate that enforcing idempotence enables model to make more reliable predictions while reducing catastrophic forgetting. Both combined with naive rehearsal-based method experience replay (HR) (Riemer et al., 2019), compared with NPCL, our approach achieves lower calibration error evaluated by Expected Calibration Error (ECE) (Guo et al., 2017), higher accuracy, and requires smaller parameter numbers, is shown in Figure 1.
More specifically, IDER integrates two components to enforce idempotence for CL models. Firstly, adapt the training loss to train the current model be idempotent with data from the current task. Secondly, we introduce idempotence distillation loss for both buffer data and the current data stream enforce idempotence between last task model checkpoint ft-1 and current model ft- We verify that incorporating the current data stream into idempotence achieves further performance improvements, suggesting that idempotence decision boundary drift over time.
This yields simple method that only requires two forward passes of the model almost without additional parameters. Our approach can be integrated into existing CL methods and experiments show that this simple change boosts both prediction reliability and final accuracy by large margin. Especially on the Split-Clie MdittCIFARRO dataset, enforcing idempotence improves the baseline method ER (Riemer al., 2019) by up 26%, achieving state-of-the-art class incremental learning accuracy. Through extensive empirical validation on challenging generalized class-incremental learning (Mi et al., 2020; Sarfraz et al., 2025), we demonstrate that this simple and powerful principle improves the reliability of predictions while mitigating catastrophic forgetting in real-world scenarios.
The contributions of this paper can summarized as follows:

---

Published as conference paper at ICLR 2026
MIFA LAB
We propose novel framework for continual learning based on the idempotent property, which is simple and robust method. Our method demonstrates that fundamental mathematical properties can be effectively utilized to address catastrophic forgetting for CL.
We show that IDER can be easily integrated into other state-fftth--rt methods, leading to more reliable predictions with comparable performance.
Extensive experiments on several benchmarks demonstrate that our approach achieves strong performance in both mitigating catastrophic forgetting and making reliable predictions.
2 RELATED WORK
Continual Learning. The goal of continual learning (CL) is to achieve the balance between learning plasticity and memory stability (Wang et al., 2024). Approaches in CL can be divided into three main categories. Regularization-basse in parameter space of the model (Farajtabar al., 2020; Kirkpatrick et al., 2017). Rehearsal-based Method (Chaudhry et al., 2019) use a memory buffer to store task data and replay them during new task training. Architecture-bact expand the network to allocate distinct parameters for preserving each task's s knowledge. Recently, CL has also been studied in more practical settings such as continual post-training of multi-modal LLMs (Wei et al.; Xu et al., 2025; Yan et al., 2026), continual offline RL (Hu et al., 2025a;b), and federated continual learning (Yao et al., 2024). Among them, Rehearsal-based methods are general in various CL scenarios and can be naturally combined with knowledge Distillation (KD) techniques.
methods primarily rely on regularization loss to penalize changes
methods (Rusu al., 2016; Wang et al., 2022) incrementally
The baseline Experience Replay (ER) (Riemer al., 2019) mixes the current task data with stored samples from past tasks in the memory buffer during training. DER (Buzzega et al., 2020) store old training samples together with their logits and preserve the old knowledge by matching the saved logits with logits obtained by current model. Its improved version XDER (Boschini al., 2022) improves performance at the sacrifice of computational costs due to sophisticated mechanisms. CLSER (Arani et al., 2022) introduce a fast module for plastic knowledge and a slow learning module for stable knowledge. BFP (Gu et al., 2023) uses a learnable linear layer to perform knowledge distillation in the feature space. SCOMMER (Sarfraz al., 2023) and SARL (Sarfraz et al., 2025) enforces sparse coding for efficient representation learning. Neural Processes for Continual Learning (NPCL) (Jha et al.. 2023) explore uncertainty-awerr aware CL models using neural processes (NPs).
Idempotence in Deep Learning. Idempotence is a property of a function whereby the result of applying the function once the same as applying it multiple times sequence. Recent work has explored the application of idempotence in deep learning. In particular, it is defined that the results obtained by the model will not change when applying the model multiple times in practice (f(())) f(x)). The Idempotent Generative Network (IGN) (Shocher et al., 2023) firstly proposes this idea in deep learning for generative modeling and has the capability of producing robust outputs in a single step. Another work ZigZag (Durasov et al., 2024a) introduces idempotence in neural networks for the measuring uncertainty, which is based on IterNet (Durasov et al., 2024b). IterNet proves that for iterative architectures, which their own output as input, the convergence rate of their successive outputs is highly correlated with the accuracy of the value to which they converge. ZigZag recursively feeds predictions back inputs, measuring the distance between successive results. A small distance indicates high confidence, while a large one signals uncertainty or -itirro--dsttiutiionn (OOD) data. Recent work ITTT (Durasov et al., 2024c) combines idempotence with Test-Tine Time Training. These works proves the potential of idempotence in deep learning while these works are based on static batch learning.
METHOD
In this section, deliver details of the proposed IDER. We first define both class-incremental learning and generalized class-incremental learning settings. Then, we elaborate on how to introduce idempotence in continual learning. Finally, we introduce the overall objective. An overview of IDER is depicted in Figure 5.

---

Published as conference paper at ICLR 2026
MIFA LAB
3.1 PROBLEM DEFINTTION
Continual learning (CL) aims to develop models that learn from a stream of tasks while preserving previously acquired knowledge. In this paper, we focus typical class-incremental learning (CIL) and generalized caas-inncremenal learning. Generalized class- baas-inccrementl learning (GCIL) is more close to real-world incremental learning. The key GCIL properties can be summarized as follows: (i) the number classes across different tasks is not fixed: (ii) classes shown in prior tasks could reappear in later tasks; (iii) training samples are imbalanced across different classes in each task.
In a typical class-incremental learning setting, a model ʃ trained on sequential tasks T T1. T2.... ..., Te Each task T consists of data points and these data points are unique within each task, which means T; {x; m)) and T:NT, = D. The optimization objective is to minimize the overall loss over all the tasks:
=" arg min Σ
(1)
where L is the loss function for the tasks and is the ground truth for x. However, in the continual setting, only the data from current task T₂ are available and the model should preserve the previous knowledge from the tasks beforeTi,.... Ti-1. As result, additional memory buffer or additional regularization term C may be chosen to avoid catastrophic forgetting and the actual objective on the current task should be:
S' arg min (B (F(S(z), v) + Lx]-
where M stands for the memory buffer to store the data from previous tasks.
3.2 MODIFIED ARCHITECTURE
To enable idempotence with respect to the second input, we modify the original backbone as shown in Figure 2. We divide the backbone ResNet (He et al., 2016) denoted ft, into two parts ft and f? on the t-th task. The second input (either a one-hot vector y or uniform distribution over all classes standing for "empty" input 0) is first trans- formed into a label feature vector. This is achieved by a linear layer with an output dimension that matches the
ResNet
ft
Image
Oatpat
N
Feature
dimensions of ft 's output, followed by LeakyReLU ac- tivation function. The image first is processed by ft to produce an intermediate feature map. The label feature is then added to this intermediate feature map, which is fed into f². The output of f² which the logits for target classes, can work as the second input for model after soft- max normalization. In this way, the backbone can accept two inputs and achieve idempotence with respect to the second argument after training.
one hot "cet" or uniform distribation "compty"
Feature
Figure 2: Modified Architecture.
We modify the architecture of back- bone(ResNet) and enable the model to accept two inputs.
3.3 STANDARD IDEMPOTENT MODULE: MODULE:TRAININS TRAINING THE NETWORK IDEMPOTENT
First, we rely on the model train being idempotent. To achieve this, Standard Idempotent Module is used for training the model on data from the current task. Following Durasov et al. (2024a;b), when learning new tasks, we minimize the loss which consists of two cross-entropy losses obtained by the logits from the first and second forward propagation of model and the ground truth y:
Lice
Σ ((,, + Loe (f((z, fx(x, v")) (x.8)ET;
where T, is the current task and y" is the second input that is set to either the ground-truth one-hot vector or the neutral "empty" signal input O. We randomly select y with probability 1 - P and the neutral "empty" signal input with probability P. The empty signal 0 defined uniform distribution over all classes.

