Abstract

Large Language Models (LLMs) suffer severe catastrophic forgetting when adapted sequentially to new tasks in a continual learning setting. Existing approaches are fundamentally limited: replay-based methods are impractical and privacy-violating, while strict orthogonality-based methods collapse under scale: each new task is projected onto an orthogonal complement, progressively reducing the residual degrees of freedom and eliminating forward transfer by forbidding overlap in learnt representations. In this work, we introduce ELLA, a training framework built on the principle of selective subspace de-correlation. Rather than forbidding all overlap, ELLA explicitly characterizes the structure of past updates and penalizes alignments along their high-energy, task-specific directions, while preserving freedom in the low-energy residual subspaces to enable transfer. Formally, this is realized via a lightweight regularizer on a single aggregated update matrix. We prove this mechanism corresponds to an anisotropic shrinkage operator that provably bounds interference, yielding a penalty that is both memory- and compute-constant regardless of task sequence length. ELLA requires no data replay, no architectural expansion, and negligible storage. Empirically, it achieves state-of-the-art CL performance on three popular LLM benchmarks, with accuracy gains of up to 9.6% and a 35x smaller memory footprint. Further, ELLA scales robustly across architectures and actively enhances the model's zero-shot generalization on unseen tasks, establishing a principled and scalable solution for truly constructive lifelong LLM adaptation.