Age of Learning: Temporal Persistence of Prediction Errors as a Learning Signal

The Continual Learning (CL) literature has long been driven by the goal of mitigating catastrophic forgetting. This objective rests on an often unstated assumption: that a lifelong learner should approximate the Joint-Task Learning (JTL) solution and retain all previously acquired knowledge. We challenge this retention-centered premise, arguing that in non-stationary environments prioritizing retention can impede real-time adaptation. Shifting the focus to the Average Lifelong Error (ALE), we formalize CL as an online optimization problem governed by the interaction between environmental and learning dynamics. We introduce Transfer Efficiency as a quantitative measure of the tension between Instability, the bias inherited from conflicting past experience, and Transient Error, the optimization cost of learning new tasks from scratch. Under mild convergence conditions, holding across linear and neural network models, this decomposition yields a Critical Task Duration: a closed-form threshold beyond which historical knowledge transitions from a warm-start advantage to an optimization liability whenever retention induces a positive stationary bias. We validate these theoretical predictions on continual image classification and reinforcement learning benchmarks. Finally, by connecting continual learning to the online learning framework of predictable sequences, we show that JTL is only one instance of a broader family of objectives, and we propose a new general class of continual learning algorithms, which we call Predictive Continual Learning. Predictive CL algorithms optimize expected future performance under an explicit, dynamically updated model of future tasks. As a proof of concept, we analyze a Window algorithm that interpolates between JTL and Independent-Task Learning (ITL), outperforming both under controlled distributional drift.

With the widespread adoption of deep learning in visual tasks, Class-Incremental Learning (CIL) has become an important paradigm for handling dynamically evolving data distributions. However, CIL faces the core challenge of catastrophic forgetting, often manifested as a prediction bias toward new classes. Existing methods mainly attribute this bias to intra-task class imbalance and focus on corrections at the classifier head. In this paper, we highlight an overlooked factor -- temporal imbalance -- as a key cause of this bias. Earlier classes receive stronger negative supervision toward the end of training, leading to asymmetric precision and recall. We establish a temporal supervision model, formally define temporal imbalance, and propose Temporal-Adjusted Loss (TAL), which uses a temporal decay kernel to construct a supervision strength vector and dynamically reweight the negative supervision in cross-entropy loss. Theoretical analysis shows that TAL degenerates to standard cross-entropy under balanced conditions and effectively mitigates prediction bias under imbalance. Extensive experiments demonstrate that TAL significantly reduces forgetting and improves performance on multiple CIL benchmarks, underscoring the importance of temporal modeling for stable long-term learning.

Deep learning models in computer vision face significant challenges when trained on long-tailed datasets, where a few majority classes dominate while many minority classes are severely underrepresented. Such imbalances frequently arise in real-world scenarios such as rare species recognition, manufacturing fault detection, and medical image understanding, leading to biased models that underperform on tail classes. Existing reweighting methods typically rely on static class frequencies to penalize the model, ignoring the dynamic nature of how effectively a network actually learns a class over time. We address this by introducing a novel Learning-Dynamics Aware Loss (LDAL) function that shifts the focus from static sample counts to dynamic learning progress. LDAL framework adjusts class weights continuously by leveraging: (i) the strength of learned feature representations (semantic scale), (ii) the intrinsic learning difficulty of each class, measured via the Shannon entropy of its predictions, and (iii) an inter-epoch regularizer term that tracks prediction shifts between consecutive epochs to stabilize training and avoid local minima. LDAL is purely a objective function which incurs negligible computational overhead while adapting to the feature learning of the model. Experimental results on multiple benchmark datasets demonstrate that our approach significantly surpasses state-of-the-art reweighting loss functions, providing an optimal trade-off between accuracy and generalizability. The source code is available at https://github.com/sdm2026/ldal