---

Published as conference paper at ICLR 2026
MIFA LAB
Idempotence Histograms CIFAR100
Recency Blas
0.8
1.0
0.7
uniform distribution Input
Task
one-hot
0.6
incorrect prediction input
Task Probability
0.9
Task
Densis
0.5
0.8
Task
Task
0.4
0.3
0.7
0.7
0.0
3 Idempotence Distance
7
DER+
ER+ (Ours)
Figure 3: We plot the distribution of idempotence errors, measured by the distance [x (x, =))- fzx 2)I. Inputs with second incorrect predic- tion imput exhibit significantly larger idempo- tence errors. Thus, this distance can be used as a idempotent distillation loss.
Figure 4: Probability of predicting each task at the end of training for models trained CIFAR- 10 with 500 buffer size. Idempotent distillation loss effectively mitigates the bias to the recent tasks and provides a more uniform probability size across different tasks.
By minimizing Lice, can be obtained by:
train the model idempotent with respect the second argument, which
fz 0) my. ( f(x, 2
flz. 0)) = f((x, 0).
(4)
Thus, fe has been adjusted so that the model fe is idempotent as possible for all x in distribution. The model will map the data (z, 0) to the stable manifold (x. y) f(x, y = y) Fig. 3 illustrates this in the case of network trained on data from the first task on CIFAR- 100. With different second input the idempotence distance distribution varies. The input which contains incorrect prediction input exhibits significantly larger idempotence errors. Thus, this distance be used distillation loss for iterative prediction refinement to make reliable predictions.
3.4 IDEMPOTENT DISTILLATION MODULE: DISTILLING THE NETWORK FOR CONTINUAL LEARNING
In the CL setting, the model tends have recency bias toward newly introduced classes, which negatively influences the performance and results in overconfidence predictions. Rehearsal- methods suffer from this problem, Wang et al. (2022) point out that when new task is presented to the net, an asymmetry arises between the contributions of replay data and current examples to the weights updates: the gradients of new examples outweigh. To mitigate this issue, require the model to maintain stable predictions on data from previous tasks even after parameter updates induced by new knowledge, as self-consistency indicates that the network's output is aligned with the learned in-distribution manifold and can make reliable (well-calle calib-aaibrated) prediction. This condition can be translated into enforcing idempotence. Thus, we propose minimize idempotence distances to mitigate recency bias and prediction distribution drift in CL.. A naive way would be to minimize the loss function:
Lide
Σ (T..)
())((x,0) - fe(x, fe(2, f(x,
However, this can produce undesirable side effects in CL settings. As fe has bias towards current data streams and yo fz 0) may be an incorrect prediction, minimizing 14y1 y1112 may cause = fe(r, 30) to be pulled towards the incorrect yo. thereby magnifying the error.
To address this, keep the model checkpoint at the end of the last task fe-1 together with the current trained model fc- We then modify the idempotence distillation loss to be:
Lide
Σ
llfe(z 0) (z, fo 0)>1
(6)
(2.0)ETT.M
Thus, the first prediction Yo = (xx 0) is computed before, but the second one, 1/1 ft- 1 (Ir, vo). is made using the last model checkpoint f:-1 By updating only ft and keeping fi-1 frozen, which preserves more previous knowledge and stable prediction distribution for buffer data, we ensure that Yo is adjusted to minimize the discrepancy with yı, without pulling y1 towards an incorrect yoo Thus,

---

Published as conference paper at ICLR 2026
MIFA LAB
y1
Lide
Lice
Lde
f-1
Lice
ft
IDM
SIM
Yn
ft
ft
A
empty
emppt
"Day"
1-P
cut,
desk,
fish,
dog...
lion...
Task
Task
Task
Figure 5: Overall framework Idempotent Experience Replay (IDER). Our method consists two modules for continual learning: (1) Standard Idempotent Module that trains current model idempotent with data from the current task. (2) Idempotent Distillation Module that enforce the current model become idempotent with respect the last task model checkpoint, utilizing data from both the current task and buffer memory. IDER can be integrated into existing CL approaches to make reliable predictions while mitigate catastrophic forgetting.
we could prevent manifold expansion that would include mistaken outputs, focusing optimization solely on the first pass prediction and thereby avoiding error reinforcement.
This design achieves idempotence by ensuring that processing an input through the current model and then through the last model checkpoint yields nearly identical output distribution. This self- consistency between the current model and the last model satisfy the requirement for idmpotence condition for sequential tasks in CL. What's more, Lide can also serve as the distillation loss to mitigate catastrophic forgetting. Unlike traditional distillation in Buzzega et al. (2020), which only aligns the final output probabilities, our method anchors the model's representation to the stable manifold already learned by the frozen model, thereby maintaining balanced predictive performance across all tasks, as is shown in Figure 4. As a result, enforcing idempotence can help CL models mitigate catastrophic forgetting while make reliable preidctions.
3.5 OVERALL ORJECTIVE
We introduce idempotence into experience replay (ER) framework (Riemer et al., 2019), where keep a buffer M storing training examples from old tasks. We keep the model checkpoint at the end of the last task ft-1 together with the current trained model fc. During continual learning, the current model fe is trained on the batch from data stream of the current task T. using the adapted training loss Lice in Eq. 3. We sample batch from M and combine the current batch compute idempotence distillation loss Lide in Eq. 6.
Meanwhile, we sample another batch from M for experience replay. The experience replay loss froppicc ine in ER is:
Grep-ice ice
Σ (fc((((( + Lec(fe fe (2:2))M
The total loss function used in IDER is the weighted sum of the losses above, formally:
LIDER = Lice + aLLide + Brep-ice-
(8)
In addition, our method is simple and robust, which can be combined with other methods, such as BFP (Gu et al., 2023), to achieve higher performances. Details are shown in the appendix.

---

Published as conference paper at ICLR 2026
MIFA LAB
Table 1: Comparison of Final Average Accuracy (FAA) across different continual learning methods. All experiments are repeated 5 times with different seeds. Results for SARL (Sarfraz et al., 2025) from our implementation. The best results are highlighted in blue. second best results highlighted in green.
CIFAR-10
CIFAR-100
Timy-TmageNet
Method
Buffer 200
Buffer 500
Buffer 500
Buffer 2000
Buffer 500
Buffer 4000
Joint (upper bound)
91.93+0.29
71.15=0.51
59.52=0.33
iCaRL (Rebuffi et al., 2017)
58.3743.51
62.49a5.42
46.8110.41
52.51a0.44
22.5310.62
26.38+0.23
ER (Riemer et al., 2019)
44.46+2.87
58.8413.85
23.41
40.4720.95
10.13+0.39
25, 25.1220.56
BIC (Wu ct al., 2019)
52.61
71.95
37.82+1667
47.17
15.36
18.6740.57
LUCIR (Hou et al., 2019)
49.1827.61
65,2642.54
37.91
50.4220.76
28.79+0.51
31.6420.51
DER (Buzzega et al., 2020)
57.92#1.91
68.65+1.82
34.83+2.09
50.12=0075
15,14+1.29
20.35=0.35
DER++ (Buzzega ct al., 2020)
62.1941.94
70.10a1.65
37.6910.97
51.82&1044
19.43 1.63
36.891 1.16
ER-ACE (Caccia et al., 2021)
62.1921.67
71.15+1008
37.81
49.77.0.34
20.42+0.39
37.76=0.53
XDER (Boschini et al., 2022)
10.10
67.42+2,16
48. 48.1444.34
$7.57=0.84
29. 29.12+0.47
46, 12+0.46
CLS-ER (Arani ct al., 2022)
64.5622.63
74.27
43.9240.62
54.84+1.30
30,9140.59
45.1720.89
SCoMMER (Sarfraz et al., 2023)
66.95#1.52
73.6420.43
39.05#0.79
49.42+0085
21.47+0.54
37 37.2=0.70
BFP (Gu et al., 2023)
68. 64+2.33
73.51
46.70+1.45
57.3990075
18.71+0.55
43, 43.1741..9
SARL (Sarfraz et al., 2025)
68.87+1.37
73.98+0.46
46.6990079
57.0620048
28.44+2.30
38.83=0.81
ER+ID(Ours)
71.02+1.98
74.74=0.42
44.82+0.85
56.59+0.35
29. 19.88
43,05=1.40
BFP+ID (Ours)
71.9940.98
76.6540.63
48.5340.95
57.7410.64
30.6240.47
43.51
CLS-ER+ID (Ours)
70.32a1.12
75.4840.91
47.44=2.0
56.3610.78
31.6240.57
46.17=0.22
100
CIFR-110 200
100
CIFAR-10 500
83
TinylmageNet
90
92
70
Accuracy (56
Accuracy (%)
82
50
20
60
30
50
DR DFF+10 (Dun))
40
D1P
10
Number of tasks
Number tasks
Number lasks
Figure 6: Results on CIFAR- and Tiny-ImageNet with different buffer size. It shows the trend of the average test-set accuracy on the observed tasks.
4 EXPERIMENTS
Continual Learning Settings. We follow Gu al. (2023) and conduct experiments on state-of-the-ar rehearsal- based models in CIL setting which splits the dataset into a sequence of tasks, each containing a disjoint set of classes, while task identifiers are not available during testing. Following Sarfraz et al. (2025), we also evaluate methods in the generalized class incremental learning (GCIL) setting (Mi et al., 2020) which is closest to the real-world scenario as the number of classes in each task is not fixed, the classes can overlap and the sample size for each class can vary.
Evaluation Metrics. Following Boschini et al. (2022); Buzzega et al. (2020), we use Final Average Accuracy (FAA) and Final Forgetting (FF) reflect the performances of mitigating catastrophic. We report well- established Expected Calibration Error (ECE) (Guo et al., 2017) to assess the reliability of continual learning methods. More details are shown in the appendix.
Training Details. We adopt the standard experimental protocols following Boschini et al. (2022); Gu et al. (2023). All methods use a ResNet-18 backbone (He al., 2016) trained from scratch with an SGD optimizer. For fair comparison, we employ uniform settings across all methods (including epochs, batch sizes, and optimizer configurations). Datasets are split as follows: 5 tasks for CIFAR-10, and 10 tasks each for CIFAR- 100 and TinylmageNer We report the average results

