Training Beyond Reach: Recursive Self-Improvement with Verifiable Circuit Tasks

Circuit-design agents must coordinate structural edits, repair, and tuning to satisfy coupled specifications, yet complete-design successes can be scarce, limiting self-training. We propose (Verifiable Escalation and Reduction for self-training Agents), which uses verified circuits to supply recovery practice and seed further task generation. Reduction changes the starting state to lower the remaining decision burden, normally retaining the seed's full specifications, and certifies a feasible recovery path. Within successful learner rollouts, action selection identifies verified progress, repair, and completion steps for supervision. After each update, the improved learner searches for stronger-specification seeds that yield a fresh recovery-task bank under a fixed verifier. A bootstrap bank derived from human-constructed seeds supplies 1,200 selected actions. One update raises the 9B learner's held-out complete-design success from 0/180 to 77/180 (42.8%). Success-trajectory SFT on the same trajectories reaches 47/180 (26.1%); also improves performance on two external circuit benchmarks. After three updates, the learner reaches 123/180 (68.3%), exceeding fixed-bank recollection and frozen-search controls. These results support linking accessible recovery practice to model-driven renewal of circuit training tasks. Our source code is at https://anonymous.4open.science/r/anonymous_code1-F4C3/.