# An Explainable Deep Semantic Coding for Binary-Classification-Oriented Communication
## 3 Deep Variational Semantic Coding
### The DVSC Model and Training Algorithm
### Extended Evaluation on the CIFAR-10 Dataset

To further evaluate the generalizability of the proposed DVSC-Opt algorithm, we conduct additional experiments on the CIFAR-10 dataset following the same experimental

\[\mathcal{B}_{X_{1}}\subset\mathcal{S}_{1},\ \mathcal{B}_{X_{2}}\subset \mathcal{S}_{2}\]3 Compression rate and classification accuracy vs. \(D\). \[\mathcal{B}_{X_{1}}\subset\mathcal{S}_{1},\ \mathcal{B}_{X_{2}}\subset \mathcal{S}_{2}\]4 Visualization of reconstructed images for different \(D\) at \(\mu=100\). pipeline as described above. The CIFAR-10 dataset contains 60,000 color images evenly distributed across 10 object categories. For this evaluation, we select two semantically similar categories, deer and horse, to perform mixed-source semantic coding and binary classification with the DVSC model. The results of these experiments are reported in Figures 8 and 9. As shown in Figure 8a, when the distortion constraint is fixed at \(D=0.05\), increasing the weight coefficient \(\mu\) leads to improvements in both compression rate and classification accuracy, until the performance reaches a saturation point. This trend corresponds well with the visualization results in the first three rows of Figure 9, where larger \(\mu\) values result in more prominent class-discriminative features. On the other hand, when the weight coefficient is fixed at \(\mu=100\), as illustrated in Figure 8b, increasing \(D\) results in a gradual

\[\mathcal{B}_{X_{1}}\subset\mathcal{S}_{1},\ \mathcal{B}_{X_{2}}\subset \mathcal{S}_{2}\]5 Trends of compression rate and classification accuracy on the CIFAR-10 dataset. \[\mathcal{B}_{X_{1}}\subset\mathcal{S}_{1},\ \mathcal{B}_{X_{2}}\subset \mathcal{S}_{2}\]6 Reconstructed images on the CIFAR-10 dataset. decline in both compression rate and classification accuracy, eventually stabilizing at a lower level. This effect is visually reflected in the last three rows of Figure 9, where higher distortion levels lead to progressively blurred image reconstructions. These two trends are consistent with the experimental findings on the CelebA dataset, confirming that the DVSC-Opt model consistently handles the trade-off between compression rate and binary classification performance across different datasets. ### Summary

Experiments on the CelebA dataset and the CIFAR-10 dataset demonstrate that the DVSC-Opt algorithm can effectively balance compression rate and classification performance, while ensuring the distortion under the predefined constraint. This result aligns well with our theoretical analysis. Moreover, for a given weight coefficient \(\mu\), increasing distortion constraint \(D\) also leads to a degradation in both compression efficiency and classification accuracy, indicating a trade-off among these three design objectives. From the perspective of optimization objectives, the DVSC-Opt algorithm encompasses traditional encoding scheme while offering a more comprehensive and flexible approach. ## 5 Conclusions

In this paper, we propose a theoretically-grounded and explainable deep semantic coding framework tailored for the BCOC scenario. From an information-theoretic perspective, we formulate a semantic coding problem that jointly optimizes compression rate and classification accuracy subject to predefined distortion constraints. Furthermore, we leverage deep learning techniques and variational methods to transform the theoretical optimization problem into a trainable DVSC model and propose the DVSC-Opt algorithm. Experiments on the CelebA dataset and the CIFAR-10 dataset demonstrate that the DVSC-Opt algorithm effectively balances compression efficiency and classification performance while ensuring acceptable reconstruction distortion. An important future direction is extending our coding framework to multi-class classification tasks by studying mixed multi-source semantic coding schemes.