---

Published as conference paper at ICLR 2026
MIFA LAB
Table 2: Comparison of Final Average Accuracy (FAA) across different continual learning methods on GCIL-CIFAR-IIE 100 dataset. All experiments are repeated 5 times with different seeds. Absolute gains are indicated in green.
Uniform
Longtail
Method
Ruffer 200
Batfer 500
Ruffer 200
Butfer 500
Joint tupper bound)
58.36e1.02 .2
56.94e1.56
DER+ (Buzzega et all, 2020)
19:36-0.65
33.6610 96
27.05=1.11
25 25.98+0.881
SCoMMER (Sarfraz et al., 2023)
28.56a2.20 26
35.70et)
28.47e1.12
32.99211.49
ER (Riemer et 2019)
16.3a
28.7644).66
19.55
20.0221.05
Ours (ER+ID)
26. 66.6660..5
+10.32
40.54at1.46 466
+11.78
30.04g0.58
+10.49
35.92211.35
+15.90
CLS-ER (Arami all, 2022)
22.3720:48
36 00.8010.30 34
28.34
28.3550.72
Ours (CIS-RR&ID)
31.17sl.6 62.
37.57+1.81
+4.77
34.08.0.45
+5.74
36.75+0.62
+8.40
SARL (Sarfraz et 2025)
36.20s0:45
38.73341.66
34.13
34.6/111.9
Ours (SARL+ID)
36.4520337
39.65a11.43
+0.92
35.04
35.67711.74
+1.03
over 5 independent runs with different random seeds to ensure statistical reliability. Comprchensive hyperparameter settings and further implementation details are provided in the appendix.
4.1 RESULTS
Comparison with the state-of-the-art methods. We evaluate our method against oftt-off-hhe-art continual learning approaches across three benchmark datasets with different memory buffer sizes: CIFAR-IO, CIFAR-100, and Tiny-ImageNet. The Final Average Accuracies in the class incremental learning setting on different benchmarks are reported in Table 1. Our method outperforms all rehearsal-based methods on three datasets. Notably, our method outperforms the second best method BFP by up to 3% on CIFAR-10, which shows that our method remains highly effective even on a scall-seale benchmark. Though outperforming XDER only slightly in FAA on CIFAR-100 -10 and Tiny-ImageNer our approach attains this accuracy with markedly lower computational cost, which can be shown in Figure 7 (a). Figure shows that IDER has better performance at most intermediate tasks and also the final one. In addition, Table highlights the advantage of IDER in the challenging GCIL setting, which tests the model's ability to deal with class imbalance and to continuously integrate knowledge from overlapping classes. The results in such challenging setting prove the benefits of idempotence, which encourages the model to produce more robust representations to identify concepts clearly. This ability of IDER shows the potential for realistic continual learning.
Plug-and-play with other cabearsal--aseee methods. Considering the effectiveness and simplicity of idempotence, it is natural to consider whether it can be integrated into other rehearsal-bate meth- ods. Table shows consistent performance improvements on various datasets with this integration. Enforcing idempotence boosts FAA by a significant margin, especially for ER 26% on CIFAR-10 10 with buffer size 200 and 21 % on CIFAR- 100 with buffer size 500). The results in GCIL in Table 2 can also prove that IDER, by enforcing model idempotence, is complementary to other methods in relieving forgetting. It is worth mentioning that in more challenging setting, the performance gains can be obvious in practice. Combined with CLS-ER, traditional CIL, idempotence yields gain of about 3.5% on CIFAR-100 with buffer size 500, while in GCIL, the gains can reach 8%. This additionally demonstrates the potential of this mathematical property to address catastrophic forgetting for even more challenging CL scenarios.
Idempotence Improves prediction Reliability, As previously reported byGuo et al. (2017), DNN uncalibrated, often tending towards overconfidence. Arani et al. (2022) show that this problem is pronounced in continual learning where the models tend to be biased towards recent tasks. Fol- lowing Boschini et al. (2022); Jha et al. (2023) we evaluate the calibration errors for different CL baselines using the well-established Expected Calibration Error (ECE), which is shown in Table 3. Table shows that IDER consistently reduce the calibration error. In general, IDER benefits CL models in confidence calibration which demonstrates the ability of IDER to make reliable predictions. Comparing with post-hoe uncertainty calibration methods for CIL (Hwang et al., 2025; Li al., 2024a), IDER achieves comparable performances across different datasets. This strong correlation be- tween improved calibration and higher accuracy suggests that by producing more reliable confidence estimates, the model mitigates overconfidence on its own predictions (potentially incorrect), thereby facilitating a more stable and effective learning process that leads to better overall performance.

---

Published as conference paper at ICLR 2026
MIFA LAB
Table 3: Comparison of Expected Calibration Error (ECE) across different continual learning methods on CIFAR-10 10 and CIFAR-100 dataset. All experiments are repeated 5 times with different seeds. Results of NPCL are imported from its original work (Gu al., 2023). Absolute improvements (lower ECE) are indicated in red.
CIFAR-10
CIFAR-106
Timy- -Tay-Imagehet
Method
Butter 200
Butter 500
Butter 500
Butfer 2000
Butter 500
Butler 4000
A
DER (Ruzegret 2020y
16:20
22,80
NPCL Olti 2023)
21.03
19:95
(16 2014s)
16.39
12.84
19:43
19.31
21.32
16.49
T-CIL (Hwang 2025)
22.50
10.51
15.79
14.50
10.30
BR (Riemer et al., 2018)
45,53
32,69
64.89
45.64
67,50
$1.37
Ours (ER+ID)
11.75
13.65
21.55
11.14
-40.23
RFP (Gn al., 2023)
9.83
9:40
11.93
9.78
9:45
8.25
Ours (BFP+ID)
9.30
4.53
863
4.77
8,92
-3.01
8.29
-0,99
7.77
-1.68
6.35
-1.9
4.2 ADDITIONAL ANALYSIS
Backbone Modification. To enforce idempotence, we introduce lightweight architectural modifi- cation by dividing the backbone into two parts (see Section 3.2) so that the model can incorporate the second input. We first evaluate whether this structural change alone affects performance on Split CIFAR- 100 with a buffer size of 500. As shown in Table 4, the modified structure performs similarly to the normal backbone, indicating that the architectural change itself does not alter the baseline performance; therefore, the observed gains mainly come from the proposed idempotent loss rather than the modified architecture. We further ablate different partition points using ResNet- 18 on Split CIFAR-100 100 and Tiny-ImageNet. Table 5 shows that shallower splits amplify noise and destabilize training, whereas deeper splits attenuate the second signal and weaken the idempotence effect. Based on these results, we split the backbone at a mid-layer, which yields the most consistent and strongest performance across different datasets overall.
Table Comparison of performances using the normal vs. modified backbone. Similar results indicate that the architectural change itself does not affect baseline performance.
Table Comparisons with different partition points on Split CIFAR-100 and ImageNt using ResNet-18. Mid-layer partitioning yields the most stable and best performance.
Model
Method
Accuracy
Forgetting
Layer Selection
CIFAR-100
Tiny-ImageNet
ResNes-18
Finetune
8.29
90.52
Shallower (5th layer)
40.51
42.10
ER
24.36
71,30
Deeper (13th layer)
43.09
42.28
Modified ResNet-18
Finctune
8,23
90.58
Ours (9th layer)
44.82
43.05
24.73
70.61
Idempotence improves forgetting. The Figure 7 (b) shows Final Forgetting (FF) measured on the Split CIFAR-100 dataset with different buffer sizes. Our method consistently reduces forgetting, which shows that enforcing idempotence improves accuracy while mitigating the forgetting problem.
On training time. Figure 7 (a) compares the training times of various methods. As expected, our proposed method introduces minimal computational overhead when integrated into existing replay-based methods. In practice, IDER only adds one extra forward pass, whereas X-DER involves additional training components (c.g., additional update steps beyond standard replay), leading to notably higher runtime.Thin This highlights IDER's practicality as a lightweight and effective method.
Comparison with different distance metrics. The figure 7 (c) shows the effect of different distance metrics for computing the Idempotent distillation loss. While both MSE and KL divergence well-established metrics for quantifying loss distance, MSE provides better performance. The reason that MSE avoids the information loss occurring in probability space due to the squashing function.
Visualizations of concrete example. To explore how enforcing idempotence mitigates recency bias and improves calibration,
visualize predictions for test examples using ER and ER+ID on Split CIFAR-100 with a buffer size of 500 and 10 incremental tasks. Figure 8 shows top-5 predictions after learning the first two tasks on Split CIFAR-I00. ER exhibits clear recency bias: classes from the current task (class ids from 10 to 19) receive inflated scores, leading to misclassifications Integrated

