IDER: IDempotent Experience Replay for Reliable Continual Learning

Conference: ICLR 2026 arXiv: 2603.00624 Code: GitHub Area: Model Compression Keywords: Continual Learning, Idempotency, Experience Replay, Calibration Error, Catastrophic Forgetting

TL;DR

This paper introduces idempotence into continual learning, enforcing output self-consistency during new task acquisition via two components—a Standard Idempotent Module and an Idempotent Distillation Module—simultaneously improving prediction reliability (reduced calibration error) and significantly mitigating catastrophic forgetting.

Background & Motivation

Continual learning faces the core challenge of catastrophic forgetting—models rapidly lose knowledge of previous tasks when learning new ones. Replay-based methods (e.g., ER, DER++) mitigate this by storing old samples in a buffer, yet tend to be overconfident and poorly calibrated (high ECE), with particular bias toward recent tasks. In safety-critical domains such as healthcare and autonomous driving, models must not only be accurate but also "know what they do not know."

Existing uncertainty-aware CL methods (e.g., NPCL) employ neural processes but suffer from: (1) non-negligible parameter growth; and (2) incompatibility with logits-based replay methods due to the stochasticity of Monte Carlo sampling. There is thus a need for a lightweight and compatible principle for building reliable CL systems.

Core Idea: Idempotence—a function that yields the same result when applied repeatedly (\(f(f(x)) = f(x)\)). If a model remains idempotent on old data, its outputs lie on a learned stable manifold, indicating self-consistent and reliable predictions.

Method

Overall Architecture

IDER augments the experience replay framework with two modules: (1) a Standard Idempotent Module that enforces idempotence on current-task data; and (2) an Idempotent Distillation Module that imposes cross-task idempotent constraints using an old model checkpoint. Only two forward passes are required, introducing virtually no additional parameters.

Key Designs

1. Modified Network Architecture:

   • Function: Enables the model to accept two inputs—an image and an auxiliary label signal.
   • Mechanism: The ResNet backbone is split into \(f_t^1\) (front half) and \(f_t^2\) (back half). A second input (one-hot label \(y\) or a uniform "null" signal \(\mathbf{0}\)) is transformed via a linear layer followed by LeakyReLU into a feature of the same dimensionality as the output of \(f_t^1\), added to the intermediate feature map, and then passed into \(f_t^2\). The model output (softmax over logits) can be recycled as the second input.
   • Design Motivation: At inference time, when no ground-truth label is available, \(\mathbf{0}\) is used as the second input to obtain a prediction, which is then fed back to verify idempotence.

2. Standard Idempotent Module:

   • Function: Trains the model to be idempotent on current-task data.
   • Mechanism: Minimizes the cross-entropy of two forward passes against the ground truth: \(\mathcal{L}_{ice} = \sum_{(x,y)\in\mathcal{T}_t} [\mathcal{L}_{ce}(f_t(x,y^*),y) + \mathcal{L}_{ce}(f_t(x,f_t(x,y^*)),y)]\) where \(y^*\) is chosen as the ground-truth label with probability \(1-P\) and as the null signal \(\mathbf{0}\) with probability \(P\).
   • Design Motivation: After training, \(f_t(x,\mathbf{0}) \approx y\) and \(f_t(x,f_t(x,\mathbf{0})) \approx y\), achieving self-consistent predictions.

3. Idempotent Distillation Module:

   • Function: Leverages old model checkpoints to constrain the current model and prevent prediction distribution drift.
   • Mechanism: Rather than naively minimizing \(\|f_t(x,\mathbf{0}) - f_t(x,f_t(x,\mathbf{0}))\|^2\) (which may reinforce erroneous predictions due to the bias of \(f_t\) toward current data), the frozen old checkpoint \(f_{t-1}\) is used for the second forward pass: \(\mathcal{L}_{ide} = \sum_{(x,y)\in\mathcal{T}_t,M} \|f_t(x,\mathbf{0}) - f_{t-1}(x,f_t(x,\mathbf{0}))\|_2^2\)
   • Design Motivation: Freezing \(f_{t-1}\) preserves prior knowledge and a stable distribution; only \(f_t\) is updated, guiding \(y_0\) in the correct direction and avoiding error reinforcement. This simultaneously serves as knowledge distillation.

Loss & Training

The total loss is a weighted sum of three terms: \(\mathcal{L}_{IDER} = \mathcal{L}_{ice} + \alpha\mathcal{L}_{ide} + \beta\mathcal{L}_{rep\text{-}ice}\), where the replay loss \(\mathcal{L}_{rep\text{-}ice}\) also applies idempotent training on buffer data. IDER can be integrated as a plug-and-play component into methods such as ER, BFP, and CLS-ER.

Key Experimental Results

Main Results (Final Average Accuracy)

Method	CIFAR-10 Buf200	CIFAR-10 Buf500	CIFAR-100 Buf500	CIFAR-100 Buf2000
ER	44.46	58.84	23.41	40.47
DER++	62.19	70.10	37.69	51.82
XDER	64.10	67.42	48.14	57.57
BFP	68.64	73.51	46.70	57.39
ER+ID (Ours)	71.02	74.74	44.82	56.59
BFP+ID (Ours)	71.99	76.65	48.53	57.74

Ablation Study (GCIL-CIFAR-100 Uniform)

Method	Buf200	Gain	Buf500	Gain
ER	16.34	—	28.76	—
ER+ID	26.66	+10.32	40.54	+11.78
CLS-ER	22.37	—	36.80	—
CLS-ER+ID	31.17	+8.80	37.57	+0.77

Key Findings

• ER+ID achieves a gain of up to 26% on CIFAR-10 Buf200 (44.46→71.02), the largest improvement among all methods evaluated.
• Idempotent distillation effectively alleviates recency bias, yielding more uniform prediction probabilities across tasks.
• ECE (calibration error) is consistently reduced across all baselines, indicating more "honest" model predictions.
• Improvements are even more pronounced in the more challenging GCIL setting (e.g., CLS-ER+ID gains 8.4% under the Longtail configuration).

Highlights & Insights

• The paper elegantly maps the algebraic notion of idempotence directly to a "prediction self-consistency" constraint in CL, offering a mathematically clear and principled intuition.
• The method is extremely lightweight—requiring only one additional forward pass and the previous checkpoint, with virtually no parameter overhead.
• Its plug-and-play nature makes it a general-purpose tool for enhancing the reliability of existing CL methods.

Limitations & Future Work

• Storing the previous checkpoint \(f_{t-1}\) is required, which, while modest in storage cost, increases system complexity.
• All experiments are conducted on ResNet-18; the effectiveness on Transformer backbones and larger models remains unexplored.
• The theoretical foundation of the idempotency assumption warrants further strengthening—a formal analysis of why idempotence necessarily leads to better generalization is absent.

Related Work & Insights

• vs. NPCL: NPCL incurs parameter growth through neural processes and is incompatible with logits-based methods, whereas IDER is lightweight and general-purpose.
• vs. DER++: DER++ simply stores and matches logits, while IDER provides stronger regularization through idempotent constraints.

Rating

• Novelty: ⭐⭐⭐⭐⭐ — Applying idempotence to CL represents a genuinely novel perspective.
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ — Covers CIL, GCIL, ECE, and plug-and-play validation comprehensively.
• Writing Quality: ⭐⭐⭐⭐ — Logic is clear; the derivation from motivation to method flows naturally.
• Value: ⭐⭐⭐⭐ — Provides a new mathematical principle and practical tool for the CL community.

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