# Unlocking Efficiency in Fine-Grained Compositional Image Synthesis: A Single-Generator Approach
## 4 Experiments and Results
### Results
#### 4.2.2 Compositional and Disentanglement Properties  
**Sequential Part Composition. ** Sequential Part Composition (SPC) is a task that involves sequentially adding components to an object for composition. This task serves as an intuitive demonstration of both the model's compositional ability and its disentanglement property. In terms of compositional property, a desirable model should accurately add each semantic part. Regarding the disentanglement property, there should be minimal interference with previously added components when a new component is introduced. As SSSGAN utilizes a single local generator for all parts, it is possible that there are stronger interactions between the features of different parts, resulting in a higher degree of entanglement. The evaluation results for the SPC task are depicted in Figure 4. It is evident that SSSGAN successfully added the correct semantic part at each step, indicating its compositional ability. When comparing it with SemanticStyleGAN (Figure 3(a)), a stronger entanglement between the part features in SSSGAN can be observed; for example, in Figure 3(b), the lip color and even the gender changed in the first and second samples, respectively. Furthermore, it can be observed that the most significant change occurred when the hair was added. This observation can be attributed to the fact that the hair is a prominent part of the human face, occupying a large portion of the image's pixels. Consequently, more neural activity is dedicated to representing its features. Given the limited resources, SSSGAN learned to exert greater control over facial attributes through interactions with the larger part (i.e., the hair). Although there was entanglement between the parts in SSSGAN, it occurred in a coherent manner. For instance, consider the skin: while its appearance changes after the addition of hair, a shared coarse structure remains before and after the change, indicating that the coarse structure is disentangled. This aspect may initially seem like a drawback, in terms of image attribute editing; however, we argue that entanglement also offers an advantage, in terms of representation efficiency. This entanglement enables the model to re-use learned features to represent a wider range of attributes. This ability becomes particularly crucial under limited computational resources. **Entanglement Mechanism. ** The next question was the following: how does this entanglement occur? As we did not employ any style-mixing tricks during training, the only source of disentanglement came from the supervision of the segmentation mask. We speculate that information leakage occurred in the spatial dimension, from one part to another. Figure 5 illustrates the proposed mechanism of entanglement between the parts. The coarse mask in Equation (5) was computed using a softmax activation function. It is possible that SSSGAN learns to decrease the intensity of the pseudo depth map to create a softer mask. Taking the situation in Figure 5 as an example, when the temperature is higher, the segmentation mask becomes softer. As a result, the features of part B may leak  
Figure 4: Sequential part composition: (**a**) SemanticStyleGAN, and (**b**) SSSGAN. Each sample consists of three rows: The synthesized image, the pseudo depth map and the segmentation mask. to parts A and C, enabling part B to influence the attributes of parts A and C through their interaction. Conversely, when we lower the temperature in Equation (5), the coarse mask becomes harder, making it more challenging for information to leak to neighboring parts. To validate our hypothesis, we decreased the temperature in Equation (5) from the default value of 1.0 to 0.01 and generated the second sample in Figure 4b again. The result is shown in the last sample of Figure 4b. It can be observed that, through the sequential composition process, there was minimal change in previous results when a new part was added and the gender of the individuals remained unchanged.