---

Published as conference paper at ICLR 2026
MIFA LAB
ER
MSE
DERPS
Forgetting (%6
50
50
KL Divergence
Accuracy
4g
BR+10 (Oun)
BPPIID (Ours
SARL
20
XOER
500
2000
Accuracy
Forgetting
Time [hours]
Buffor size
Metrics
(a) Training Times
(b) Forgetting on CIFAR-100
(c) Distance Metrics
Figure 7: Results for model analysis. (a) the training time of different methods on Split ImagenteeNet
with buffer 500. (b) the Final Forgetting (FF) measures on Split CIFAR- 100 with different buffer sizes. (c) the performances Split CIFAR- 100 using different distance metries for idempotent distillation loss.
Case 1: ER
Case 1: ER+ID
Case 2: ER
Case ER+ID
18
14
12
19
18 8
10
11
17
7
Figure 8: Visualizations of the predictions on Split CIFAR-100. It shows top-5 prediction probability produced by ER and ER+ID (ours) after training the first two tasks. The first 10 classes (class ids from 0 to 9) belong to task and the next 10 classes (class ids from 10 to 19) belong to task 2. The ground-trute truth class highlighted with red boxes.
with idempotence loss, the predictions get corrected as true class is promoted to top-1 prediction and overconfidence on new classes notably reduced.
Poos--Plafform Performance. To assess the hardware sensitivity of our results, run ER+ID with the same configuration on two different platforms: NVIDIA RTX 4090 and Huawei Ascend 910B. As Table shows, the performance is consistent across platforms: the differences small suggesting that the gains from IDER are not surdware-speciffe Minor discrepancies are expected due to differences in kernels, numerical precision, and non-determinism in deep learning libraries.
Table 6: Performance comparison for ER+ID between NVIDIA RTX 4090 and Huawei Ascend 910B. All experiments are repeated 5 times with different seeds.
CIFAR-10
CIFAR-100
ImageNmaeeNet Buffer 4000
Platform
Buffer 200
Buffer 500
Buffer 500
Buffer 2000
RTX 4090
71.02+1.98
74.7410.42
44.8220.85
56.5920.35
43. 13.05+1.40
Ascend 910B
13+0922
74.68+0.37
44.87=0.76
56.44+0.41
43.01 13.01+1.220 #1.26
5 CONCLUSION
In this paper, we propose Idempotent Experience Replay (IDER), a simple and effective method designed to mitigate catastrophic forgetting and improve predictive reliability continual learning. Our approach adapts the training loss and introduces idempotence distillation loss for CL methods to encourage. Extensive experiments demonstrate that IDER consistently improves performance across multiple datasets and diverse continual learning settings. Our results show that enforcing idempotence enables a balance between stability and plasticity while yielding better calibrated predictions. Our method, requiring only two forward passes without additional parameters and scamlessly integrated with other CL approaches, shows promise for deployment of CL models real-world scenarios. We hope this work inspires future research to place greater emphasis uncertainty- aware continual learning. We also plan to explore the potential of idempotence property in different domains.

---

Published as conference paper at ICLR 2026
MIFA LAB
ACKNOWLEDGEMENT
This project supported by the National Natural Science Foundation of China (No. 62406192). the Shanghai Municipal Special Program for Basic Research on General AI Foundation Models (Grant No. 2025SH1217XX226000)) Opening Project of the State Key Laboratory of General Artificial Intelligence (No. SKLAGI2024PP12, the Tencent WeChat Rhino-Bin Focused Research Program, Kuaishou Technology, and the SJTU Kunpeng & Ascend Center Excellence.
REFERENCES
Elahe Arani, Fahad Sarfraz, and Bahram Zonooz. Learning fast, learning slow: A general continual learning method based complementary learning system. arXiv preprint arXiv:2201.126/1 2022.
Matteo Boschini, Lorenzo Bonicelli, Pietro Buzzega, Angelo Porrello, and Simone Calderara. Class- incremental continual learning into extended der verse. IEEE transactions on pattern analysis and machine intelligence. 45(5):5497-55 2022.
Pictro Buzzega, Mattco Boschini, Angelo Porrello, Davide Abati, and Simone Calderara. Dark experience for general continual learning: a strong, simple baseline. Advances in neural information processing systems, 33: 15920-15930, 2020.
Pietro Buzzega, Matteo Boschini, Angelo Porrello, and Simone Calderara. Rethinking experience replay: bag of tricks for continual learning. In 2020 25th International Conference Puttern Recognition (ICPR), pp. 2180-2187, IEEE, 2021.
Lucas Caccia, Rahaf Aljundi, Nader Asadi, Tinne Tuytelaars, Joelle Pineau, and Eugene Belilovsky, New insights on reducing abrupt representation change in online continual learning. arXiv preprint arXiv:2104.05025, 2021.
Arslan Chaudhry, Marcus Rohrbach, Mohamed Elhoseiny, Thalaiyasingam Ajanthan, Dokania, P Torr, and M Ranzato. Continual lcarning with tiny episodic memories. In Workshop on Multi-Task and Lifelong Reinforcement Learning, 2019.
Nikita Durasov, Nik Dorndorf, Hieu Le, and Pascal Fua. Zigzag: Universal sampling-fre uncertainty estimation through two-step inference. Transactions on Machine Learning Research, 2024a. ISSN 2835- -856.
Nikita Durasov, Doruk Oner. Jonathan Donier, Hieu Le, and Paseal Fua. Enabling uncertainty estimation in iterative neural networks. In Forty-first International Conference on Machine Learning, 2024b.
Nikita Durasov, Assaf Shocher, Doruk Oner, Gal Chechik, Alexei Efros, and Pascal Fua. It3: Idempotent test-time training. arXiv preprint arXiv:2410.04201, 2024c.
Mehrdad Farajtabar, Navid Azizan, Alex Mott, and Ang Li. Orthogonal gradient descent for continual learning. In International conference artificial intelligence and statistics, pp. 3762-3773, PMLR, 2020.
Qiao Gu, Dongsub Shim, and Florian Shkurti. Preserving linear separability in continual learning by backward feature projection. In Proceedings the IEEE/CVF Conference Computer Vision and Pattern Recognition. pp. 24286 24295, 2023.
Chuan Guo, Geoff Pleiss, Yu Sun, and Kilian Weinberger. On calibration of modern neural networks. In International conference on machine learning, pp. 1321-1330. PMLR, 2017.
Kaiming He, Xiangyu Zhang, Shaoqing Ren, Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 770-778, 2016.
Saihui Hou, Xinyu Pan, Chen Change Loy, Zilei Wang, and Dahua Lin. Learning unified classifier incrementally via rebalancing. In Proceedings of the IEEE/CVF conference computer vision and puttern recognition, pp.
831 839, 2019.
Jifeng Hu, Sili Huang, I. Shen, Zhejian Yang, Shengchao Hu, Shisong Tang, Hechang Chen, Lichao Sun, Yi Chang, and Dacheng Tao. Tackling continual offline rl through selective weights activation aligned spaces. In The Thitt Annual Conference on Neural Information Processing Systems, 2025a.
Jifeng Hu, Shen, Sili Huang. Zhejian Yang. Hechang Chen, Lichao Sun. Yi Chang, and Dacheng Tao. Continual diffuser (cod): Mastering continual offline rl with experience rehearsal. IEEE Transactions on Neural Networks and Learning Systems, 2025b.

