# Table 1 Time complexity in training and test phases (for one input sample)

PhaseStepsTime complexityDimension description
Training phase1. Convolution layers$$\mathcal {O}(P_{\ell } D_{\ell } M_{\ell } C)$$
2. Fully-connected (f.-c.) layer$$\mathcal {O}(I^{2} C^{2})$$$$S^{(c)} \in \mathbb {R}^{K\times D}$$
3. Frobenius norm on conv. layers$$\mathcal {O}\left (P_{\ell } M_{\ell } C\right)$$$$T_{\ell }^{(c)}\in \mathbb {R}^{P_{\ell }\times M_{\ell }}$$
4. Frobenius norm on f.-c. layer$$\mathcal {O}(I^{2} C^{2})$$$$\text {flat}(X^{(c)})\in \mathbb {R}^{K\times I}$$
5. log-det on conv. layers$$\mathcal {O}(P_{\ell }^{2} M_{\ell } C)$$$$\widetilde {T_{c}} \in \mathbb {R}^{I \times O}$$
6. log-det on f.-c. layer$$\mathcal {O}(I^{3}C^{2})$$
Testing phaseStep 1. + Step 2.Step 1. + Step 2.
1. D = input sample size – K = num. of samples – C = num. of channels – L = num. of layers
2. P = filter size at layer M = num. of filters at layer D = output sample size at layer
3. I=DLML is the num. of output features per sample at last convolution layer
4. O=αIC (with α[0,1]) is the num. of output features per sample at the fully connected layer 