Algorithm A1 PDC-KD Training Procedure

1: Input: Dataset D, teacher model T, student model S 2: Initialize student parameters ${\theta }_{\mathrm{S}}$; set Cholesky factor $L=I$ 3: Load precomputed Teacher Fisher matrix $F_T$ and projection operator $P_T$ 4: for epoch $=1$ to 200 do 5:    if epoch $<10$ then 6:        Apply linear warm-up 7:    end if 8:    for batch $(x,y)\in D$ do 9:         Compute teacher output ${\tau }_T=T\left(x_{\mathrm{cwt}}\right)$ 10:        Compute student output ${\tau }_S=S\left(x_{\mathrm{raw}}\right)$ 11:        Apply SG filtering to obtain $({\dot{\omega }}_{\mathrm{filt}},{\omega }_{\mathrm{filt}})$ 12:        Compute equivalent inertia tensor $I_{\mathrm{eff}}=L{L}^{\top }$ 13:        Compute ${\mathcal{L}}_{\mathrm{data}},{\mathcal{L}}_{\mathrm{KD}},{\mathcal{L}}_{\mathrm{Fisher}},{\mathcal{L}}_{\mathrm{subspace}},{\mathcal{L}}_{\mathrm{phy}}$ 14:        Aggregate total loss ${\mathcal{L}}_{\mathrm{total}}$ (Equation (10)) 15:        Perform backpropagation with gradient clipping to update ${\theta }_{\mathrm{S}}$ and L 16:    end for 17: end for 18: Output: Trained student model S