---

Published as conference paper at ICLR 2026
MIFA LAB
Seong-Hyeon Hwang, Minsu Kim, and Steven Fuijong Whang. T-cil: Temperature scaling using adversarial perturbation for calibration in class-incremental learning. In Proceedings of the Computer Vision and Pattern Recognition Conference, pp. 15339-15348, 2025.
Saurav Jha, Dong Gong, He Zhao, and Lina Yao. Npel: Neural processes for uncertainty-awaat aware continual learning. Advances in Neural Information Processing Systems, 36:34329 34353, 2023.
Saurav Jha, Dong Gong, and Lina Yao. Clap4clip: Continual learning with probabilistic finetuning for vision- language models. Advances in neural information processing systems, 37: 111112966-11286, 2024.
James Kirkpatrick, Razvan Pascanu, Neil Rabinowitz, Joel Veness, Guillaume Desjardins, Andrei A Rusu, Kieran Milan, John Quan, Tiago Ramalho, Agnieszka Grrabska-Barwinste et al. Overcoming catastrophic forgetting in neural networks. Proceedings of the national academy of sciences, 1 114(13):5521-322 2017.
Yann Le and Xuan Yang. Tiny imagenet visual recognition challenge. CS 231N, 7(7)33, 2015.
Yann LeCun, path towards autonomous machine intelligence version 0.9. 2022-06-27. Open Review, 62(1): 1-62, 2022.
Lanpei Li. Elia piccoli, Andrea Cossu, Davide Bacciu, and Vincenzo Lomonaco. Calibration of continual learning models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 4160-4169, 2024a.
Yuting Li, Yingyi Chen, Xuanlong Yu, Dexiong Chen, and Xi Shen. Sure: Survey recipes for building reliable and robust deep networks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 17500-17510, 2024b.
Michael McCloskey and Neal J Cohen. Catastrophic interference in connectionist networks: The sequential learning problem. Psychology of learning and motivation, volume 24, pp. 109-165. Elsevier, 1989.
Fei Mi, Lingjing Kong, Tao Lin, Kaicheng Yu, and Boi Faltings. Generalized class incremental learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition workshops, pp. 240 2401 2020.
Sylvestre-Alvis Rebuffi, Alexander Kolesnikov, Georg Sperl, and Christoph II Lampert. icarl: Incremental classifier and representation learning. In Proceedings of the IEEE conference on Computer Vision and Puttern Recogmition, pp. 2001-2010, 2017.
Matthew Riemer, Ignacio Cases, Robert Ajemian, Miao Liu, Trina Rish, Yuhai Tu, and Gerald Tesauro. Learning to learn without forgetting by maximizing transfer and minimizing interference. arXiv preprint arXiv: /810./ 00000//990/ /910, 2018.
Matthew Riemer, Ignacio Cases, Robert Ajemian, Miao Liu, Irina Rish, Yuhai Tu, and Gerald Tesauro. Learning to learn without forgetting by maximizing transfer and minimizing interfierence. In ICLR (Poster), 2019.
Andrei A Rusu, Neil C Rabinowitz, Guillaume Desjardins, Hubert Soyer, James Kirkpatrick, Koray Kavukcuoglu, Razvan Pascanu, and Raia Hadsell. Progressive neural networks. arXiv preprint arXiv:1606.. (4671, 2016.
Fahad Sarfraz, Elahe Arani, and Bahram Zonooz. Sparse coding in dual memory system for lifelong learning. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 37, pp. 9714-9722, 2023.
Fahad Sarfraz, Flahe Arani, and Bahram Zonooz. Semantic aware representation learning for lifelong learning. In The Thirteenth International Conference on Learning Representations, 2025.
Assaf Shocher, Amil Dravid, Yossi Gandelsman, Inbar Mosseri, Michael Rubinstein, and Alexci A Efros. Idempotent generative network. arXiv preprint arXiv:231 1.01161 2023.
Jeffrey S Vitter. Random sampling with a reservoir. ACM Transactions on Mathematical Software (TOMS), 11 (1):37-57, 1985.
Liyun Wang, Xingxing Zhang, Hang Su, and Jun Zhu. A comprehensive survey continual learning: Theory, method and application. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024.
Zifeng Wang, Zizhao Zhang, Chen- Yu Lee, Han Zhang. Ruoxi Sun, Xiaoqi Ren, Guolong Su. Vincent Perot, Jennifer Dy, and Tomas Plister. Learning to prompt for continual learning. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition,
139-149, 2022.
Lai Wei, Yuting Li, Chen Wang, Yue Wang. Linghe Kong, Weiran Huang, and Lichao Sun. First sft, second third upt: Continual improving multi-modal Ilm reasoning via unsupervised post-training. In The Thirty-ninth Annual Conference on Neural Information Processing Systems.

---

Published as conference paper at ICLR 2026
MIFA LAB
Yue Wu, Yinpeng Chen, Lijuan Wang. Yuancheng Ye, 7icheng Liu, Yandong Guo, and Yun Fu. Large scale incremental learning. In Proceedings the IEEE/CVF conference computer vision and pattern recognition, pp. 374-382, 2019.
Guowei Xu, Peng Jin, Ziang Wu, Hao Li, Yibing Song. Lichao Sun, and Li Yuan. Llava-cot: Let vision language models reason step-by-step. In Proceedings of the IEEE/CVF International Conference Computer Vision, pp. 2087-2098, 2025.
Zhiling Yan, Dingjie Song, Zhe Fang. Yisheng Xiang Li. Quanzheng Li, and Lichao Sun. Livemed- bench: contamination- medical benchmark Ilms with automated rubric evaluation. arXiv preprint arXiv:2602.13377, 2026.
Dezhong Yao, Sanmu Li, Yutong Dai, Zhiqiang Xu, Shengshan Hu, Peilin Zhao, I. Lichao Sun, Variational bayes for federated continual learning. arXiv preprint arXiv:2405. 14291, 2024.

---

Published as conference paper at ICLR 2026
MIFA LAB
Appendix
A EXTENDED DISCUSSION: RELATED IDEMPOTENCE TO CONTINUAL LEARNING
This section presents the theoretical motivation and formulation of the idempotence loss in continual learning by revisiting prior applications of idempotence and elaborating how the proposed loss improves prediction calibration and mitigates catastrophic forgetting
Uncertainty Measurement
Durasov et al. (2024a) first train the model to satisfy f(r,0) = y and f(z, v) = for each pair (x,3) by minimizing the following loss:
Luain Ilf y/1 [lf v) yll
(9)
Then they define the uncertainty loss as:
(xx) 11yl yoll
(10)
where the network is applied recursively: yo fzz 0), y f0, vo)- The rationale is follows:
1. If is in-distribution, then yo y. and since the network is trained that fxx v) y. they have y1 R yo- Therefore, the loss is small.
2. If x is OOD, then yo unlikely to approximate the true label. this case, the pair (ar yo) is not valid input as pretraining, leading yı to be unpredictable and significantly different from yo, resulting in a large ((r).
Thus, the magnitude of |лy -yoll serves as a proxy for prediction certainty.
Introducing Idempotence in Continual I Learning
In CL. models often poorly calibrated and over-confident, problem exacerbated by recency bias toward new tasks. To mitigate this issue, we require the model to maintain stable predictions on data from previous tasks even after parameter updates induced by new knowledge, as self-consistency indicates that the network's output is aligned with the learned in-distribution manifold and can make reliable (well-calibrated) prediction. As before, this condition can be translated into enforcing idempotence. We can formalize the desired idempotence condition as fa (ax 0)) fz, 0). where x is from both previous and current tasks and fi represents the current model. practice, as data from previous tasks can't 't be obtained, the loss can be defined as:
L Σ (1. - f( fz 0))
(11)
(x.
where M is the buffer memory which stores data from previous tasks.
Minimizing this loss drives the network toward the condition that repeated application of Se(x,) ) does not change the output, which is needed for model to make reliable predictions in CL.
However, minimizing the idempotence loss in CL not trivial. First, we propose Lice to train model idempotent for sequential tasks. Second, We modify the idempotence distillation loss by using the model checkpoint at the end of the last task for the second application, which can rewritten as
Lide
Σ
IIf((z,)) fe-1 fe(x
(12)
(N.N)TT.M
The modification has two benefits:
It prevents training collapse and bias error amplification. Consistent with Shocher al. (2023) and Durasov et al. (2024c) directly optimizing the idempotence loss induces two gradient pathways: A desirable pathway that updates fe(1,, 0) toward the correct in-distribution manifold. 2. An undesirable pathway that may cause the manifold to

