# On the Rate-Distortion Theory for Task-Specific Semantic Communication
## 5 Experimental Results
### Results for Generation Tasks
#### 5.2.4 Perceptual Quality Under Different Divergences  
In Figure 6, we demonstrate the visual results of generated image samples of our proposed model under Wasserstein distance and reverse KL divergence. We also consider a baseline model where a VAE encoder-decoder pair is adopted for our framework. We see that a higher transmission rate results in increased perceptual quality, which coincides with the theoretical observation of the tradeoff relationship between rate and semantic distance for Gaussian semantic rate-distortion functions. We also observe that the generative quality of our proposed models consistently outperforms the traditional VAE-based coding scheme. The method optimizing reverse KL divergence produces images with the best perceptual quality. This is aligned with the empirical observation in [31] that leveraging reverse KL divergence can improve the sharpness of generated samples. The inferior perceptual quality of VAE-based approaches can be attributed to their optimization objective: by minimizing standard KL divergence, VAEs prioritize generating easily classifiable samples at the expense of human-oriented perceptual fidelity [31]. This fundamental tradeoff between discriminative performance and perceptual quality underscores the advantages of our proposed divergence metrics for semantic communication. In order to make a fair comparison between the perceptual quality of generated samples under different divergence constraints, we adopt a widely used metric that quantifies the perceptual quality of generated images, the Inception score (IS) [22]. It provides a way  
Figure 6: Visual results of the generated image samples under different divergences. The “Source” row displays the ground-truth images available at the encoder. The subsequent rows show reconstructed images at transmission rates of 4 bits, 8 bits, and 12 bits. The columns labeled “WD” and “VAE” demonstrate reconstruction results using our proposed semantic communication architecture optimized for Wasserstein distance and reverse KL divergence respectively. of measuring both the clarity of the generated images and their diversity. Formally, the IS of an image source \(p_{G}\) is calculated using the following formula:  
\[\text{IS}=\exp\bigl{(}H_{p}(K)-E_{X\sim p_{G}}[H_{p_{G}}(K|\hat{S})]\bigr{)} \tag{26}\]  
where \(p\) is the induced distribution of the Inception-V3 network, \(\hat{S}\) is the random variable of generated images, and \(K\) is the corresponding class label of \(\hat{S}\). The generative quality of generated images increases with IS. In Figure 7, we present the comparison of Inception scores across the evaluated models at varying transmission rates. Here, \"MSE\" denotes the model minimizing MSE distortion only, which is realized by taking \(\lambda_{\text{gen}}=0\) in the loss function in (23). Both the results on MNIST in Figure 7a and those on CIFAR10 in Figure 7b demonstrate clear positive correlation between transmission rate and Inception score for all models, which directly corroborate the rate-semantic distance trade-off relationship illustrated in Figure 4a. This observation confirms our theoretical expectation that higher transmission rates enable better preservation of semantic information, as reflected in improved Inception scores. Moreover, we observe that the models with additional divergence constraints produce images with higher perceptual quality with a huge margin, particularly at low-bit regimes, compared to the model that implicitly minimizes the MSE distortion. This means that our proposed architecture is able to obtain much higher human-oriented perceptual quality compared to traditional bit-wise loss function-based models.