## 3 Proposed Approach
### Optimization Strategy  
**Model Training Strategy. ** Due to the potential instability in the training process of Generative Adversarial Network (GAN), a two-stage training approach was employed to enhance stability and improve the quality of generated images. In the initial phase, training network operates without GAN, which only use z to help reconstruct secret image. Once a relatively stable state is reached in the quality of the generated loss information r and the \begin{table}
\begin{tabular}{l l l} \hline \hline
**Layers** & **Process** & **Output Size** \\ \hline Input & / & \(3\times 256\times 256\) \\ Layer 1 & \(3\times 3\) Conv + LeakyReLu & \(64\times 256\times 256\) \\ Layer 2 & \(4\times 4\) Conv + BatchNorm + LeakyReLu & \(64\times 128\times 128\) \\ Layer 3 & \(3\times 3\) Conv + BatchNorm + LeakyReLu & \(128\times 128\times 128\) \\ Layer 4 & \(4\times 4\) Conv + BatchNorm + LeakyReLu & \(128\times 64\times 64\) \\ Layer 5 & \(3\times 3\) Conv + BatchNorm + LeakyReLu & \(256\times 64\times 64\) \\ Layer 6 & \(4\times 4\) Conv + BatchNorm + LeakyReLu & \(256\times 32\times 32\) \\ Layer 7 & \(3\times 3\) Conv + BatchNorm + LeakyReLu & \(512\times 32\times 32\) \\ Layer 8 & \(4\times 4\) Conv + BatchNorm + LeakyReLu & \(512\times 16\times 16\) \\ Layer 9 & \(3\times 3\) Conv + BatchNorm + LeakyReLu & \(512\times 16\times 16\) \\ Layer 10 & \(4\times 4\) Conv + BatchNorm + LeakyReLu & \(512\times 8\times 8\) \\ Layer 11 & CBAM & \(1\times 32\),768 \\ Layer 12 & FC & \(1\times 100\) \\ Output & FC & \(1\times 1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The structure of the discriminator network. It employs convolution kernels of various scales to perform dimensionality reduction on the input, effectively extracting meaningful features. The CBAM [40] self-attention mechanism was employed to enhance the representation of these features. secret image reconstructed by the auxiliary variable z, the training proceeds to the second phase. In the second phase, a discriminator network is utilized to train the reconstructed secret image to distinguish it from the original secret image. This aims to ensure that the distribution of secret images reconstructed by CHASE aligns with the distribution of the original secret images, thereby enhancing the quality and fidelity of the generated images. The two-stage training strategy is implemented to address potential challenges in GAN training, promoting stability and aligning the generated images more closely with the desired distributional properties. **Loss Function. ** To ensure the fidelity of both the stego and reconstructed secret images to the original cover image and secret image, respectively, two crucial losses are employed throughout the training process:  
* Hiding Loss. In the forward hiding process, the network conceals the secret information within the cover image to generate the stego image. The objective is to make the stego image visually close to the cover image. Hence, the hiding loss is defined as follows, where N represents the number of reversible blocks: \[L_{hid}(\Theta)=\sum_{n=1}^{N}\mathcal{e}_{\text{hid}}\left(X_{h}^{(n)},X_{c }^{(n)}\right)\] (8)
* Reconstruction Loss. The secret image reconstructed by the backward reconstruction process should be kept consistent with the original secret image, and for this purpose, the reconstruction loss is defined in the following form, where \(N\) represents the number of reversible blocks: \[L_{rec}(\Theta)=\sum_{n=1}^{N}\mathcal{e}_{\text{rec}}\left(X_{s}^{(n)}, \overline{\overline{X}}_{s}^{(n)}\right)\] (9) And the next two loss functions are used in each of the two stages of training. * Loss information \(r\) loss. In stage 1, we performed \(L2\) regularization of the loss information r as a distribution loss function to constrain the loss information distribution to be more concentrated around values close to zero, thus reducing the complexity of the model, making the model smoother and the training more stable.