Paper:
Compact Generalized Non-local Network
The non-local module [27] is designed for capturing long-range spatio-temporal dependencies in images and videos. Although having shown excellent performance, it lacks the mechanism to model the interactions between positions across channels, which are of vital importance in recognizing fine-grained objects and actions. To address this limitation, we generalize the non-local module and take the correlations between the positions of any two channels into account. This extension utilizes the compact representation for multiple kernel functions with Taylor expansion that makes the generalized non-local module in a fast and low-complexity computation flow. Moreover, we implement our generalized non-local method within channel groups to ease the optimization. Experimental results illustrate the clear-cut improvements and practical applicability of the generalized non-local module on both fine-grained object recognition and video classification. Code is available at: https://github.com/KaiyuYue/cgnl-network.pytorch.

Review:
This paper proposes a novel network module to exploit global (non-local) correlations in the feature map for improving ConvNets. The authors focus on the weakness of the non-local (NL) module [31] that the correlations across channels are less taken into account, and then formulate the compact generalized non-local (CGNL) module to remedy the issue through summarizing the previous methods of NL and bilinear pooling [14] in a unified manner. The CGNL is evaluated on thorough experiments for action and fine-grained classification tasks, exhibiting promising performance competitive to the state-of-the-arts.  Positives: + The paper is well organized and easy to follow. + The generalized formulation (8,9) to unify bilinear pooling and non-local module is theoretically sound. + Good performance.  Negatives: - Less discussion on the linear version of CGNL using dot product for f. - Missing fundamental comparison to the simple ResBlock.  The authors nicely present the generalized formulation toward CGNL by unifying the two previous works of bilinear pooling and non-local module. Though the kernelized (non-linear) correlation function f is well theoretically motivated, the actual form of f that achieves the better empirical performance is a “linear” form (dot product). In this regard, the reviewer has the following concerns.  - Less discussion about the linear form. If the reviewer correctly understands the CGNL formulation, the linear function f of dot product f (line 204) can greatly simplify the CGNL into Y = X * W_theta * tr[(X*W_phi)’ * (X*W_g)] = X * W_theta * tr[(X’X)* W_g* W_phi’]   = s * X * W_theta, where s = tr[(X’X) * W_g * W_phi’]= tr[(X’X)* W] is just a scalar and W = W_g*W_phi’. This reformulation would be beneficial from the following viewpoints. > It reduces the parameters from {W_theta, W_phi, W_g} to {W_theta, W}, which facilitates the implementation. > It is closely related to squeeze-and-excitation (SE) module [9]. The above formulation can be regarded as a bilinear extension of SE from “squeeze” viewpoint since it “squeezes” the feature map X into the bilinear form of X’X while SE simply employs an average-pooling.   Such discussions as above would help the readers to further understand the methods and to further extend the method.  - Missing comparison. Based on the above discussion, one can think that the baseline for the linear CGNL is a simple ResBlock of  Z = BatchNorm( X * W_z ) + X, while the linear CGNL is  Z = BatchNorm( s * X * W_theta * W_z ) + X    = BatchNorm( s * X * W_tz ) + X. The only difference is the scaling factor s that is also build on X. Through batch normalization, such a scaling might be less effective (during the training) and thus by comparing these closely-related methods, the authors have to clarify its effectiveness of CGNL empirically. Due to this concern, the reviewer can not fairly evaluate the impact of the method on classification performance.  [After Rebuttal] The reviewer appreciates the authors’ efforts to perform the comparison experiments in such a short rebuttal period. The comparison with the standard ResBlock clarifies the effectiveness of the proposed method as well as helps us to further understand how it works.