## 2 Methodology
### Design Concept Extraction Module
The multi-head attention layer is formulated as follows [30]:  
\[F_{Attn}(\mathbf{H})=MultiHead(\mathbf{H})[0] \tag{5}\]  
\[MultiHead(\mathbf{H})=Concat(\mathbf{head_{1}},\ldots,\mathbf{head_{h}})\mathbf{W^{o}} \tag{6}\]  
\[\textit{Attention}(\mathbf{Q},\mathbf{K},\mathbf{V})=softmax\bigg{(}\frac{\mathbf{Q}\mathbf{K}^{ \top}}{\sqrt{d_{k}}}\bigg{)}\mathbf{V} \tag{7}\]  
where \(\mathbf{H}\in\mathbb{R}^{d_{m}\times d_{n}}\) is the input matrix of the multi-head attention layer, \(h\) is the number of heads in the multi-head attention layer, \(\mathbf{W^{Q}_{i}}\in\mathbb{R}^{d_{n}\times d_{k}}\), \(\mathbf{W^{K}_{i}}\in\mathbb{R}^{d_{n}\times d_{k}}\), \(\mathbf{W^{V}_{i}}\in\mathbb{R}^{d_{n}\times d_{w}}\), \(\mathbf{W^{o}}\in\mathbb{R}^{hd_{w}\times d_{w}}\) are the parameter matrices, \(\textit{Concat}\) denotes splicing multiple matrices along the columns, and \(F_{Attn}\) denotes the extraction of the first column from the output of \(MultiHead(\mathbf{H})\). The image encoder has a ResNet-18 [31] architecture followed by an additional multi-head attention layer to map the extracted image features to the shared semantic space. The ResNet-18 architecture processes the sketch to obtain the local features \(\mathbf{v}\in\mathbb{R}^{512\times 7\times 7}\), and then it is reshaped into a local feature matrix \(i\in\mathbb{R}^{512\times 50}\), with the last column representing the average of all the local feature vectors. Subsequently, the final global feature of the sketch in the shared semantic space, denoted as \(\mathbf{I}\in\mathbb{R}^{512}\), is obtained through an additional multi-head attention layer. The image encoder can be formulated as  
Figure 1:0  
Figure 1:1  
where \(\mathbf{x}\) is the input sketch and \(f_{\textit{re}}\), \(F_{ResNet}\), and \(F_{Attn}\) denote the average and reshape operators, ResNet-18, and the other multi-head attention layer, respectively. The loss function of the CTIMM is designed to maximize the cosine similarity between the conceptual image and text features for matching pairs while minimizing the cosine similarity between text features for mismatching pairs in the shared semantic space. The objective loss function is defined as follows:  
\[\mathcal{L}_{CTIMM}=\sum_{ \begin{subarray}{c}i=1,j=1\\ i\
eq j\end{subarray} }^{n}\left\langle\mathbf{I}_{i},\mathbf{T}_{j}^{T}\right\rangle- \sum_{ \begin{subarray}{c}i=1,j=1\\ i=j\end{subarray} }^{n}\left\langle\mathbf{I}_{i},\mathbf{T}_{j}^{T}\right\rangle \tag{10}\]  
where \(\left\langle\,\right\rangle\) denotes the dot product operation between two vectors, and \(\mathbf{I}_{i}\in\mathbb{R}^{512}\) and \(\mathbf{T}_{j}\in\mathbb{R}^{512}\) are the extracted feature vectors of the \(i\)-th sketch and \(j\)-th description for the same batch, respectively. The CTIMM is trained using Algorithm 1. ```
Contrastive text-image matching model: AdamW optimizer with \((\beta_{1},\beta_{2})=(0.9,0.99)\), \(\textit{eps}=1\times 10^{-8}\), \(\textit{weight\_decay}=0.25\), \(\textit{lr}=0.0001\); CosineAnnealingWarmRestarts lr_scheduler with \(T\_0=400\), \(T\_mult=1\), \(\textit{eta\_min}=0\), \(\textit{last\_epoch}=-1\).