---

Published as conference paper at ICLR 2026
MIFA LAB
expand, thereby including an incorrect ft(2,0) 0)- For example, if yo fa, 0) is an incorrect prediction, then minimizing 1/30 81ll may cause y1 fe(z, yo be pulled toward the incorrect and expand the manifold following the wrong gradient pathways, thereby magnifying the error. Another potential problem the identity function, which is trivially idempotent and may cause training collapse. To counteract the latter gradient pathways, a frozen copy of the network is often used.
encourage fz(2, become
It designed for enforcing idempotence in CL and serve as distillation loss. According to eq 3, under empirical risk minimization, we can assume that:
fe(2, fe = ft(z.0).
(13)
Thus, we rewrite the Lide as:
Lide
Σ
11fe fe(x, 0)) - fe-1 (e fe(x,
(14)
(Z.))ETL.M
First, according to the same input for fi and fi-1 in eq 14, this idempotent distillation loss could serve standard regularization loss:
Lre
Σ
l[f())) - f
(15)
(M.M)TT..M
which is often used in CL. methods (Gu et al., 2023; Sarfraz et al., 2025) to mitigate catastrophic forgetting.
Second, when incorporating the second input that conveys logits from the loss steers the current model Se to update in a direction where the predictions remain correctly interpretable by the previous model fi-1- Consequently, in sequential tasks, fi-1 and driven toward idempotence, feeding back ft 's own output does not alter the prediction of ft-1, yielding more reliable predictions across tasks and improving calibration continual learning.
B I-SNE VISUALIZATION OF VARIOUS METHODS
In this section, show more t-SNE visualization of various methods on first task testing data on CIFAR- 100 with 500 buffer size. The task number is 10. t-SNE figures shows our method has the better capability of resisting catstrophic forgetting compared with ER, DER and BFP. We observed that the feature clusters of the 10 classes from the first task become increasingly blurred as the model learns knowledge from new tasks in these methods. However, this phenomenon alleviated in our method.
task 1
task 2
task
lask
Lask
task 3
ER
BFP
task 1
task 2
task
task
task:
task 3
DER
ER+ID (Ours)
Figure 9: We perform I-SNE visualization of the features extracted from the first task testing data on CIFAR- 100 across training tasks. The figures show how the feature clusters of the 10 classes from the first task change when the model train data from new tasks.

---

Published as conference paper at ICLR 2026
MIFA LAB
Table 7: Comparison of Final Forgetting (PF) across different continual learning methods. All experiments are repeated 5 times with different seeds. The best results (lowest forgetting) highlighted in blue. The second best results are highlighted green.
CIFAR-10
CIFAR-100
Tiny-ImageNet
Method
Buffer 200
Buffer 500
Buffer 500
Butfer 2000
Buffer 500
Buffer 4000
Joint
0.00
0.00
0.00
0.00
0.00
0.00
iCaRL. (Rebuff et al,, 2017)
36.00+7.29
30.19+3.38
28.58=0.84
24.24+0.58
20.82+1.31
15.29+0.53
ER (Riemer ol., 2018)
71.35:7.77
52.1247.56
71.92:0.74
51.82:0.75
74.7920.67
57.4720.57
BIC (Wu 2019)
53.63+7.18
24.87=0.98
48.87=0.91
38.50s1 09
67.57+1
63,48s0.25
LUCIR (Hou al., 2019)
19.79+10.16
37.58+3.88 80
30.22+1.26
32.48+0:76
35 36.0240.56
30,39+0.95
DER (Buzzega et al., 2020)
45.31
32.0442.88
56.6642.55
34.4142.05
68.43a2.73
59.5426.13
DER+ (Buzzega et al., 2020)
36.2014.15
27.9313.34
51.8521.61
34.4421.42
61.45a3.12
39.1113.66
ER ACE (Caccia et al., 2021)
19.52+1.23
12.87+1.06
38.61=1.15
28.42+0.55
40.97+1.38
29.37+1.09
XDER (Boschini et al., 2022)
16.3640.11
12.81
24.15=1.37
11.17
42.90s0.54
18.87=1.08
BFP (Gu 2023)
22.53+5.00
16.81=1.11
35.32+3.94
19.76++087
30.0244.37
19s6.956
Ours (ER+ID)
15.28+2.41
11,93+044
29.98=2.52
17.46et
36.63+3.37
22.46
Ours (BFP+ID)
15.79u2.73
12.11
26.56a2.56
12.52a1 29
27.41a3.92
16.6840.44
C FORGETTING COMPARISON OF DIFFERENT REHEARSAL-BASEE CONTINUAL LEARNING METHODS
Instead of FAA, Final Forgetting (FF) reflects the model's anti-forgetting capacity. To make fair comparison, we exclude the Exponential Moving Average (EMA) based methods, the highest model performance
each task is from working model instead of EMA model, thereby reducing FF following Eq. 16 appendix. FF measures the drop from each task's historical peak accuracy (its best accuracy when first learned) to its final accuracy after all tasks, while EMA artificially smooths performance drops by reducing the accuracy Table 7 shows Final Forgetting (FF) of different continual learning methods. The results show that the idempotence loss yields a lower FF, indicating improved stability. worth noting that compared with XDER, there just forwarding pass the model twice.
first learned, thus understating true forgetting. The
additional architectures learnable parameters introduced in our method,
D EXPERIMENTAL SETTING
We evaluate our method on three standard continual learning benchmarks under Class-IL. setting, where task identifiers are unavailable during testing, making it challenging scenario for maintaining performance across tasks.
Datasets. Our experiments three datasets with varying complexity:
Split CIFAR-10- The CIFAR-10 dataset is divided into 5 sequential tasks, each containing 2 classes. Each class comprises 5,000 training and 1,000 test images of size 32x32.
Split CIFAR-100: CIFAR- 100 is split into 10 tasks with 10 classes per task. Each class contains 500 training and 100 test images of size 32x32.
Split TinyImageNer TinylmageNet is divided into 10 tasks with 20 classes each. Each class has 500 training images, 50 validation images, and 50 test images.
Evaluation Metrics. We use two standard metrics to evaluate continual learning performance:
Final Average Accuracy (FAA): Measures the average accuracy across all tasks after training is complete. For model that has finished training on task f, let at denote the test accuracy on task i. FAA is computed as the mean accuracy across all tasks.

---

Published as conference paper at ICLR 2026
MIFA LAB
Final Forgetting (FF): Quantifies how much knowledge of previous tasks is forgotten, defined as:
1 T-1 max je(1, 17-1)
(a) - a!)
(16)
where lower values indicate better retention of previously learned tasks.
Expected Calibration Error (ECE): Quantifies the mismatch between model's predicted confidence and its actual accuracy. Predictions are partitioned into M confidence interval bins mm The ECE is computed the weighted average of the absolute difference between the average confidence (conf (Bm)) and the average accuracy (ace( Bm )) within each bin:
M
Bm N
ECE
Σ
cconf (Bm) (oc(Bm)).
(17)
===
where N the total number of samples. A lower ECE indicates a better-calibrated model whose confidence estimates more reliable.
D.I IMPLEMENTATION DETAILS SUPPLEMENTARY
Besides the details mentioned above, we train 50 epochs per task for Split CIFAR-10 and Split CIFAR-100 and 100 epochs per task for Split TinylmageNet (Le Yang, 2015). For Split CIFAR 100, the learning rate is decreased by factor of 0.1 at epochs 35 and 45, while for Split TinyImageNer,the learning rate is decreased by a factor 0.1 at epochs 35, 60 and 75. The learning rate may vary in the light of different continual learning methods, while for fair comparison, we use the same initial learning rate as DER and BFP for our methods. not specified, all baselines use the rescrvoir sampling algorithm (Vitter, 1985) update memory, while BFP (Gu et al., 2023) uses class-balanced reservoir sampling (Buzzega et al., 2021) for pushing balanced examples into the buffer.
D.2 HYPERPARAMETERS
In this section, we show hyperparameter combination that used in our experiments. These hyperpa- rameters are adopted from Boschini et al. (2022); Buzzega et al. (2020); Gu et al. (2023) to make fair comparison.
SPLIT CIFAR-
Buffer size 200
iCaRL: Ir = 0.1, wd = 10
LUCIR: Anaee = 5, mom = 0.9, 2, epochaning = 20, 0.03, &raming 0.01, m 0.5
BiC: - 2, epochsppic = 250, Ir 0.03
ER-ACE: Ir 0.03
ER: Ir 0.1
DER: Ir 0.03, = 0.3
DER++ Ir = 0.03, = 0.1, 3 = 0.5
XDER: a = 0.3, m = 0.7, B = 0.9, 7 0.85, wd = 1e 06, À = 0.03, 0.001,
0.03, T 5, mom 0.9
DEP++ w/ BEP: Ir 0.03, Cdsttil 0.1, = 0.5, 0bfp =
Buffer size 500
iCaRL: 1r = 0.1, wd 10
LUCIR: Anoee = 5, mom = 0.9, & = 2, epoch = 20, Ir= 0.03, rriiing 0.01, m 0.5

