# An Explainable Deep Semantic Coding for Binary-Classification-Oriented Communication
## 3 Deep Variational Semantic Coding
### The DVSC Model and Training Algorithm
(**a**) Evolution of \(\lambda_{1}\) over epochs; (**b**) Evolution of \(\lambda_{2}\) over epochs. #### 4.3.1 Trade-Off Analysis: Influence of \(\mu\) with Fixed \(D\)

To investigate the trade-off influenced by \(\mu\), we fix the distortion constraint \(D\) and systematically adjust \(\mu\) to examine its effect on the compression rate and classification performance. Additionally, we conduct multiple experiments under varying values of \(D\). The corresponding results are illustrated in \[\mathcal{S}_{1}=\big{\{}x_{1,i}\mid x_{1,i}\sim P_{1}(X)\big{\}},\ \mathcal{S}_{2}=\big{\{}x_{2,i}\mid x_{2,i}\sim P_{2}(X)\big{\}},i=1,2,\dots,N;\]8

Across all subfigures in Figure 4, a common trend shows that as \(\mu\) increases, both the compression rate and classification performance improve. This behavior suggests a shift in the optimization focus, where a larger \(\mu\) places greater emphasis on classification accuracy at the expense of compression efficiency. This trend aligns well with our theoretical analysis. Moreover, when \(\mu>10\), the rate of improvement gradually diminishes. Beyond \(\mu=100\), both the compression rate and classification accuracy reach a plateau, indicating that the preservation of task-critical information has an inherent upper bound. Figure 5 presents the qualitative evaluation of the coding schemes for different values of \(\mu\) under a fixed distortion constraint of \(D=0.02\). Notably, when \(\mu=0\), the coding algorithm degrades to the conventional source coding scheme. We can observe that as \(\mu\) increases, gender-related features become more distinct, therefore leading to an improvement in classification accuracy. \[\mathcal{S}_{1}=\big{\{}x_{1,i}\mid x_{1,i}\sim P_{1}(X)\big{\}},\ \mathcal{S}_{2}=\big{\{}x_{2,i}\mid x_{2,i}\sim P_{2}(X)\big{\}},i=1,2,\dots,N;\]9 Compression rate and classification accuracy vs. \(\mu\). #### 4.3.2 Trade-Off Analysis: Influence of \(D\) for Fixed \(\mu\)

Similarly, we fix \(\mu\) and examine the relationships between compression rate and distortion constraint \(D\), as well as classification accuracy and \(D\). The corresponding curves are depicted in \[\mathcal{B}_{X_{1}}\subset\mathcal{S}_{1},\ \mathcal{B}_{X_{2}}\subset \mathcal{S}_{2}\]0 A general trend observed across these subfigures is that when \(D>0.02\), both the compression rate and classification accuracy exhibit a decreasing pattern as \(D\) increases. This trend suggests that increasing \(D\) allows for more efficient compression; however, it also leads to severer loss of task-critical information, ultimately degrading classification performance. Figure 7 presents the qualitative evaluation of the coding schemes for different values of \(D\) at \(\mu=100\). As expected, when \(D\) increases, the images become progressively blurred, leading to a noticeable loss of gender-related features and consequently a decline in classification accuracy. \[\mathcal{B}_{X_{1}}\subset\mathcal{S}_{1},\ \mathcal{B}_{X_{2}}\subset \mathcal{S}_{2}\]1 Visualization of reconstructed images for different values of \(\mu\) at \(D=0.02\). \[\mathcal{B}_{X_{1}}\subset\mathcal{S}_{1},\ \mathcal{B}_{X_{2}}\subset \mathcal{S}_{2}\]2 _Cont._

#### 4.3.3 Comparison with the Traditional Source Coding Scheme

As previously discussed, setting \(\mu=0\) corresponds to the conventional source coding scheme, as illustrated in Figure 6d. Compared with Figure 6a-c, Figure 6d achieves the highest compression efficiency but at the cost of the lowest classification accuracy. For instance, at \(D=0.02\), \(\mu=100\) in Figure 6a, the coding scheme achieves a peak classification accuracy of 96%, outperforming the traditional scheme by 11% subject to the same distortion constraint, albeit with a 3.6-bit loss in compression rate. From the perspective of the optimization objectives, since conventional coding scheme does not account for classification performance, the overall effectiveness is inherently lower than that of the semantic coding scheme, despite achieving superior data compression efficiency.