Algorithm 1 DIMCO training procedure.

Initialize network parameters $\theta$ repeat    Sample a batch $\left\{({\mathbf{x}}^n,y^n)\right\}$    Compute logits $\left\{l_{i,j}^n\right\}=f({\mathbf{x}}^n;\theta )$            via (1)    Compute probs $\left\{p_{i,j}^n\right\}=\mathrm{softmax}\left(\left\{l_{i,j}^n\right\}\right)$     via (2)    Update $\theta$ to minimize loss $\mathcal{L}(\left\{p_{i,j}^n\right\},\left\{y^n\right\})$   via (10) until converged