ELGAR: Execution-Linked Gating for Adapter Routing in Continual Learning

Selecting a visual expert changes the representation that language experts must process. Execution-Linked Gating for Adapter Routing (ELGAR) turns this dependency into an allocation rule: an instruction-conditioned gate selects a visual projector, and a language gate observes that same projector's output to combine frozen low-rank adaptation (LoRA) updates, with one projector and one autoregressive path at deployment. Our finite-candidate analysis characterizes when an observation supports an optimal allocation and shows how a pooled bank mean can hide distinctions preserved by the selected output. Three paired source-order repeats on six UCIT tasks with 3,000 examples each give 75.53 mean final average score (FAA) for selected-output routing, versus 74.85 for bank-mean routing and 73.75 for static allocation. The additional 0.68-point gain is positive in every repeat with the visual route and task-origin supervision fixed. Separate matched pairs favor output content over projector identity in every repeat, with a mean gain of 0.62 points. Complete ELGAR reaches 75.63 FAA on UCIT–LLaVA and leads reproduced continual baselines in FAA and backward transfer across all four UCIT/DCL–backbone settings. Thus observing the executed representation adds measurable allocation value beyond knowing which branch ran.