text: General comment ==============  Low-rank decomposing convolutional filters has been used to speedup convolutional networks at the cost of a drop in prediction performance. The authors a) extended existing decomposition techniques by an iterative method for decomposition and fine-tuning convolutional filter weights, and b) and algorithm to determine the rank of each convolutional filter. The authors show that their method enables a higher speedup and lower accuracy drop than existing methods when applied to VGG16. The proposed method is a useful extension of existing methods but needs to evaluated more rigorously. The manuscript is hard to read due to unclear descriptions and grammatical errors. Major comments ============= 1. The authors authors showed that their method enables a higher speedup and lower drop in accuracy than existing methods when applied to VGG16. The authors should analyze if this also holds true for ResNet and Inception, which are more widely used than VGG16. 2. The authors measured the actual speedup on a single CPU (Intel Core i5). The authors should measure the actual speedup also on a single GPU. 3. It is unclear how the actual speedup was measured. Does it correspond to the seconds per update step or the overall training time? In the latter case, how long were models trained? 4. How and which hyper-parameters were optimized? The authors should use the same hyper-parameters for all methods (Jaderberg, Zhang, Rank selection). The authors should also analyze the sensitivity of speedup and accuracy drop depending on the learning rate for ‘Rank selection’. 5. Figure 4: the authors should show the same plot for more convolutional layers at varying depth from both VGG and ResNet. 6. The manuscript is hard to understand and not written clearly enough. In the abstract, what does ‘two-pass decomposition’, ‘proper ranks’, ‘the instability problem’, or ‘systematic’ mean? What are ‘edge devices’, ‘vanilla parameters’? The authors should also avoid uninformative adjectives, clutter, and vague terms throughout the manuscript such as ‘vital importance’ or ‘little room for fine-tuning’. Minor comments ============= 1. The authors should use ‘significantly’ only if a statistical hypothesis was performed. 2. The manuscript contains several typos and grammatical flaws, e.g. ‘have been widely applied to have the breakthrough’, ‘The CP decomposition factorizes the tensors into a sum of series rank-one tensors.’, ‘Our two-pass decomposition provides the better result as compared with the original CP decomposition’. 3. For clarity, the authors should express equation 5 in terms of Y_1, Y_2, Y_3, and Y_4. 4. Equation 2, bottom: C_in, W_f, H_f, and C_out are undefined at this point.