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

TL;DR

This paper reveals a hidden failure mode in gradient modification with Adam in continual learning and proposes an adaptive decoupled routing method as a simple, effective repair to prevent collapse.

Contribution

It identifies a failure mode caused by gradient projection in Adam and introduces an adaptive decoupled routing technique that stabilizes continual learning across multiple methods.

Findings

Shared-routing projection baselines collapse to vanilla forgetting.

Adaptive decoupled routing remains stable and improves performance.

The failure is linked to Adam's second-moment pathway inflation.

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.