# Hidden Failure Modes of Gradient Modification under Adam in Continual Learning, and Adaptive Decoupled Moment Routing as a Repair

arXiv: https://arxiv.org/abs/2604.22407 · HTML: https://mlsanity.com/paper/2604.22407/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 41 references that are in the map.
- First posted on arXiv 24 Apr 2026.

## Builds on (most cited first, 30 of 32)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [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)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [On the Convergence of Adam and Beyond](https://mlsanity.com/paper/1904.09237/) (2019)
- [Learning to Learn without Forgetting by Maximizing Transfer and Minimizing Interference](https://mlsanity.com/paper/1810.11910/) (2018)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2404.00228/) (2024)
- [Adaptive Gradient Methods with Dynamic Bound of Learning Rate](https://mlsanity.com/paper/1902.09843/) (2019)
- [Understanding the Role of Training Regimes in Continual Learning](https://mlsanity.com/paper/2006.06958/) (2020)
- [Continual Learning of Context-dependent Processing in Neural Networks](https://mlsanity.com/paper/1810.01256/) (2018)
- [Training Networks in Null Space of Feature Covariance for Continual Learning](https://mlsanity.com/paper/2103.07113/) (2021)
- [TRGP: Trust Region Gradient Projection for Continual Learning](https://mlsanity.com/paper/2202.02931/) (2022)
- [Layerwise Optimization by Gradient Decomposition for Continual Learning](https://mlsanity.com/paper/2105.07561/) (2021)
- [Addressing Loss of Plasticity and Catastrophic Forgetting in Continual Learning](https://mlsanity.com/paper/2404.00781/) (2024)
- [Continual Learning with Scaled Gradient Projection](https://mlsanity.com/paper/2302.01386/) (2023)
- [Continual Learning with Recursive Gradient Optimization](https://mlsanity.com/paper/2201.12522/) (2022)
- [Two Complementary Perspectives to Continual Learning: Ask Not Only What to Optimize, But Also How](https://mlsanity.com/paper/2311.04898/) (2023)
- [Sculpting Subspaces: Constrained Full Fine-Tuning in LLMs for Continual Learning](https://mlsanity.com/paper/2504.07097/) (2025)
- [MoFO: Momentum-Filtered Optimizer for Mitigating Forgetting in LLM Fine-Tuning](https://mlsanity.com/paper/2407.20999/) (2024)
- [An Adaptive and Momental Bound Method for Stochastic Learning](https://mlsanity.com/paper/1910.12249/) (2019)
- [Class Gradient Projection For Continual Learning](https://mlsanity.com/paper/2311.14905/) (2023)
- [Continual Gradient Low-Rank Projection Fine-Tuning for LLMs](https://mlsanity.com/paper/2507.02503/) (2025)
- [SplitLoRA: Balancing Stability and Plasticity in Continual Learning Through Gradient Space Splitting](https://mlsanity.com/paper/2505.22370/) (2025)
- [Continuous Subspace Optimization for Continual Learning](https://mlsanity.com/paper/2505.11816/) (2025)
- [Restricted Orthogonal Gradient Projection for Continual Learning](https://mlsanity.com/paper/2301.12131/) (2023)
- [Beyond Static Models: An Evolving Framework for Continual Learning in Large Language Models across Training Stages](https://mlsanity.com/paper/2603.12658/) (2026)

## Abstract (arXiv)

Many continual-learning methods modify gradients upstream (e.g., projection, penalty rescaling, replay mixing) while treating Adam as a neutral backend. We show this composition has a hidden failure mode. In a high-overlap, non-adaptive 8-domain continual LM, all shared-routing projection baselines collapse close to vanilla forgetting (12.5--12.8 vs. 13.2). A 0.5% replay buffer is the strongest shared alternative but still reaches 11.6, while fixed-strength decoupling falls below vanilla at 14.1. Only adaptive decoupled routing remains stable at 9.4, improving over vanilla by 3.8 units. On a 16-domain stream, its gain over the strongest shared-routing projection baseline grows to 4.5--4.8 units. The failure is largely invisible on clean benchmarks. We explain this effect through Adam's second-moment pathway: in the tested regime, projection induces a 1/(1-alpha) inflation of the old-direction effective learning rate, matching measurements within 8% across eight alpha values. The same conflict appears with penalty methods, replay mixing, and at 7B scale under LoRA. Our fix routes the modified gradient only to the first moment while preserving magnitude-faithful second-moment statistics, with overlap-aware adaptive strength. This simple change is the only tested configuration that consistently avoids collapse across methods, optimizers, and scale.