# Reliable Replay through Spatial Coherence in Online Continual Learning

arXiv: https://arxiv.org/abs/2609.33725 · HTML: https://mlsanity.com/paper/2609.33725/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 46 of its 53 references that are in the map.
- First posted on arXiv 27 Sep 2026.

## Builds on (most cited first, 30 of 46)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Dark Experience for General Continual Learning: a Strong, Simple Baseline](https://mlsanity.com/paper/2004.07211/) (2020)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [CodeRL: Mastering Code Generation through Pretrained Models and Deep Reinforcement Learning](https://mlsanity.com/paper/2207.01780/) (2022)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [Task-Free Continual Learning](https://mlsanity.com/paper/1812.03596/) (2018)
- [New Insights on Reducing Abrupt Representation Change in Online Continual Learning](https://mlsanity.com/paper/2104.05025/) (2021)
- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Episodic Memory in Lifelong Language Learning](https://mlsanity.com/paper/1906.01076/) (2019)
- [Understanding the Role of Training Regimes in Continual Learning](https://mlsanity.com/paper/2006.06958/) (2020)
- [Anatomy of Catastrophic Forgetting: Hidden Representations and Task Semantics](https://mlsanity.com/paper/2007.07400/) (2020)
- [Continual Prototype Evolution: Learning Online from Non-Stationary Data Streams](https://mlsanity.com/paper/2009.00919/) (2020)
- [Supervised Contrastive Replay: Revisiting the Nearest Class Mean Classifier in Online Class-Incremental Continual Learning](https://mlsanity.com/paper/2103.13885/) (2021)

## Abstract (arXiv)

Continually adapting models to new tasks requires retaining earlier knowledge under limited memory and computation. Experience replay addresses this challenge, but priorities based on individual loss increases overlook how related memories respond to the same update and can overemphasize isolated responses. We introduce SPatial coHErent risk control for REplay (SPHERE), a general replay-allocation method applicable across a broad range of learning settings. SPHERE uses a representation kernel to aggregate signed prospective loss changes, attenuating unsupported spikes while retaining coherent increases. It then formulates allocation as entropy-regularized transport, redistributing uniform source mass toward supported high-risk regions while penalizing long-distance transfers. We derive replay coefficients from the transport objective's sensitivity to the original loss changes and blend them with uniform replay to maintain baseline rehearsal. Our analysis establishes conditions under which kernel aggregation improves risk estimation and bounds transport-value inflation due to residual noise and smoothing bias. Experiments demonstrate that SPHERE improves accuracy and reduces forgetting across noisy-label vision tasks, continual language-model instruction tuning, and code-generation reinforcement learning with incomplete test rewards.