Response by Authors
Dear Reviewer nM6o,
Thank you for your feedback on our paper. We sincerely apologize for any confusion or misunderstanding caused by our insufficient description of our method. We appreciate the opportunity to clarify the details of our approach.
**The self-supervised labels $\mathbf{\omega}$ in different augmentations**
Regarding the use of color, translation, and cutout as self-supervised signals, we would like to clarify that we employ separate self-supervised discriminators for each task, and they are not shared. In other words, our method includes four losses for the discriminator component: one for the original discriminator $D$ and one each for the color, translation, and cutout self-supervised discriminators ($\hat{D}\_\text{color},\hat{D}\_\text{translation},\hat{D}\_\text{cutout}$). These four networks share a common backbone $\phi$ and differ only in the final layer ($\psi,\varphi\_\text{color},\varphi\_\text{translation},\varphi\_\text{cutout}$), respectively. Therefore, different augmentations do not share the same $\mathbf{\omega}$, as can be seen from lines 122-124, where the dimensions of $\mathbf{\omega}\_\text{color}\in\mathbb{R}^3$ and $\mathbf{\omega}\_\text{translation}\in\mathbb{R}^2$ are not the same.
We will rewrite Eqs. 7 and 8 as the following to make the details of our method more clear.
$$
\min\_{D,\hat{D}\_\text{color},\hat{D}\_\text{translation},\hat{D}\_\text{cutout}} \mathcal{L}\_D^\text{da}+\lambda\_d\cdot\left(\mathcal{L}\_{\hat{D}\_\text{color}}^\text{color}+\mathcal{L}\_{\hat{D}\_\text{translation}}^\text{translation}+\mathcal{L}\_{\hat{D}\_\text{cutout}}^\text{cutout}\right)
$$
$$
\min\_{G} \mathcal{L}\_G^\text{da}+\lambda\_g\cdot\left(\mathcal{L}\_{G}^\text{color}+\mathcal{L}\_{G}^\text{translation}+\mathcal{L}\_{G}^\text{cutout}\right)
$$
where $\mathcal{L}^{\text{color}}\_{\hat{D}\_\text{color}}$ and $\mathcal{L}^{\text{color}}\_G$ are defined as follows:
$$
\mathcal{L}^{\text{color}}\_{\hat{D}\_\text{color}} = \mathbb{E}\_{\mathbf{x},\boldsymbol{\omega}}\left[\|\hat{D}\_\text{color}(T(\mathbf{x};\boldsymbol{\omega}),\mathbf{x})-\boldsymbol{\omega}\_\text{color}^+\|\_2^2\right] + \mathbb{E}\_{\mathbf{z},\boldsymbol{\omega}}\left[\|\hat{D}\_\text{color}(T(G(\mathbf{z});\boldsymbol{\omega}),G(\mathbf{z}))-\boldsymbol{\omega}\_\text{color}^-\|\_2^2\right]
$$
$$
\mathcal{L}^{\text{color}}\_G = \mathbb{E}\_{\mathbf{z},\boldsymbol{\omega}}\left[\|\hat{D}\_\text{color}(T(G(\mathbf{z});\boldsymbol{\omega}),G(\mathbf{z}))-\boldsymbol{\omega}\_\text{color}^+\|\_2^2\right] - \mathbb{E}\_{\mathbf{z},\boldsymbol{\omega}}\left[\|\hat{D}\_\text{color}(T(G(\mathbf{z});\boldsymbol{\omega}),G(\mathbf{z}))-\boldsymbol{\omega}\_\text{color}^-\|\_2^2\right]
$$
$\mathcal{L}^{\text{translation}}\_{\hat{D}\_\text{translation}}, \mathcal{L}^{\text{cutout}}\_{\hat{D}\_\text{cutout}}, \mathcal{L}^{\text{translation}}\_G, \mathcal{L}^{\text{cutout}}\_G$ follow the similar definition. And $\mathbf{\omega}$ represents all augmentations, i.e., data $\mathbf{x}$ is sequentially transformed using color, translation, and cutout augmentations.
**Concret experimental evidence on AHM divergence**
We are very grateful for your constructive questions. However, it is difficult to directly verify the feedback robustness of AHM through experiments, as we cannot truly construct and obtain the results of the f function. Nevertheless, based on current experiments, we can assist in verifying the advantages of our method from the loss curve of the discriminator in data-limited scenarios. Specifically, the lower the loss in the discriminator, the more obvious the overfitting phenomenon, and the **higher** it indicates that **overfitting can be alleviated**. Unfortunately, we are no longer able to upload the loss curve through a PDF. According to the existing experimental records, as shown in the table below, the average value of the training loss on the DiffAugment discriminator is significantly smaller than that on our AugSelf-GAN, indicating that AugSelf-GAN can effectively further alleviate the overfitting of DiffAugment.
| D_loss | CIFAR-10 | CIFAR-10 20% | CIFAR-10 10% | CIFAR-100 | CIFAR-100 20% | CIFAR-100 10% |
| --- | --- | --- | --- | --- | --- | --- |
| DiffAugment | 1.0902 | 0.7157 | 0.6964 | 1.0474 | 0.6404 | 0.8974 |
| AugSelf-GAN | **1.4564** | **1.2364** | **1.1331** | **1.3818** | **1.1073** | **1.1719** |
Thank you again for your coment. We sincerely hope that our response can address your question.