Algorithm 2: Offline GPD Model Fitting.
	Require: Trained encoder parameters $\varphi$ and prototype set $C={\left\{c_k\right\}}_{k=1}^K$; Complete training dataset ${\mathcal{D}}_{train}={\left\{\left(x_i,y_i\right)\right\}}_{i=1}^N$; Quantile q for determining the tail threshold (in this paper, q = 0.9).
	Ensure: Parameters for the global GPD model: threshold ${\omega }_{global}$, scale parameter $\sigma$, shape parameter $\xi$.
1	Initialize an empty list for distance scores: ${\mathcal{D}}_{scores}\leftarrow []$.
2	Global Intra-class Distance Aggregation
3	For each sample $\left(x_i,y_i\right)$ in ${\mathcal{D}}_{train}$ do:
4	Extract feature: $z_i\leftarrow E_{\varphi }\left(x_i\right)$;
5	Retrieve the corresponding class prototype: $c_{y_i}\leftarrow C\left[y_i\right]$;
6	Compute the squared Euclidean distance: $d_i\leftarrow {‖\begin{array}{c}{z}_i-c_{y_i}\end{array}‖}_2^2$;
7	Append distance to the list: $d_i\to {\mathcal{D}}_{\mathrm{scores}}$.
8	End for
9	GPD Parameter Estimation
10	(a) Determine the Tail Threshold
11	${\omega }_{\mathrm{global}}\leftarrow Quantile\left({\mathcal{D}}_{\mathrm{scores}},q\right)$;
12	(b) Extract Tail Data (Exceedances)
13	${\mathcal{T}}_{\mathrm{global}}\leftarrow \left\{d-{\omega }_{\mathrm{global}}\mid d\in {\mathcal{D}}_{\mathrm{scores}}\right.,\left.d>{\omega }_{\mathrm{global}}\right\}$;
14	(c) Fit GPD Model using Maximum Likelihood Estimation
15	$\left(\sigma ,\xi \right)\leftarrow FitGPD\_MLE\left({\mathcal{T}}_{\mathrm{global}}\right)$ .
16	Return ${\omega }_{\mathrm{global}},\sigma ,\xi$