Online continual learning requires models to learn from non‑stationary data streams while retaining prior knowledge. We identify an overlooked phenomenon—knowledge fragility—where correctly learned instances are rapidly forgotten after minor parameter updates. Our analysis attributes this fragility to a temporal–spatial dual mechanism: temporal instability, high-frequency parameter oscillations cause forgetting to outpace adaptation; and spatial vulnerability, fragile instances lie in sharp, high‑curvature regions of the loss landscape that are extremely sensitive to optimization noise. These insights motivate PDFK (Perturbing to Defend Fragile Knowledge), a unified framework that defends fragile knowledge along both dimensions. Temporally, we apply exponential moving averaging to smooth parameter evolution and stabilize long‑term memory. Spatially, we inject minimal structured perturbations with a consistency constraint to flatten sharp regions and enhance robustness. PDFK requires no task‑boundary annotations. Extensive experiments demonstrate that PDFK substantially improves knowledge retention and outperforms strong baselines under diverse and challenging continual learning settings.

Logit-based knowledge distillation (KD) is commonly used to mitigate catastrophic forgetting in class-incremental learning (CIL) caused by data distribution shifts. However, the strict match of logit values between student and teacher models conflicts with the cross-entropy (CE) loss objective of learning new classes, leading to significant recency bias (i.e. unfairness). To address this issue, we rethink the overlooked limitations of KD-based methods through empirical analysis. Inspired by our findings, we introduce a plug-and-play pre-process method that normalizes the logits of both the student and teacher across all classes, rather than just the old classes, before distillation. This approach allows the student to focus on both old and new classes, capturing intrinsic inter-class relations from the teacher. By doing so, our method avoids the inherent conflict between KD and CE, maintaining fairness between old and new classes. Additionally, recognizing that overconfident teacher predictions can hinder the transfer of inter-class relations (i.e., dark knowledge), we extend our method to capture intra-class relations among different instances, ensuring fairness within old classes. Our method integrates seamlessly with existing logit-based KD approaches, consistently enhancing their performance across multiple CIL benchmarks without incurring additional training costs.

Class-Incremental Learning (CIL) enables models to continuously learn new classes while mitigating catastrophic forgetting. Recently, Pre-Trained Models (PTMs) have greatly enhanced CIL performance, even when fine-tuning is limited to the first task. This advantage is particularly beneficial for CIL methods that freeze the feature extractor after first-task fine-tuning, such as analytic learning-based approaches using a least squares solution-based classification head to acquire knowledge recursively. In this work, we revisit the analytical learning approach combined with PTMs and identify its limitations in adapting to new classes, leading to sub-optimal performance. To address this, we propose the Momentum-based Analytical Learning (MoAL) approach. MoAL achieves robust knowledge memorization via an analytical classification head and improves adaptivity to new classes through momentum-based adapter weight interpolation, leading to forgetting outdated knowledge. Importantly, we introduce a knowledge rumination mechanism that leverages refined adaptivity, allowing the model to revisit and reinforce old knowledge, thereby improving performance on old classes. MoAL facilitates the acquisition of new knowledge and consolidates old knowledge, achieving a win-win outcome between plasticity and stability. Extensive experiments on various incremental settings show MoAL’s state-of-the-art performance1.