\subsection{Extended Implementation Details}
\label{sec:appendix:impl}

We provide the full set of hyperparameters and scheduling rules for reproducibility. Unless otherwise specified, all experiments are trained with Adam for 30k iterations on a single NVIDIA RTX 3090 GPU. 

\paragraph{Learning rates.}
The Gaussian center learning rate decays exponentially from $1.6{\times}10^{-4}$ to $1.6{\times}10^{-6}$ with a delay multiplier of $0.01$. Other attributes use fixed learning rates: $2.5{\times}10^{-3}$ for SH features, $5{\times}10^{-2}$ for opacity, $3{\times}10^{-2}$ for scaling, and $1{\times}10^{-3}$ for rotation.

\begin{table}[h]
\centering
\caption{Training hyperparameters of our framework.}
\label{tab:train-hparams}
\resizebox{0.7\textwidth}{!}{
\begin{tabular}{ll}
\toprule
Parameter & Value \\
\midrule
Optimizer & Adam \\
Iterations & 30k \\
Learning rate (centers) & $1.6{\times}10^{-4} \to 1.6{\times}10^{-6}$ (exp. decay) \\
Learning rate (SH) & $2.5{\times}10^{-3}$ (fixed) \\
Learning rate (Opacity) & $5{\times}10^{-2}$ (fixed) \\
Learning rate (Scaling) & $3{\times}10^{-2}$ (fixed) \\
Learning rate (Rotation) & $1{\times}10^{-3}$ (fixed) \\
Warm-up length & 2k iterations \\
Densification start & 500 iterations \\
Pruning start & 500 iterations \\
Densification interval & 100 iterations \\
Opacity reset interval & 3k iterations \\
Pruning threshold & 0.005 \\
Graph rebuild frequency & $T_{\text{build}}$ iterations \\
GNN subsample ratio & $0.25$ \\
Graph neighbors & $k{=}8$ (Mahalanobis) \\
SRB activation & after 20k iterations \\
Final representation & Standard 3DGS-compatible set \\
\bottomrule
\end{tabular}}
\end{table}

\paragraph{Topology-aware graph regularizer.}
Activated every 1k iterations after a 2k warm-up. Small components with fewer than 100 Gaussians are pruned. Holes are either bridged across components ($B{=}5000$) or filled by tangent-plane initialization. New Gaussians inherit attributes from neighbors, start with reduced opacity, and are protected from pruning for 1k iterations.

\paragraph{Densification and pruning.}
Following 3DGS~\citep{kerbl2023gaussiansplatting}, cloning or splitting occurs every 100 steps, opacity resets every 3k steps, and pruning combines low-opacity thresholding, radius-based culling, and GNN survival scores.

\paragraph{GNN-based appearance propagation module.}
We use a 3-layer GATv2~\citep{brody2022gatv2} with hidden size 64 and heads $[4,4,1]$. Graphs are constructed with $k=8$ neighbors and rebuilt periodically once enabled. Updates are blended with visibility-adaptive weights (initialized at $0.1$). GNN refinement starts after $29.7$k steps in long runs.

\paragraph{Semantic-rarity and boundary-aware
modulator.}
Pseudo-labels are obtained from OneFormer~\citep{jain2023oneformer}. Rare classes are defined as those below the 25th percentile in pixel count (excluding background), and boundaries are identified by 4-neighborhood changes. SRB loss is applied after 20k iterations with weights $w_{\mathrm{rare}}=w_{\mathrm{edge}}=1.0$ and $w_{\mathrm{base}}=0.2$.

\paragraph{Training-only modules.}
All auxiliary components (graph regularizer, GNN propagation module, SRB modulator) are applied only during training. After optimization, the model reduces to a standard Gaussian set $(\mathbf{p},o,\mathbf{s},\mathbf{r},\mathbf{k})$ fully compatible with the original 3DGS rasterizer.