---

Published as conference paper at ICLR 2026
MIFA LAB
BIC: r 2, epochspic = 250, Ir = 0.03
ER-ACE: Ir 0.03
ER: |y 0.1
DER: 0.03, a 0.3
DER++ Ir 0.03, 0.1, 0.5
XDER: 0.3,
0.7, 0.9, 0.85, wd le -66, À 0.0, 7 0.001,
0.03, T == 5, mom 0.9
DEP++ w/ BFP: Ir 0.03, Odiatili 0.2, Oice 0.5, Obfe
SPLIT CIFAR-100
Buffer size = 500
ICaRL: Ir 0.3, wd 10-
LUCIR: Abase 5, mom 0.9, & == epoch 20, 1== 0.03, Traming 0.01, m 0.5
BiC: r 2, epochspic = 250, Ir = 0.03
ER-ACE: Ir 0.03
ER: |r 0.1
DER: 0.03, a = 0.3
DER++ Ir 0.03, 0.1, 3 == 0.5
XDER: 0.3,
0.7, 3 0.9, 7 0.85,
wd le 06, À 0.05, 7 0.001,
0.03, T 5, mom 0.9
DEP++ w/ BFP: Ir 0.03, Odistili 0.1, Oice 0.5, Obfp
Buffer size 2000
ICaRL: Ir 0.3, wd 10
LUCIR: Ause = 5, mom = 0.9, & = 2, epoch 20, Ir = 0.03, Iriming 0.01, m 0.5
BiC: r = 2, epochspic = 250, Ir = 0.03
ER-ACE: Ir 0.03
ER: |y 0.1
DER: 0.03, a = 0.3
DER++: Ir 0.03, 0.1, 3 0.5
XDER: 0.3,
0.7, 3 0.9, 7 0.85, wd le 06, À = 0.05, 0.001, br
0.03, T 5, mom
DEP+ w/ BFP: Ir 0.03, Odistill 0.1, Oice 0.5, abfp =1
SPLIT TINYIMAGENET
Buffer size = 4000
iCaRL: Ir 0.03, wd = -5
LUCIR: Aroee 5, mom 0.9, &: = epoch 20, Ir 0.03, |riiing 0.01, m 0.5
BiC: - 2, epochspic = 250, Ir = 0.03
ER-ACE: Ir = 0.03
ER: Jy 0.1
DER: 0.03, a
DER++ Ir 0.03, 0.1, 0.5
18

---

Published as conference paper at ICLR 2026
MIFA LAB
XDER: = 0.3, 0.7, 3 0.9, 0.85, wd = 1e-16, A = 0.0, 0.001, Ir = 0.03,
mom 0.9
DEP++ w/ BFP: Ir 0.03, Odistsii 0.3, 0.8, Obfp
D.3 INTERGRATED IDER INTO BFP
As Gu et al. (2023) introduces BFP distillation loss, which focuses on features. We can easily incorporate our method into BFP framework. The BFP loss is:
LBFP
Σ
||Ab,( 0) (2,
(18)
(I.y)TTI,
where h, is feature extractor in model fe on the t-th task and A is linear transformation aimed to preserve the linear separability of features backward in time.
During training on the task the model and A are optimized respectively, Thus, the LBFP+ID can be:
CBFP+ID Lice + aLide 3rrepiee + BLBFP.
(19)
D.4 COMPLEXITY AND TRAINING COST
We train all experiments on NVIDIA RTX 4090 and Ascend 910B. The additional parameters we need for modified architecture are very small. Using ResNet-18 as the backbone, the normal architecture contains 11 1.22MM parameters on CIFAR- 100 while the modified architecture increases the parameter count to 11.91M 91 parameters, Although we need two forward passes to train the model, which leads slightly longer training time compared with DER++, the longer training time is acceptable increases the performance by significant margin.
E LIMITATIONS
Naive Implementation. As we first introduce idempotence property into continual learning, the method should be very simple. In the future, we try to combine our method with more complementary techniques to further improve performance. addition, we also plan explore the application of the idempotence property in data sampling strategies for continual learning.
F
ABLATION RESULTS
F.1 CONTRIBUTION OF EACH COMPONENT
We conduct a component ablation study to isolate the contributions of each part of the overall objective: the Standard Idempotent Module (SIM), the Idempotent Distillation Module (IDM), and Experience Replay (ER). We focus on the ER+ID method for this study. The ablation study results are shown in Table 8. Using only the Standard Idempotent Module (SIM) or combing SIM with ER produces similar performance compared with finetuning or ER baseline, indicating that SIM alone trains model to be idempotent on the current task, which making it well-suited for sub- sequent idempotent distillation and doesn't 't mitigate catas- trophic forgetting. It also demonstrates that modified archi- tecture does not influence performance and the observed improvements benefit from idempotent distillation loss. Whta's more, adding the Idempotent Distillation Module (IDM) yields substantial performance gains, which further improves accuracy to 44.82%. This validates the effective- ness of idempotence distillation loss.
Table 8: Ablation study of different com- ponents Split CIFAR-100.
SIM
IDM
ER
FAA
X
8.23
/
X
/
24.73
/
44.82

---

Published as conference paper at ICLR 2026
MIFA LAB
F.2 HYPERPARAMETER SENSITIVITY
We performed ablations on CIFAR- 100 with 500 buffer size under CIL setting. We ablate on ER+ID method, as it consistently yields substantial improvements over ER baseline across all datasets and does not introduce any additional hyperparameters, Both and / are from the set (0.1, 0.2, 0.5, } Table 9 demonstrates that IDER is not overly sensitive to specific hyperparameter values, as multiple configurations yield consistent performance improvements. This reliability underscores IDER's practicality and suitability for wide range of continual learning applications.
Table 9: Impact of hyperparameters and 3 for ER+ID on Final Average Accuracy (FAA) on Split CIFAR- 100. We use learning rate as 0.03 and training epoch as 50.
beta
alpha=0.1
alpha=0.2
alpha=0.5
alpha=1
0.1
44.77
44.24
41.74
40.42
0.2
44.41
44.43
44.25
43,02
0.5
43.82
44.33
44.82
43.87
41.20
41.58
42.72
40.93
F.3 PROBABILITY SELECTION
We provide ablation study of the probability P used in the Standard Idempotent Module, which determines whether the second input is set to the empty signal or the ground-truth one-hot vector. We perform sensitivity ablation on Split CIFAR- 100 with 500 buffer size and on ER+ID method. In our ablation study, the second input is set to the neutral "empty" signal input O with probability P and the ground-tran truth one-hot vector y with probability - P. Table 10 shows that as P increases, FAA consistently improves and peaks at P 0.9, which reaches 44.82. Then there is slight drop at P = 1.0, where FAA 43.26. Therefore, we use P 0.9 by default. For simplicity, we can also set P 1.0, which yields comparable performance.
Table 10: Impact of the probability P Final Average Accuracy (FAA) Split CIFAR-100.
P
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
FAA
20.9
22.24
27.03
29.19
31.46
37.48
42.24
44.82
43.26
G STATEMENT ON THE USE OF LARGE LANGUAGE MODELS
hereby declare that large language models (LLMs), specifically GPT-5, were used during the preparation of this manuscript. The use of LLMs was strictly limited to: aiding and polishing writing. The LLM was used solely as an assistive tool for prose refinement and did not contribute to the intellectual content of the research.
20


