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Context: In ShuffleNet units, group number g controls the connection sparsity of pointwise convolutions. Table 1 explores different group numbers and we adapt the output channels to ensure overall computation cost roughly unchanged (\sim140 MFLOPs). Obviously, larger group numbers result in more output channels (thus more convolutional filters) for a given complexity constraint, which helps to encode more information, though it might also lead to degradation for an individual convolutional filter due to limited corresponding input channels. In Sec 4.1.1 we will study the impact of this number subject to different computational constrains. From the results, we see that models with group convolutions (g>1) consistently perform better than the counterparts without pointwise group convolutions (g=1). Smaller models tend to benefit more from groups. For example, for ShuffleNet 1\times the best entry (g=8) is 1.2% better than the counterpart, while for ShuffleNet 0.5\times and 0.25\times the gaps become 3.5% and 4.4% respectively. Note that group convolution allows more feature map channels for a given complexity constraint, so we hypothesize that the performance gain comes from wider feature maps which help to encode more information. In addition, a smaller network involves thinner feature maps, meaning it benefits more from enlarged feature maps. Table 2 also shows that for some models (e.g. ShuffleNet 0.5\times) when group numbers become relatively large (e.g. g=8), the classification score saturates or even drops. With an increase in group number (thus wider feature maps), input channels for each convolutional filter become fewer, which may harm representation capability. Interestingly, we also notice that for smaller models such as ShuffleNet 0.25\times larger group numbers tend to better results consistently, which suggests wider feature maps bring more benefits for smaller models. Finally, we evaluate the actual inference speed of ShuffleNet models on a mobile device with an ARM platform. Though ShuffleNets with larger group numbers (e.g. g=4 or g=8) usually have better performance, we find it less efficient in our current implementation. Empirically g=3 usually has a proper trade-off between accuracy and actual inference time. As shown in Table 8, three input resolutions are exploited for the test. Due to memory access and other overheads, we find every 4\times theoretical complexity reduction usually results in \sim2.6\times actual speedup in our implementation. Nevertheless, compared with AlexNet [21] our ShuffleNet 0.5\times model still achieves \sim13\times actual speedup under comparable classification accuracy (the theoretical speedup is 18\times), which is much faster than previous AlexNet-level models or speedup approaches such as  [14, 16, 22, 42, 43, 38].

Question: What will be the effect in performance if group numbers for convolution is increased?
For ShuffleNet, having more than 1 group seems to show consistently better results for all complexities. As the model gets smaller, the performance gain seems to increase more as the number of groups increases. However, for larger models, a too large number of groups led to saturation or a drop in classification error, possibly due to reduced representative capabilities.