Exploiting Function-Family Structure in Analog Circuit Optimization

Analog circuit optimization is typically framed as black-box search over arbitrary smooth functions, yet device physics constrains performance mappings to structured families: exponential device laws, rational transfer functions, and regime-dependent dynamics. Off-the-shelf Gaussian-process surrogates impose globally smooth, stationary priors that are misaligned with these regime-switching primitives and can severely misfit highly nonlinear circuits at realistic sample sizes (50--100 evaluations). We demonstrate that pre-trained tabular models encoding these primitives enable reliable optimization without per-circuit engineering. Circuit Prior Network (CPN) combines a tabular foundation model (TabPFN v2) with Direct Expected Improvement (DEI), computing expected improvement exactly under discrete posteriors rather than Gaussian approximations. Across 6 circuits and 25 baselines, structure-matched priors achieve $R^2 \approx 0.99$ in small-sample regimes where GP-Mat\'ern attains only $R^2 = 0.16$ on Bandgap, deliver $1.05$--$3.81\times$ higher FoM with $3.34$--$11.89\times$ fewer iterations, and suggest a shift from hand-crafting models as priors toward systematic physics-informed structure identification. Our code will be made publicly available upon paper acceptance.