## 3 Materials and Methods
### Mamba-like Linear Attention (MLLA) Block
#### 3.3.2 Computational Optimization and Spatial Gating Enhancement  
MLLA overcomes Transformer's computational bottlenecks in long-range dependency modeling by unifying SSMs with linear attention. Through further model optimization, MLLA not only enhances computational efficiency but also preserves strong modeling capabilities, making it suitable for training on large-scale datasets and tackling complex tasks. The computational workflow is formalized as follows:  
\[F_{1}=\sigma(\mathcal{L}(DwConv(x))), \tag{12}\]  
\[F_{2}=\sigma(\mathcal{L}(x)), \tag{13}\]  
\[F_{atten}=LinearAttention(F_{1}), \tag{14}\]  
\[F_{output}=\mathcal{L}(F_{atten}\odot F_{2}), \tag{15}\]  
where \(x\) and \(DwConv(\cdot)\) denote the raw features of the input sequence and depthwise convolution, respectively. \(\mathcal{L}(\cdot)\) and \(\sigma(\cdot)\) represent the linear transformation and SiLU activation function, respectively. \(\odot\) represents the Hadamard (element-wise) product. We replace the MLP layers in each MLLA module with a Spatial Gated Feedforward Network [40], as illustrated in Figure 3c. The SGFN addresses the limited spatial modeling capacity of conventional feedforward networks by incorporating a spatial gating mechan  
Figure 3: The derivation of MLLA from SSM. (**a**) Linear Attention. It replaces the traditional self-attention with linear attention for efficiency, combined with a feed-forward network. (**b**) Momba: It introduces a structured state space (SSM) block and convolution for sequence modeling. (**c**) MLLA: It integrates linear attention and convolution within the SSM framework to enhance local-global feature extraction. nism that regulates channel-wise information flow. For an input feature \(X\in R^{H\times W\times C}\), the SGFN operation is defined as follows:  
\[X^{\prime}=\sigma\left(W_{p}^{1}X\right),\ \left[X_{1}^{\prime},X_{2}^{\prime} \right]=X^{\prime}, \tag{16}\]  
\[SGFN(X)=W_{p}^{2}\left(X_{1}^{\prime}\odot\left(W_{d}X_{2}^{\prime}\right) \right), \tag{17}\]  
where \(W_{p}^{1}\) and \(W_{p}^{2}\) denote the learnable weights of the first and second linear projection layers, respectively. \(\sigma\) denotes the GELU activation function. \(W_{d}\) denotes the parameters of the depthwise convolution layer. \(X_{1}^{\prime}\), \(X_{2}^{\prime}\in R^{H\times W\times\frac{C}{2}}\), where \(C\prime\) denotes the SGFN's hidden dimension. Unlike conventional FFNs that apply uniform transformations across spatial dimensions, the SGFN decouples spatial and channel processing. It introduces a spatial gating mechanism and deep convolution to better capture nonlinear spatial information, reducing channel redundancy in fully connected layers, thereby enhancing the model's expressive capacity. Specifically, the adaptive feature weighting implemented by the SGFN suppresses channel redundancy by applying a depthwise convolution-based gating to one half of the channel-split features. This allows the network to selectively retain informative channels while filtering out less significant ones, especially those that contribute little to spatial structure reconstruction. The remaining channels are directly bypassed and concatenated with the gated features, enabling lightweight yet expressive aggregation. It is worth noting that our use of the MLLA block represents a domain-level adaptation rather than a direct reuse. Originally designed for image classification and long-sequence modeling, MLLA has not been applied to the SISR task to the best of our knowledge. In this work, we are the first to integrate MLLA into a lightweight super-resolution framework, enabling efficient global context modeling for pixel-level restoration tasks. Furthermore, we introduce an architectural refinement by replacing the conventional MLP component in MLLA with a SGFN. This modification improves spatial feature selectivity and supports more stable attention distribution under high-resolution inputs.