text: Authors of this paper derived an efficient quantum-inspired learning algorithm based on a hierarchical representation that is known as tree tensor network, which is inspired by the multipartite entanglement renormalization ansatz approach where the tensors in the TN are kept to be unitary during training.  Some observations are: The limitation of learnability of TTN strongly depends on the physical indexes and the geometrical indexes determine how well the TTNs approximate the limit;  TTNs exhibit same increase level of abstractions as CNN or DBN;  Fidelity and entanglement entropy can be considered as some measurements of the network. Authors introduced the two-dimensional hierarchical tensor networks for solving image recognition problems,  which suits more the 2-D nature of images.  In section 2, authors stated that the choice of feature function is arbitrary,  and a specific feature map was introduced in Section 4.  However, it is not straightforward to connect (10) to (1) or (2).  It is better to clarify this connection  because some important parameters such as the virtual bond and input bond are related to the complexity of the proposed algorithm as well as the limitation of learnability.  For example, the scaling of the complexity O(dN_T(b_v^5 + b_i^4)) is not easy to understand.  Is it related to specific feature map?  How about the complexity of eigen-decomposition for one tensor at each iterates.  And also, whether the tricks used to accelerate the computations will affect the convergence of the algorithm?  More details on these problems are required for readers’ better understanding. From Fig 2, it is difficult to see the relationship between learnability and parameters such input bond and virtual bond  because it seems there are no clear trends in the Fig 2(a) and (b) to make any conclusion.  It is better to clarify these relationships with either clear explanation or better examples. From Fig 3, authors claimed that TN obtained the same levels of abstractions as in deep learning.  However, from Fig 3 only, it is hard to make this conclusion.  First, there are not too many differences from Fig 3(a) to Fig 3(e).   Second, there is no visualization result reported from deep learning on the same data for comparison.  Hence, it is not convincing to draw this conclusion only from Fig 3.  In Section 4.2, what strategy is used to obtain these parameters in Table 1? In Section 5, it is interesting to see more experiments in terms of fidelity and entanglement entropy.