Textual Gradients Have Scope: Rethinking Federated Textual Optimization

Federated textual optimization enables clients to improve prompts locally and aggregate natural-language updates without centrally pooling data. Existing approaches, however, typically compress distributed textual updates into a single prompt shared by all clients, implicitly treating useful textual gradients as broadly applicable. We show that this assumption often fails under heterogeneous client distributions. Across 2,070 textual-gradient rules from 108 federated runs over six language models, only 0.4% are empirically classified as globally beneficial under the default validation protocol, while 85.4% exhibit partial client scope. Motivated by this observation, we introduce textual-gradient scope, which captures the client-wise support of rule-level utility, and propose SCOPED-FEDTEXTGRAD, a scope-preserving framework for federated textual optimization. SCOPED-FEDTEXTGRAD atomizes local prompt revisions into independently routable rules, measures their target-client utility, and composes only scope-compatible updates under a hard prompt-token budget. A validation-gated variant, SAFE-SCOPED, further falls back to the local solution when scoped sharing is not supported by validation evidence. SCOPED-FEDTEXTGRAD improves average accuracy over Local TextGrad, while using approximately 73% fewer prompt tokens than unconstrained concatenation. The gains persist across model scales and families, and validation gating reduces negative transfer by more than half. These results suggest that federated textual gradients should be shared according to where they are useful, rather than compressed into a universally shared description. Anonymous code is available at https://anonymous.4open.science/r/Scope-FedTextual.