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

arXiv: https://arxiv.org/abs/2609.32593 · HTML: https://mlsanity.com/paper/2609.32593/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 54 references that are in the map.
- First posted on arXiv 26 Sep 2026.

## Builds on (most cited first, 30 of 40)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [Training Region-based Object Detectors with Online Hard Example Mining](https://mlsanity.com/paper/1604.03540/) (2016)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Not All Samples Are Created Equal: Deep Learning with Importance Sampling](https://mlsanity.com/paper/1803.00942/) (2018)
- [Remix: Rebalanced Mixup](https://mlsanity.com/paper/2007.03943/) (2020)
- [Long-Tailed Recognition via Weight Balancing](https://mlsanity.com/paper/2203.14197/) (2022)
- [Heavy-Tailed Class Imbalance and Why Adam Outperforms Gradient Descent on Language Models](https://mlsanity.com/paper/2402.19449/) (2024)
- [Age of Information: An Introduction and Survey](https://mlsanity.com/paper/2007.08564/) (2020)
- [Online Continual Learning under Extreme Memory Constraints](https://mlsanity.com/paper/2008.01510/) (2020)
- [How Re-sampling Helps for Long-Tail Learning?](https://mlsanity.com/paper/2310.18236/) (2023)
- [VideoLT: Large-scale Long-tailed Video Recognition](https://mlsanity.com/paper/2105.02668/) (2021)
- [Online Learning with Optimism and Delay](https://mlsanity.com/paper/2106.06885/) (2021)
- [Learning to Re-weight Examples with Optimal Transport for Imbalanced Classification](https://mlsanity.com/paper/2208.02951/) (2022)
- [Scheduling Policies for Minimizing Age of Information in Broadcast Wireless Networks](https://mlsanity.com/paper/1801.01803/) (2018)
- [Reweighting Augmented Samples by Minimizing the Maximal Expected Loss](https://mlsanity.com/paper/2103.08933/) (2021)
- [Dynamic Loss-Based Sample Reweighting for Improved Large Language Model Pretraining](https://mlsanity.com/paper/2502.06733/) (2025)
- [Focal-SAM: Focal Sharpness-Aware Minimization for Long-Tailed Classification](https://mlsanity.com/paper/2505.01660/) (2025)
- [Improved Balanced Classification with Theoretically Grounded Loss Functions](https://mlsanity.com/paper/2512.23947/) (2025)

## Abstract (arXiv)

Current machine learning algorithms primarily rely on instantaneous signals such as loss, margin, and prediction confidence to characterize model behavior. These signals indicate how difficult a prediction is at the current optimization step, but they do not capture how long the model has remained incorrect. We study this temporal dimension of learning and introduce Age of Learning (AoL), a learning-state variable that measures the persistence of prediction errors over time. AoL increases while an error remains unresolved and resets when a correct prediction is achieved, thereby distinguishing persistent under-learning from transient mistakes. We develop AoL-based training strategies for both offline and streaming settings. In offline learning, sample-level AoL is accumulated over training and aggregated into class-level states that guide adaptive reweighting and resampling. In streaming learning, where full historical access is unavailable, we maintain lightweight class-level AoL states using current and buffered observations. Across long-tailed classification settings, AoL improves or matches standard training baselines, with larger benefits when learning difficulty persists over time. Multi-seed streaming experiments further show reproducible gains under temporally stable imbalance. Analysis of class frequency, loss, and margin shows that AoL is related to conventional difficulty measures but captures additional information about error duration. These results suggest that temporal persistence provides a useful complementary signal for characterizing and controlling learning dynamics in imbalanced and non-stationary environments.