Reviews:
[{"review_id": "69tcoW2wXa", "reviewer": "Reviewer_f4Fu", "summary": "This paper aims to improve accuracy and calibration in continual learning by extending idempotence enforcing loss function into the continual learning setting with experience replay. A function is called idempotent if consecutive applications of it gives the same result as one application. \nIn the single task setting, the idempotence enforcing loss function encourages the model $f(x, y)$ to be idempotent with respect to its second input $y$. This work introduces a new loss function to adapt adaptation of this idea in the continual learning setting. This new loss function can be combined with some existing techniques to improve them\nThe improved calibration and accuracy claims are supported by experimental results.", "questions": "Please see the weakness section. \nIn general providing more intuition, especially on why this loss function helps with calibration would be great.", "limitations": "", "rating": 10, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 4, "strengths": "The paper is well written and organized. Adaptation of the idempotence loss function to the continual learning setting is creative and nuanced. The experimental results are promising.", "weaknesses": "I think giving more intuition about the loss function would be helpful for the reader. For example, in lines 250-252, it is stated that minimizing equation 5 biases $f_t$ towards the wrong label (even though with probability $1-P$ that objective would be minimized in eq 5), but why would $f_{t-1}$ not have the same problems? Expanding that explanation would be great.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XmBxIje7h0", "reviewer": "Reviewer_xwPR", "summary": "This manuscript introduces the idempotent property to mitigate catastrophic forgetting, a fundamental challenge in incremental learning. The authors design two complementary loss functions: one enforces idempotence on current data, while the other distills this property from a previous model checkpoint using a memory buffer of historical samples. Extensive experiments are conducted to validate the effectiveness of the proposed approach.", "questions": "• A simple theoretical proposition or a more in-depth discussion connecting the idempotence loss to established continual learning theory would significantly strengthen the foundation.\n• Test IDER in settings like online continual learning or with tasks containing out-of-distribution samples to better probe its limits and robustness.\n• Perform a more systematic hyperparameter sensitivity analysis, showing how performance varies with different values of α and β across key datasets.\n• Add comparisons with regularization-based and memory-free methods in the main experiments.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 3, "strengths": "• The manuscript introduce idempotence, a mathematical property, to tackle catastrophic forgetting and poor model calibration in continual learning.\n• The proposed IDER is a lightweight framework and functions as a plug-and-play module for performance gains", "weaknesses": "• The paper primarily relies on intuition and empirical success to introduce idempotence. It lacks a rigorous theoretical analysis or hypothesis for why enforcing output stability should directly mitigate catastrophic forgetting at a fundamental level.\n• The empirical validation is comprehensive on CIFAR-10, CIFAR-100, and Tiny-ImageNet. However, to firmly establish the method's practicality and generalizability, evaluation on a large-scale dataset, e.g., ImageNet-1K.\n• The hyperparameter sensitivity analysis for α and β is relatively brief.\n• The experimental comparisons are heavily focused on replay-based methods, which is natural as IDER is a plug-in for this paradigm. However, comparing against strong representatives from other CL fmethods, such as regularization-based methods or memory-free approaches, would more comprehensively position IDER's contribution within the entire field and highlight its unique value.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "k1P7qyuVhy", "reviewer": "Reviewer_aMu3", "summary": "The paper introduces IDER (Idempotent Experience Replay), a novel approach for continual learning that addresses the issue of catastrophic forgetting in replay-based methods. The key idea is to make the replay process idempotent, meaning that repeatedly revisiting the same experiences does not alter the model representation undesirably. The method achieves this by enforcing idempotent updates through the standard idempotent module and the idempotent distillation module. Experiments on several continual learning benchmarks demonstrate consistent performance gains over standard replay-based baselines.", "questions": "Please refer to the weakness section.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The idea of using idempotent property to mitigate issues of poor calibration and recency bias is straightforward and intuitive.\n\nThe paper is well-written and easy to follow.\n\nThe proposed method is shown to be effective.", "weaknesses": "As stated in Lines 71–74, the paper claims a strong correlation between the idempotence distance and prediction error. However, it remains unclear whether this relationship has been formally analysed. Could the authors provide empirical evidence or theoretical justification for this claim?\n\nTo enable idempotence with respect to the second input, the proposed method divides the backbone into two parts. What principles guide this division? Does choosing different partition points (e.g., splitting at shallower or deeper layers) affect model performance or stability? It would be helpful if the authors could provide theoretical insight or experimental analysis on how the division point influences the effectiveness of idempotent learning.\n\nLines 207–209 describe the probability P that determines whether the second input is set to the ground-truth label or the empty signal. Is there any hyperparameter analysis that explores the sensitivity of the method to P? How should this value be selected in practice?\n\nThe overall loss function combines three components: the Standard Idempotent Module, Idempotent Distillation Module, and Experience Replay. Are there ablation experiments isolating the contribution of each component? Furthermore, the paper states that the proposed method primarily addresses poor calibration and recency bias. However, these issues are often mitigated in modern replay-based methods. Why does this approach not integrate or compare directly with more recent baselines such as L2P [1], HIDE-prompt [2], or VQ-prompt [3]? Has the proposed method been evaluated under online continual learning settings to validate its general applicability?\n\nTable 1 shows improvements when integrating IDER with ER, BFP, and CLS-ER. However, could the proposed method also be compatible with other state-of-the-art baselines such as SCoMMER or SARL? It would be valuable to verify whether the idempotent mechanism consistently enhances these methods as well. \n\nRegarding the experiments, I noted that the evaluation is primarily conducted on small-scale datasets like the CIFAR series and Tiny-ImageNet. I encourage the authors to validate the method's effectiveness on larger-scale and more diverse datasets. Furthermore, a concrete example illustrating how the proposed method achieves error correction in practice would greatly enhance the paper’s clarity and impact.\n\n[1] Wang et al., Learning to prompt for continual learning. CVPR 2022\n\n[2] Wang et al., Hierarchical Decomposition of Prompt-Based Continual Learning: Rethinking Obscured Sub-optimality. NIPS 2023\n\n[3] Li et al., Vector Quantization Prompting for Continual Learning. NIPS 2024", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "7kECVXGSsr", "reviewer": "Reviewer_WbzD", "summary": "This paper introduces Idempotent Experience Replay (IDER), a method for class-incremental learning (CIL) that exploits the mathematical property of idempotence to improve accuracy, forgetting, and uncertainty calibration. The method consists of two components: 1) a standard idempotent module that trains the current model to be idempotent on the current task; and 2) an idempotent distillation module that enforces idempotence between the previous and current model checkpoints. Experiments on standard datasets demonstrate improvements in both accuracy and calibration.\n\n\n**Recommendation**\nI lean toward rejecting the paper in its current form. While the core idea of applying idempotence to continual learning is novel and the empirical results are encouraging, the paper suffers from significant theoretical and experimental gaps which prevent a rigorous and clear assessment of the paper.", "questions": "See above.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. **Novel application of idempotence to continual learning:** while idempotence has been explored in deep learning for other tasks, this appears largely under-explored in continual learning settings.\n2. **Plug-and-play design with rehearsal-based approaches:** the method can be integrated with existing rehearsal-based approaches (e.g., ER) with minimal overhead, making it practically appealing in those cases.\n3. **Experimental evaluation on general-CIL:** the method has also been tested on more realistic conditions (i.e., general class-incremental learning), making it interesting from a practical point of view.", "weaknesses": "1. **Limited theoretical justification:** while the paper takes inspiration from prior work on idempotence, the theoretical connection between idempotence and mitigation of both catastrophic forgetting and uncertainty miscalibration is not clear. Although being demonstrated empirically, it is unclear why enforcing idempotence specifically helps with continual learning problems in the first place. The intuition lacks formal analysis. Can you provide explanations on why idempotence should help with catastrophic forgetting and uncertainty calibration?\n2. **Equation 6:** the idempotent distillation loss uses $f_{t-1}(x, f_t(x, 0))$ rather than $f_t(x, f_t(x, 0))$ to avoid pulling predictions toward incorrect output, but this breaks the true idempotence property since $f_{t-1}$ and $f_t$ are two different functions. What happens if you use $f_t(x, f_t(x, 0))$ instead of $f_{t-1}(x, f_t(x, 0))$ in Equation 6?\n3. **Missing evaluation with calibration methods for CL:** one of the main focus of the paper is reliability (i.e., reducing the calibration error). However, the paper does not consider recent work on uncertainty calibration for class-incremental learning [1,2].\n4. **Limited comparison with other CL methods:** apart from rehearsal-based methods, it would be interesting to include comparison with, e.g., regularisation-based or parameter-isolation approaches to demonstrate broader applicability. \n5. **Incomplete experimental analysis:**\n    1. Hyperparameter sensitivity: no analysis of sensitivity to $\\alpha$ and $\\beta$ introduced in Equation 8.\n    2. Probability $P$: the probability is not reported nor ablated.\n    3. Backbone architecture: only ResNet18 is tested. What will happen when using a different architecture? Again, this would demonstrate broader applicability.\n    4. Limited experiments on GCIL (Table 2): it would be interesting to see the results on the other considered datasets.\n    5. Limited calibration results (Table 3): as anticipated above, the paper is missing recent work on calibration in continual learning. Furthermore, why is Tiny-ImageNet not included? Finally, since the results from NPCL were copied from the original work, do you assure that the experimental setting is exactly the same? Otherwise, the comparison is not meaningful. \n\n**Minor issues**\n1. No analysis on larger task sequences (e.g., 20 tasks on Tiny-ImageNet).\n2. Figures 3, 4, and 5 are difficult to parse.\n3. Writing style can be overall improved.\n\n[1] Li, Lanpei, et al. \"Calibration of continual learning models.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2024.\n\n[2] Hwang, Seong-Hyeon, Minsu Kim, and Steven Euijong Whang. \"T-CIL: Temperature Scaling using Adversarial Perturbation for Calibration in Class-Incremental Learning.\" Proceedings of the Computer Vision and Pattern Recognition Conference. 2025.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)