Past, Future, All at Once: Mitigating Stability-Plasticity Dilemma via Post-hoc JANUS Rectification

TL;DR - JANUS is a post-hoc, fine-tuning-agnostic method that projects parameter updates into a model’s Jacobian null space to recover historical knowledge after adaptation. It addresses catastrophic forgetting while aiming to preserve performance on newly learned tasks.

• Establishes Parameter Space Orthogonality as the necessary and sufficient first-order condition for preserving historical performance.
• Uses multi-step adaptive rectification to verify the Jacobian approximation’s trust region and dynamically adjust step sizes.
• Introduces ghost projection, orientation comparison, and sequence-level SVD compression to improve temporal and spatial efficiency.
• Experiments show compatibility with multiple fine-tuning methods and reduced forgetting without disrupting downstream adaptation.