DLER: Dual-Logit Experience Replay for Online Continual Learning

Huiwei Lin; Shanshan Feng; Kong Aik Lee

cs.LGNov 3, 2026

DLER: Dual-Logit Experience Replay for Online Continual Learning

Authors: Huiwei Lin, Shanshan Feng, Kong Aik Lee

Organizations: The Hong Kong Polytechnic University, Hong Kong SAR, China · Wuhan University, Wuhan 430072, China

Abstract

Online continual learning aims to continuously train neural networks on a non-stationary data stream in a single pass. Rehearsal-based methods alleviate catastrophic forgetting by replaying stored samples, but the imbalance between current and previous data often leads to predictions biased toward current classes. Many approaches have been proposed to overcome the forgetting problem by correcting the bias; however, they still need to be improved in an online fashion. By decomposing the dot-product logits into an angle factor and a norm factor, our analysis reveals that the angle factor efficiently captures novel knowledge but is particularly susceptible to prediction bias, whereas the norm factor helps preserve historical knowledge. Based on these observations, we propose Dual-Logit Experience Replay (DLER), which exploits dual-logits for both model optimization and memory management. Specifically, DLER learns current samples using cosine logits and incorporates additional dot-product logits when replaying previous samples to mitigate prediction bias. To strengthen dual-logit learning under limited replay memory, an auxiliary supervised contrastive objective promotes angular compactness within each class, extending corrections learned from limited replay samples to other samples of the same class. Meanwhile, we introduce a memory update strategy that preferentially retains samples for which dot-product prediction assigns a higher probability to the correct class than cosine prediction, aligning sample selection with dual-logit training. Extensive experiments on three datasets demonstrate the effectiveness of DLER, particularly under limited memory budgets.

Figures & tables

Fig. 1: Illustration of our work. (a) The dot-product logits can be decomposed into a norm factor and an angle factor; (b) Existing studies, which learn all samples by calculating logits in the same way; (c) Different from existing studies, the model in our work learns current samples only by the angle factor, while replays previous samples by both the angle factor and the norm factor. (d) By leveraging the norm factor, the model can correctly classify samples.

Panel of Figure 2 — Fig. 2: Average accuracy rate on observed learning stages on three datasets when the memory buffer size is 1000.

	Components					Buffer size
Method	Dual-logits	$\alpha$	SC	BM	Advantage	400	1000	2000	4000
ER						5.2 $\pm$ 0.6	7.6 $\pm$ 0.5	10.1 $\pm$ 0.9	12.7 $\pm$ 1.1
Dual-logit training (Fixed)	$\checkmark$					8.0 $\pm$ 0.6	10.9 $\pm$ 0.7	14.2 $\pm$ 0.8	16.1 $\pm$ 0.8
Dual-logit training	$\checkmark$	$\checkmark$				9.7 $\pm$ 0.4	13.4 $\pm$ 0.5	16.2 $\pm$ 0.7	18.9 $\pm$ 0.8
Dual-logit training + SC	$\checkmark$	$\checkmark$	$\checkmark$			10.0 $\pm$ 0.5	13.9 $\pm$ 0.3	17.2 $\pm$ 0.5	19.6 $\pm$ 0.7
Dual-logit training + SC + CB	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$		10.2 $\pm$ 0.5	14.5 $\pm$ 0.3	17.4 $\pm$ 0.8	19.7 $\pm$ 0.5

TABLE II: Ablation study on Split TinyImageNet with different memory buffer sizes.

Panel of Figure 4 — Fig. 3: Average accuracy rate of previous classes, current classes, and their average on Split MiniImageNet with a 1000 memory buffer size.

Panel of Figure 5 — Fig. 4: Improvement of existing methods with dual-logits training on three datasets while the buffer size is 1000.

Fig. 5: The performance of dual-logits training on Split CIFAR100 (buffer size=1000) with different values of

\alpha

Method Setting	All Classes	Current Classes	Previous Classes
ER	$15.6\pm 2.6$	$50.5$	$11.7$
ER-ACE	$18.9\pm 0.9$	$17.3$	$19.1$
OBC	$18.3\pm 0.7$	$17.5$	$18.4$
Dual-logit training (feature)	$18.6\pm 1.0$	$30.6$	$17.2$
Dual-logit training (predictor)	$19.6\pm 1.5$	$34.7$	$18.0$
Dual-logit training (both)	$\mathbf{20.1\pm 1.2}$	$31.8$	$18.8$

TABLE III: Final accuracy (%) on Split CIFAR100 with a buffer of 1,000 samples after adding a linear layer to the feature extractor.

Fig. 6: Conditional coverage and previous-class accuracy of dual-logits training and its enhancement with SC on Split TinyImageNet.

Metric	High-score	Low-score
Spatial JS divergence	0.2256	0.0463
Feature norm	15.7856	12.8475
Ground-truth cosine probability	0.1173	0.0260
Gradient norm (all)	7.3114	52.7980
Gradient norm (backbone)	7.0487	51.4370
Gradient conflict rate	41.5%	44.6%

TABLE IV: Comparison of the highest- and lowest-scoring training samples within the 96 selected classes on Split TinyImageNet.

Configuration	Learning	Replaying	Testing	$A_{\mathrm{all}}$	$A_{p}$	$A_{c}$	$\overline{\\|\bm{w}\\|}_{p}$	$\overline{\\|\bm{w}\\|}_{c}$	$\mu_{W_{p}}\pm\sigma_{W_{p}}$	$\mu_{W_{c}}\pm\sigma_{W_{c}}$	$\mu_{b_{p}}$	$\mu_{b_{c}}$
	Logit configuration			Accuracy (%)			Weight norm		Weight statistics		Bias
1 (ER)	Dot	Dot	Dot	27.3	17.7	36.9	2.08	1.86	$0.0044\pm 0.0274$	$-0.0038\pm 0.0221$	$-0.22$	$0.22$
2	Dot	Dot	Cos	24.1	12.7	35.6	2.08	1.86	$0.0044\pm 0.0274$	$-0.0038\pm 0.0221$	$-0.22$	$0.22$
3 (LUCIR)	Cos	Cos	Cos	26.9	14.9	38.9	2.00	1.64	$0.0398\pm 0.0235$	$0.0471\pm 0.0146$	$-0.00$	$0.00$
4	Cos	Cos	Dot	28.2	28.8	27.6	2.00	1.64	$0.0398\pm 0.0235$	$0.0471\pm 0.0146$	$-0.00$	$0.00$
5	Dot	Cos	Dot	19.6	0.0	39.1	1.37	2.09	$0.0197\pm 0.0115$	$0.0219\pm 0.0270$	$-1.03$	$1.03$

TABLE VI: Comparison of logit configurations for training and inference on Split CIFAR100 with a memory buffer of 5,000 samples.

A_{\mathrm{all}}

A_{p}

, and

A_{c}

denote the final accuracies (%) on all, previous, and current classes, respectively.

\overline{\|\bm{w}\|}

denotes the mean class-weight vector norm;

\mu_{W}

and

\sigma_{W}

denote the mean and standard deviation of weight entries; and

\mu_{b}

denotes the mean bias. Subscripts

p

and

c

indicate previous and current classes. Dot and Cos denote dot-product and cosine logits, respectively.

Panel of Figure 11 — Fig. 7: The analysis results of different ways during the learning process on Split CIFAR100 when the memory buffer size is 5000.

Fig. 8: Examples of high-score and low-score samples and their class activation maps obtained using dot-product and cosine logits.

Online Continual Learning

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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.

Abstract

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