Adaptation Is Not Retention: Reframing Continual Low-Rank Adaptation through Response Coordinates

Low-rank adaptation (LoRA) enables parameter-efficient continual learning, but good current-task fit does not ensure subsequent retention. We identify a controlled *fit–inheritance mismatch*: changing only the task-start down-projection, with the up-projection initialized at zero, preserves the initial model function, yet can yield similar acquisition and substantially different later retention. We study this phenomenon through a response-coordinate view of LoRA, with the down-projection as a *reader* and the up-projection as a *writer*. Under a fixed local response model, we formalize a *response-coordinate bottleneck* in factorized LoRA states: the reader determines the task-response space accessible to adaptation and the local protection boundary carried into subsequent learning, while the writer can only form responses within the reader-exposed coordinates and is optimized in the resulting reader-conditioned geometry. This response-coordinate analysis yields two design principles: *response-supported reader selection* and *reader-conditioned writer optimization*. Building on these principles, we develop **InheritLoRA**, a replay-free continual adaptation method that constructs task-informed readers from response-supported coordinates, optimizes their writers in reader-conditioned geometry, and retains completed low-rank blocks. We evaluate InheritLoRA on T5-large and LLaMA 3.1–8B across the Standard and Long-Sequence continual-learning benchmarks. On the 15-task Long-Sequence benchmark, InheritLoRA matches the leading replay-free method on T5-large with substantially higher adaptation efficiency; on LLaMA 3.1–8B, it surpasses the strongest previously reported replay-free LoRA-based method and even its replay-assisted variant at markedly lower adaptation cost. Controlled interventions further probe the inheritance mechanism, showing that unprotected update components contribute to old-task interference and that inherited reader protection can alter subsequent interference even with the learned function held fixed.