Rethinking Directional Constraints in Continual Learning through Spectral Capacity

Subspace-based continual learning methods constrain update directions in seemingly contradictory ways: some isolate task updates in orthogonal subspaces to reduce interference, whereas others encourage subspace sharing to promote transfer. Despite these opposing designs, both families exhibit similar update-spectrum patterns that differ markedly from unconstrained fine-tuning. To isolate this spectral effect, we replace each method's directional constraint with a training-time constraint that matches the spectrum recorded from its updates while leaving update directions unconstrained. This spectrum-only intervention matches or even surpasses the original direction-constrained methods. We further find that precise matching of the full spectrum is unnecessary: controlling only update spectral capacity—measured by spectral energy and effective rank—through simple schedules of training factors such as LoRA rank already substantially improves continual learning. Building on this insight, we propose SPAR (Spectral Probing for Adaptive Rank), which uses a few probing updates to estimate each task's demand for update spectral capacity and allocates its LoRA rank accordingly. Across diverse benchmarks, this simple scheduler achieves competitive or superior performance without elaborate directional constraints or auxiliary mechanisms.