# FactorSpec

In structured output, relations among a record's fields could determine many tokens, yet serving engines draft from the prompt or a learned head and grammar masks enforce only syntax, so models often violate those relations. FactorSpec compiles a JSON Schema and its relations into a factor graph, treats tokens the constraint uniquely determines as certain drafts through an exact feasibility check, and picks a verify width per request. In SGLang its drafts accept up to 10.5 tokens per verify step on trip planning, up to 1.9 those of the fastest n-gram drafter shape, and decode up to 1.43 faster than speculators tuned per load, at a grammar mask's cost.

In structured output, relations among a record's fields could determine many tokens, yet serving engines draft from the prompt or a learned head and grammar masks enforce only syntax, so models often violate those relations. FactorSpec compiles a JSON Schema and its relations into a factor graph, treats tokens the constraint uniquely determines as certain drafts through an exact feasibility check, and picks a verify width per request. In SGLang its drafts accept up to 10.5 tokens per verify step on trip planning, up to 1.9 those of the fastest n-gram drafter shape, and decode up to 1.43 faster than speculators tuned per load, at a grammar mask's cost.