## 3 The Materials and Methods
### Backbone Architecture  
To achieve high recognition accuracy under complex visual conditions while maintaining computational efficiency, HUE-Net introduces a novel hybrid backbone architecture that synergistically combines the local inductive biases of Convolutional Neural Networks (CNNs) with the global contextual modeling capabilities of transformer modules. The design is tailored specifically to accommodate multispectral and event-based inputs while being lightweight enough for deployment on edge devices such as the Jetson Nano and mobile SoCs. The HUE-Net architecture is built around a carefully calibrated sequence of four interdependent stages to optimize accuracy and efficiency. It begins with two convolutional volumes that are built with depthwise separable convolutions. This method enables the extraction of local features, for example, facial shapes and textures, with a greatly reduced computational burden. The addition of transformer modules with Split Transpose Depthwise Attention (STDA) is incorporated in the latter two stages. Such modules provide reasoning at the global level that the model needs to interpret broader spatial relationships as well as spectral interactions necessary for distinguishing identities in complex scenes. After this step, LoRaLin, a low-rank linear transformation layer, acts as a bottleneck to tighten the increasingly abstract features with a compact yet informative representation. The final step in the workflow takes place with an output projection layer that sets the resulting embeddings to be fit for an angular margin-based classification. All these steps combine into one flow that lets HUE-Net learn powerful facial representations while keeping it lightweight and fast enough for real-time use in constrained settings. This hybrid architecture is formally denoted as  
\[f(X)=Proj\circ LoRaLin\ \circ\mathcal{T}_{4}\circ\mathcal{T}_{3}\circ C_{2} \circ C_{1}(X) \tag{3}\]  
where \(X\in R^{H\times W\times 6}\) is the fused multispectral event input, \(C_{i}\) are convolutional stages, \(\mathcal{T}_{i}\) are transformer stages, and \(Proj\) is the output embedding head. The first two stages utilize inverted residual bottleneck blocks with depthwise separable convolutions, spinning off MobileNetV3, to capture spatial patterns including edges, contours, and localized texture patches efficiently. Each block is defined as  
\[F^{(l)}\sigma\Big{(}BN\Big{(}DWConv\Big{(}PWConv\Big{(}F^{(l-1)}\Big{)}\Big{)} \Big{)}\Big{)} \tag{4}\]  
where \(PWConv\) denotes pointwise \(1\times 1\) convolution, \(DWConv\) is a depthwise convolution, \(BN\) is batch normalization, and \(\sigma\) is the Swish activation. These blocks significantly reduce the computational burden (FLOPs) without sacrificing representational power. To seamlessly capture the long-range dependencies and intricate relationships between spectral channels, the final stages of HUE-Net integrate modified transformer blocks based on STDA mechanisms. Unlike classical self-attention mechanisms (known for their Quad-complex computational inefficiency), STDA has developed a more streamlined approach. This improvement comes from the systematic workflow where attention is performed after the input tokens are split into nonoverlapping patches. This design allows for localized processing but performs transposition from spatial to channel dimensions for cross-spectral mixing before the application of depthwise separable attention. Global elusive contextual information is captured at minimal cost. With this design, the network can reason across space and the spectrum simultaneously, improving identity recognition performance in visually impaired and degraded conditions in the spectrum. In HUE-Net's final stages, modified transformer units based on STDA mechanisms are added to stack on long-range dependency and spectral channel relationships. Unlike self-attention mechanisms, STDA adopts a more efficient self-attention strategy.