## 3 Materials and Methods
### Feature-Semantic Interaction of Molecule-Odor Descriptor through HGNN
Although neurons at the same location share information in the same receptive field, they represent different patterns in different channels. The lateral inhibition value \(x_{ij}^{LI}\) of \(x_{ij}\) is as follows,  
\[x_{ij}^{LI}=a*e^{-\overline{x_{ij}}}+b*\sum_{uv}(d_{uv}e^{-d_{uv}}\delta(x_{uv} -x_{ij})) \tag{1}\]  
\[\delta(x)= \begin{cases}x,&if\ x>0,\\ 0,&if\ x\leq 0.\end{cases}  \tag{2}\]  
where \(x_{ij}\) denote the point at the location \((i,j)\) in the Max-map, \(\overline{x_{ij}}\) is the average value of the Lateral Inhibition Area consisting of the \(n\times n\) nearest neighbors of \(x_{ij}\) in the Max-map, \(x_{uv}\) is the neighbor point of \(x_{ij}\) in the Lateral Inhibition Area, \(d_{uv}\) is the Euclidean distance between \(x_{uv}\) and \(x_{ij}\), which is divided by \(n\), and \(a\) and \(b\) are balance coefficients. The state of a neuron is determined by the signals of itself and its neighboring neurons through the lateral inhibition model, and the neuron will not be inhibited by neighboring neurons whose value is lower than that of the neuron, as in Equation (2). The average term in Equation (1) (the first part of Equation (1)) maximizes the retention of neurons in the  
Figure 6: Lateral inhibition-inspired dynamic convolution. Figure 7: Lateral inhibition-inspired attention mechanism. high-response area, that is, the target area. The differential term in Equation (1) (the second part of Equation (1)) tries to separate the target area from the background and emphasizes the sharpening of the boundary to improve the anti-interference ability. In Equation (1), \(d_{w}e^{-d_{w}}\) has a functional surface with an inverted \"Mexican hat\", which is a computational model of lateral inhibition in neurobiology [42; 43]. It means that the nearest and farthest neighbors have the least inhibitory effect on central neurons. \[x_{ij}=\left\{ \begin{aligned} & x_{ij},&& if\ x_{ij}-x_{ij}^{LI}>0,\\ & 0,&& if\ x_{ij}-x_{ij}^{LI}\leq 0.\end{aligned} \right. \tag{3}\]  
After lateral inhibition, the activated location is retained, and all other channels in the inhibition location are set to zero, as in Equation (3). Then, feed-forward or backpropagation is continued to perform again. The gradient or response of each layer is added by channels, that is, a \(sum\) operation is performed on the values of all channels at each \((w,h)\) location. Then, the gradient or response of each layer is scaled to the same size as the input, and normalized with the L2 norm to obtain the final attention map. The attention map with lateral inhibition is added to ResNet to adjust its convolution module. Finally, the feature map \(F_{image}\in\mathbb{R}^{W\times H\times C}\) of the molecular structure graph is obtained. To learn the odor descriptors-related features, the semantic decoupling module [44] is utilized to decouple the image features of molecular structure graphs into semantic-specific feature representations through odor descriptor embeddings. The module uses a low-rank bilinear pooling method and an attention function to calculate the attention coefficients. It pays more attention to the semantic-aware regions and thus learns the feature vector corresponding to this semantic class. The initial value of the odor descriptor embedding \(\mathbf{E}_{sd}\in\mathbb{R}^{M\times N}\) is obtained by the pre-trained GloVe [45] model, where \(M\) denotes the number of odor descriptors, and \(N\) denotes the dimension of the odor descriptor feature vector. To acquire high-order semantic relations automatically, we employ a three-layer hypergraph neural network to correlate the odor descriptors-related feature vectors and propagate information through a hypergraph to explore feature-semantic interactions of molecule-odor descriptors. Following the suggestion in [46], we remove the learnable matrix and nonlinear activation function for linear transformations in a hypergraph convolution.