Hidden Failure Modes of Gradient Modification under Adam in Continual Learning, and Adaptive Decoupled Moment Routing as a Repair
Authors: Yuelin Hu, Zhenbo Yu, Zhengxue Cheng, Wei Liu, Li Song
Organizations: Shanghai Jiao Tong University · Shanghai Maritime University
Abstract
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.
LoRA is widely adopted for continual fine-tuning of Large Language Models due to its parameter efficiency, modularity across tasks, and compatibility with replay strategies. However, LoRA-based continual learning remains vulnerable to catastrophic forgetting, whose severity depends on how successive task gradients interact: when consecutive task gradients conflict, standard adapter initializations channel updates into subspaces that overwrite previously learned directions. We propose SLICE, a gradient-surgery-based initialization for LoRA adapters in continual learning. SLICE accumulates gradients from both the current task and a replay buffer of prior tasks, reconciles them through a projection operator, and decomposes the result via truncated SVD to initialize the adapter weights. We evaluate SLICE on the TRACE benchmark and sequences of Super-NI tasks, including a set of adversarial Super-NI sequences that we construct by mining task pairs with maximally opposing gradients. Compared to vanilla LoRA, LoRA-GA, and LoRAM, SLICE consistently achieves a better stability-plasticity trade-off, improving Average Performance, Final Performance and Forgetting metrics while preserving General Performance and In Context Performance across both standard and adversarial continual learning sequences.
Joana Pasquali, Ramiro N. Barros, Arthur S. Bianchessi +7
Continual learning agents with finite capacity must balance acquiring new knowledge with retaining the old. This requires controlled forgetting of knowledge that is no longer needed, freeing up capacity to learn. Weight decay, viewed as a mechanism for forgetting, can serve this role by gradually discarding information stored in the weights. However, a fixed scalar weight decay drives this forgetting uniformly over time and uniformly across all parameters, even when some encode stable knowledge while others track rapidly changing targets. We introduce Forgetting through Adaptive Decay (FADE), which adapts per-parameter weight decay rates online via approximate meta-gradient descent. We derive FADE for the online linear setting and apply it to the final layer of neural networks. Our empirical analysis shows that FADE automatically discovers distinct decay rates for different parameters, complements step-size adaptation, and consistently improves over fixed weight decay across online tracking and streaming classification problems.
Aditya A. Ramesh, Alex Lewandowski, Jürgen Schmidhuber
Parameter-efficient continual learning aims to adapt pre-trained models to sequential tasks without forgetting previously acquired knowledge. Most existing approaches treat continual learning as avoiding interference with past updates, rather than considering what properties make the current task-specific update naturally preserve previously acquired knowledge. From a knowledge-decomposition perspective, we observe that low-rank adaptations exhibit highly imbalanced singular value spectra: a few dominant components absorb most of the adaptation energy, thereby (i) more likely to disrupt previously acquired knowledge and (ii) making the update more vulnerable to interference from subsequent tasks. To enable explicit balance among components, we decouple the magnitude of the task update from its directional structure and formulate it as a constrained optimization problem on a restricted Stiefel manifold. We address this problem using a projected first-order method compatible with standard deep-learning optimizers used in vision-language models. Our method mitigates both backward and forward forgetting, consistently outperforming continual learning baselines. The implementation code is available at https://github.com/haodotgu/EBLoRA.