Algorithm 2 Annealing algorithm pseudocode.

1:input: Dataset $\mathcal{D}:={\left\{{\mathbf{x}}_i\right\}}_{i=1}^n$, hyperparameter interval $[s_{\min },s_{\max }]$. 2:output: Optimal DNN weights ${\theta }^{\star },{\varphi }^{\star }$, GMM parameters ${\psi }^{\star }=\{{\pi }_c^{\star }$, ${\mathit{\mu }}_c^{\star }$, ${\mathsf{\Sigma }}_c^{\star }{\}}_{c=1}^{\left|\mathcal{C}\right|}$, assignment probability $P_{C|\mathbf{X}}$. 3:initialization Initialize $\theta ,\varphi ,\psi$. 4:repeat 5:    Apply VIB-GMM algorithm. 6:    Update $\psi ,\theta ,\varphi$. 7:    Update s, e.g., $s=(1+{ϵ}_s)s_{\mathrm{old}}$. 8:untils does not exceed $s_{\max }$.