# A Faster Algorithm for Reducing the Computational Complexity of Convolutional Neural Networks
## 4 Simulation Results
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & **Conventional** & **Strassen** & **Winograd** & **Strassen-Winograd** \\ \hline Layer1 & \(1.25\times 10^{-6}\) & \(3.03\times 10^{-6}\) & \(2.68\times 10^{-6}\) & \(4.01\times 10^{-6}\) \\ Layer2 & \(2.46\times 10^{-5}\) & \(7.59\times 10^{-5}\) & \(4.62\times 10^{-5}\) & \(9.50\times 10^{-5}\) \\ Layer3 & \(2.65\times 10^{-5}\) & \(7.23\times 10^{-5}\) & \(4.83\times 10^{-5}\) & \(9.51\times 10^{-5}\) \\ Layer4 & \(4.94\times 10^{-5}\) & \(1.50\times 10^{-4}\) & \(9.40\times 10^{-5}\) & \(1.78\times 10^{-4}\) \\ Layer5 & \(5.14\times 10^{-5}\) & \(1.46\times 10^{-4}\) & \(1.00\times 10^{-4}\) & \(1.74\times 10^{-4}\) \\ Layer6 & \(9.80\times 10^{-5}\) & \(2.94\times 10^{-4}\) & \(1.88\times 10^{-4}\) & \(3.50\times 10^{-4}\) \\ Layer7 & \(9.92\times 10^{-5}\) & \(2.82\times 10^{-4}\) & \(1.79\times 10^{-4}\) & \(3.39\times 10^{-4}\) \\ Layer8 & \(2.09\times 10^{-4}\) & \(5.89\times 10^{-4}\) & \(3.51\times 10^{-4}\) & \(6.99\times 10^{-4}\) \\ Layer9 & \(1.84\times 10^{-4}\) & \(5.76\times 10^{-4}\) & \(3.50\times 10^{-4}\) & \(6.16\times 10^{-4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum element error of different algorithms in different layers. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Layer** & **Batch Size** & **1** & **2** & **4** & **8** & **16** & **32** \\ \hline \multirow{4}{*}{Layer1} & Conventional & 24s & 48s & 94s & 187s & 375s & 752s \\  & Strassen & 24s & 56s & 95s & 191s & 383s & 768s \\  & Winograd & 14s & 29s & 57s & 115s & 230s & 462s \\  & Strassen-Winograd & 14s & 33s & 58s & 117s & 234s & 470s \\ \hline \multirow{4}{*}{Layer2} & Conventional & 493s & 986s & 1971s & 3939s & 7888s & 15821s \\  & Strassen & 492s & 861s & 1508s & 2636s & 4625s & 8438s \\  & Winograd & 299s & 598s & 1196s & 2396s & 4787s & 9935s \\  & Strassen-Winograd & 299s & 543s & 992s & 1818s & 3348s & 6468s \\ \hline \multirow{4}{*}{Layer3} & Conventional & 245s & 490s & 980s & 1962s & 3916s & 7858s \\  & Strassen & 247s & 433s & 759s & 1328s & 2325s & 4076s \\  & Winograd & 128s & 256s & 513s & 1025s & 2049s & 4102s \\  & Strassen-Winograd & 128s & 229s & 411s & 737s & 1335s & 2417s \\ \hline \multirow{4}{*}{Layer4} & Conventional & 488s & 978s & 1954s & 3908s & 7819s & 15639s \\  & Strassen & 494s & 864s & 1513s & 2648s & 4626s & 8140s \\  & Winograd & 254s & 509s & 1017s & 2033s & 4075s & 8168s \\  & Strassen-Winograd & 254s & 4558 & 814s & 1466s & 2645s & 4811s \\ \hline \multirow{4}{*}{Layer5} & Conventional & 250s & 502s & 1007s & 2004s & 4012s & 8076s \\  & Strassen & 248s & 436s & 761s & 1328s & 2317s & 4078s \\  & Winograd & 118s & 236s & 471s & 942s & 1881s & 3776s \\  & Strassen-Winograd & 118s & 209s & 370s & 656s & 1167s & 2085s \\ \hline \multirow{4}{*}{Layer6} & Conventional & 498s & 1001s & 1998s & 3995s & 7948s & 15892s \\  & Strassen & 494s & 868s & 1507s & 2646s & 4643s & 8102s \\  & Winograd & 231s & 462s & 923s & 1844s & 3693s & 7382s \\  & Strassen-Winograd & 231s & 410s & 725s & 1286s & 2296s & 4089s \\ \hline \multirow{4}{*}{Layer7} & Conventional & 244s & 487s & 980s & 1940s & 3910s & 7820s \\  & Strassen & 241s & 421s & 739s & 1283s & 2250s & 3961s \\  & Winograd & 116s & 231s & 461s & 920s & 1839s & 3680s \\  & Strassen-Winograd & 116s & 204s & 358s & 630s & 1111s & 1961s \\ \hline \multirow{4}{*}{Layer8} & Conventional & 479s & 955s & 1917s & 3833s & 7675s & 15319s \\  & Strassen & 474s & 829s & 1453s & 2546s & 4447s & 7811s \\  & Winograd & 222s & 443s & 8848 & 1766s & 3524s & 7068s \\  & Strassen-Winograd & 223s & 391s & 686s & 1210s & 2129s & 3772s \\ \hline \multirow{4}{*}{Layer9} & Conventional & 118s & 237s & 474s & 951s & 1900s & 3823s \\  & Strassen & 117s & 206s & 362s & 631s & 1107s & 1937s \\ \cline{1-1}  & Winograd & 65s & 128s & 254s & 507s & 1009s & 2010s \\ \cline{1-1}  & Strassen-Winograd & 65s & 113s & 197s & 345s & 606s & 1063s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Runtime consumption of different algorithms. by these algorithms is negligible.