## 3 Design of FAS Structures
### Design of the FAS Search Space  
In this study, the Fast Architecture Search (FAS) operates on a search tuple \(\{(x,y)\}\), where \(x\) represents the input tensor of dimensions \((3\times H\times W)\) and \(y\) is the output tensor from the object detection head. The overall search network can be conceptually represented as \(g(x)\rightarrow\hat{y}\). More specifically, the backbone network (Inception-ResNet-SPP), denoted as \(b\), extracts feature tensors \(C\) from the input image \(x\), expressed as \(b(x)\to C\). The set of extracted feature tensors is \(C=\{C_{3},C_{4},C_{5},C_{6}\}\), where the resolution of each tensor \(C_{i}\) is \((H_{i}\times W_{i})=(H/2^{i}\times W/2^{i})\). These feature tensors \(C\) are then fed into the Feature Pyramid Network (FPN), denoted as \(f\), to generate the output feature pyramid \(P=\{P_{3},P_{4},P_{5},P_{6}\}\), represented by \(f(C)=P\). The FPN output tensor \(P\) has a size of \(((K+4+1+1)\times H\times W)\) at each layer. The term \((K+4+1+1)\) signifies the FPN's input channels, comprising \(L-K\) classification labels, four bounding box regression variables \((x,y,w,h)\), and one centrality factor, where \(L\) denotes the hierarchical index of the feature map and \(K\) denotes the label category. Finally, the detection head, denoted as \(h\), performs bounding box regression on the feature pyramid \(P\) to produce the final predicted results \(y\), expressed as \(h(P)\to y\). To prevent overfitting, the same object detection head is applied to all search instances. Given that objects of different sizes require corresponding receptive fields, the selection and fusion of feature tensors \(C\) output by the backbone network are crucial for improving the search efficiency of the fusion path. The weights in the backbone network utilize pre-trained weights from the COCO 2017 dataset, which are frozen during training, with no parameter updates. The optimal feature fusion path is searched for based on these pre-trained weights. Given that \(f\) and \(h\) represent two distinct functions, this study defines two search spaces. A novel fundamental module with a completely new overall connection scheme is constructed based on the unique characteristics of the FPN structure, and its data output is configured. Simultaneously, to reduce computational complexity, the \(h\) function employs a sequential search space. This study replaces the fusion unit structure with atomic operations and constructs a basic module \(bb\). This module first randomly selects two layers, \(b1\) and \(b2\), from a sampling pool at positions \(m1\) and \(m2\). Then, it performs two corresponding operations, \(op1\) and \(op2\), on them, respectively. Finally, the features from these two layers are merged into a single feature through a fusion operation. Table 1 presents the operations. All convolutions utilize depthwise separable convolutions to reduce the GPU memory footprint. Furthermore, to match feature maps of different scales, \(3\times 3\) and \(1\times 1\) convolutions are employed for dimension matching. The merge module is used for fusion operations. In the FPN, function \(f\) maps the feature vector \(C\) output by the backbone network to \(P\). Therefore, in this section, the sampling pool \(M_{0}\) is initialized with \(C\). \begin{table}
\begin{tabular}{c c} \hline \hline
**m** & **Operation** \\ \hline
0 & Separable convolution \(3\times 3\) \\
1 & Separable convolution \(3\times 3\) dilation rate = 3 \\
2 & Separable convolution \(3\times 3\) dilation rate = 6 \\
3 & Crosslink \\
4 & Transformable convolution \(3\times 3\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Search space operation table. The process of calling the basic module eight times through the FPN structure can be represented as \(f\to bb_{1}^{f}\circ bb_{2}^{f}\circ\cdots\circ bb_{8}^{f}\).