## 3 Materials and Methods
### Feature-Semantic Interaction of Molecule-Odor Descriptor through HGNN  
Following [7], a hypergraph is defined as \(G=(V,E,W)\), where \(V\) is a set containing \(M\) vertices and \(E\) is a set containing \(N\) hyperedges, and each hyperedge \(\epsilon\in E\) contains two or more vertices. The hypergraph is assigned a weighted matrix \(\mathbf{W}\in\mathbb{R}^{N\times N}\), which is a diagonal matrix, with \(W_{ee}\) representing the weight of hyperedge \(\epsilon\). A hypergraph can be represented as an incidence matrix \(\mathbf{H}\in\mathbb{R}^{M\times N}\), where \(H_{ie}=1\) if the hyperedge \(\epsilon\in E\) contains vertex \(v_{i}\in V\), otherwise 0. Vertex and hyperedge degree matrices are diagonal matrices, denoted by \(\mathbf{D}\) and \(\mathbf{B}\), respectively, where \(D_{ii}=\sum_{e=1}^{N}W_{ee}H_{ie}\) and \(B_{ee}=\sum_{i=1}^{M}H_{ie}\). In this paper, \(W_{ee}\) is uniformly assigned to 1, and hence, \(\mathbf{W}\) is an identity matrix. Hypergraph convolution can be regarded as a two-stage refinement of the feature transformation of \"node-hyperedge-node\" on the hypergraph structure. Through vertex-hyperedge-vertex transformation, HGNN can effectively capture semantic dependencies and explore the interaction between the features of molecular structure graphs and the semantics of odor descriptors, that is, the feature-semantic interaction of the molecule-odor descriptor. Figure 5a shows the hypergraph structure for odor molecule-odor descriptor modeling. Each colored node represents an odor descriptor. Odor descriptors connected by edges of the same color indicate that these odor descriptors co-occur in the same odor molecules. Figure 5b is the construction method of the hypergraph. Each hyperedge is abstracted as a relationship between nodes. The darker the color, the more correlated the node to the hyperedge. We can choose random values or odor descriptor embeddings to initialize \(\mathbf{H}\) and then use the sigmoid function to activate it. To speed up the convergence, we use the odor descriptor embedding as initialization in this paper. To train and validate the HGNN-based module, molecular structure graphs of size \(300\times 300\) pixels generated using RDKit were resized to \(128\times 128\) pixels. Given the molec  
Figure 5: Hypergraph construction processes. (**a**) The hypergraph structure for odor molecule–odor descriptor modeling. (**b**) The construction method of the hypergraph. ular structure graph, ResNet [40] with an olfactory lateral inhibition-inspired attention mechanism is used to extract the feature maps. The output of the ResNet part is the feature map \(F_{image}\in\mathbb{R}^{W\times H\times C}\), where \(W\), \(H\), and \(C\) denote the width, height, and channel of the feature map, respectively. Inspired by animal olfaction, we add an attention mechanism inspired by lateral inhibition [36] to the convolutional module of ResNet, as shown in Figures 6 and 7. It further adjusts the feedback signal to obtain an attention map with lateral inhibition signals, which improves sharpening and anti-interference ability. Olfactory lateral inhibition is the process by which activated neurons propagate inhibitory signals to neighboring neurons. The most relevant neurons can be grouped together through the combination of lateral inhibition and feedback signals [41]. This part will be explained in detail below. Since the ReLU layer determines which neurons can be activated, we add lateral inhibition to the ReLU layer. For the feedback signal matrix of the ReLU layer, the dimensions are \((W,H,C)\), where \(W\), \(H\), and \(C\) denote width, height, and channel. After feed-forward training, the gradients are back-propagated, and the inhibition is performed along the channel axis of the feedback signal. The maximum value in each channel axis is collected to obtain the Max-map; that is, the \(max\) operation is performed on all channel values at each \((w,h)\) location.