\section{Experimental details}
\label{app:experiment_details}

\paragraph{Baseline updates.}
Both experiments use scalar inputs. Write $s^2$ for the measurement-noise
variance and suppress the iteration index. Taylor corrections use
\[
G_{\mathrm{T2}}=g(\theta;W,Y)-\frac{s^2}{2}\partial_w^2g(\theta;W,Y),
\qquad
G_{\mathrm{T4}}=G_{\mathrm{T2}}+
\frac{s^4}{8}\partial_w^4g(\theta;W,Y),
\]
with the response held fixed. The deterministic Woolsey--Huang baseline
uses $\operatorname{Re}g^{\mathbb C}(\theta;W+is,Y)$; CCSGD instead
samples $V\sim N(0,s^2)$ at every update. Regression calibration substitutes
the exact conditional mean $\mathbb E[Z\mid W]$ under the stated latent law.
Quadratic SIMEX trains three models with additional Gaussian noise
variances $\lambda s^2$, $\lambda=0,1,2$. It extrapolates parameters in
nonlinear-feature regression and predictions in neural-network regression,
with weights $(3,-3,1)$. In the first experiment its additional-noise
expectation is integrated analytically; in the second it is sampled.
These comparisons use common data streams and step-size schedules;
SIMEX uses three training trajectories, so update counts do not equalize
computational cost.

\paragraph{Population reference lines.}
In nonlinear-feature regression, each direct baseline has a population
score $H_k\theta-r_k$. The dashed line is
$\|H_k^{-1}r_k-\theta^*\|^2$; for SIMEX it is the squared distance between
the extrapolation of the three population minimizers and $\theta^*$.
We evaluate $H_k$ by 160-node Gauss--Hermite quadrature and $r_k$ by
$128\times128$ joint quadrature over $(Z,U)$, retaining the dependence
between $Y$ and $W$. Thus the reference lines are numerical evaluations
of population squared biases, not fits to the simulated trajectories or
lower bounds at every finite iteration.