## 3 Methods
### Decoder  
In our study, the previous transformer-based decoders for 3D voxel reconstruction, attention mechanisms, have been employed to reconstruct voxel grids, and these approaches often generate low-resolution (LR) features and up-sample them rapidly to the final target resolution in the later stages of the decoder. Although this results in an incomplete reconstruction of delicate details, typical global attention [29] has difficulty handling the enormous number of tokens associated with high-resolution (HR) features. To solve this restriction, we designed a progressive hierarchical decoder that combines swin transformer blocks with 3D CNN [14] layers. This hybrid architecture progressively up-samples voxel representations, allowing the model to optimize both global and local features while preserving structural details. Our proposed decoder progressively reconstructs the voxel grid from 4\({}^{3}\) to 32\({}^{3}\) resolution using Swin 3D LR Blocks and Swin 3D HR Blocks, as illustrated in Figure 3. Each block utilized the benefits of 3D convolution for local feature extraction and swin transformer blocks for long-range dependency modeling. Together, these components work to improve voxel representations across multiple resolutions, assuring efficiency and high-fidelity reconstructions. The structure of the Swin 3D LR Block easily processes the voxel features at a low resolution to extract coarse-level information and up-samples them for subsequent refinement. As shown in Figure 3a, given an input feature map \(X\ \in\ \mathbb{R}^{s\times s\times s\times D}\), the block begins by applying a swin transformer block, which operates on non-overlapping spatial windows. Within each window, window-based attention (W-MSA) is computed independently, enabling the model to capture both local and global dependencies effectively. Next, the output of the swin transformer block then uses a 3D convolutional layer to refine local features and up-sample the feature map using a 3D transposed convolution (3D CNN). While maintaining coarse-level details, this process recovers the spatial resolution. The Swin 3D LR Block maintains an output feature map with a similar resolution \(5\times S\times S\times D\), showing that each global context and local feature is captured for future enhancement. The Swin 3D HR Block further refines voxel features at a higher resolution to preserve fine-grained spatial details, which are essential for accurate 3D reconstruction. As shown in Figure 3b, the input feature map \(X\ \in\ \mathbb{R}^{s\times s\times s\times D}\) is first reshaped and downsampled to \(\frac{s}{2}\times\frac{s}{2}\times\frac{s}{2}\times 8D\), reducing the spatial resolution while increasing the feature dimension. As a result, this increased the reconstruction efficiency and enabled the swin transformer block to process fewer tokens while capturing detailed spatial information. After that, the down-sampled features are passed through a swin transformer block, where window-based attention (W-MSA) is again applied to simulate both local and global dependencies within each window. To follow this, a 3D convolutional layer is applied to refine the voxel features further. After that, the output is then reshaped to the original resolution \(S\times S\times S\times D\). In the end, we keep the skip connections between the input and the output of the block optimized in order to preserve the fine-grained spatial details. Later, the skip features are combined with the up-sampled features utilizing element-wise augmentation to ensure that both low-level details and high-level contextual information are preserved in the voxel map reconstruction. Finally, the modified voxel representation is then generated by processing the combined information through a 3D convolutional layer. Later, the swin transformer-based decoder's hierarchical structure efficiently incorporates W-MSA and 3D convolution operations.