MGF-Skip: Mamba-Guided Fusion Skip Connection

• The paper demonstrates that MGF-Skip enhances encoder-decoder segmentation by using decoder-based gating to suppress noise and improve feature integration.
• MGF-Skip employs gated convolutions, residual reinforcement, and concatenation, enabling efficient boundary localization in medical image segmentation.
• Empirical results reveal that MGF-Skip boosts performance metrics like IoU and DSC compared to traditional concatenation and attention modules.

The Mamba-Guided Fusion Skip Connection (MGF-Skip) is a skip connection module designed to enhance semantic and spatial feature integration in encoder–decoder architectures for medical image segmentation. Introduced in HyM-UNet, MGF-Skip leverages semantically rich decoder features as gating signals to suppress noise in encoder features while enforcing fine structural detail through a residual pathway. This configuration enables improved boundary localization and noise robustness compared to conventional concatenation or attention-based skips, directly addressing the semantic gap and feature misalignment common in deep convolutional architectures (Chen et al., 22 Nov 2025).

1. Architectural Placement and Input–Output Relations

MGF-Skip replaces the standard feature concatenation employed at each encoder–decoder interface of U-Net-derived segmentation models. At a given decoder stage $i$, the module receives:

• $E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$: the spatially high-resolution, texture-rich feature map from encoder stage $i$.
• $$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$: a lower-resolution, semantically strong decoder feature from the previous decoding stage.

$D_i$ undergoes upsampling, $$D_i^{up} = \mathrm{Upsample}(D_i) \in \mathbb{R}^{H_i \times W_i \times C_d}$$, aligning spatial dimensions. The MGF-Skip module fuses $E_i$ and $D_i^{up}$ to produce $$F_{skip} \in \mathbb{R}^{H_i \times W_i \times (C_e + C_d)}$$, which is then consumed by the subsequent decoder block. Fig. 1 of (Chen et al., 22 Nov 2025) visually delineates this interface in the overall architecture.

2. Mathematical Formulation

The fusion process in MGF-Skip involves spatial gating, feature filtering, residual reinforcement, and concatenation:

1. Gate Computation: The upsampled decoder feature $D_i^{up}$ undergoes a sequence of convolutions and nonlinearities to derive a spatially-aware gate:

$E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$0

• $E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$1 maps $E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$2 channels, stride 1, padding 1.
• $E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$3 maps $E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$4.
• $E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$5 denotes the sigmoid activation.

2. Feature Filtering: The encoder features are modulated spatially:

$E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$6

where $E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$7 denotes element-wise multiplication.

3. Residual Reinforcement: The gated and original encoder features are summed:

$E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$8

4. Final Fusion: The residual-augmented encoder feature is concatenated with the upsampled decoder feature:

$E_i \in \mathbb{R}^{H_i \times W_i \times C_e}$9

This fused feature serves as input to the next decoder stage.

3. Implementation Specifics

MGF-Skip’s gating branch comprises:

• $i$0 convolution ($i$1, stride 1, padding 1)
• ReLU activation
• $i$2 convolution ($i$3)
• Sigmoid activation

Batch normalization is intentionally omitted in the gating branch to retain spatial sensitivity. Channel dimensions and kernel sizes are configured to ensure alignment between the gating mask ($i$4) and the encoder feature ($i$5). The residual addition $i$6 constitutes an internal skip within the module, ensuring information preservation.

4. Fusion Strategy and Functional Rationale

MGF-Skip is architected to achieve two critical objectives:

• Suppression of Background Noise: The sigmoid-activated gating mask $i$7, derived from deep decoder features, adaptively down-weights locations in $i$8 associated with image noise or irrelevant structures (e.g., artifacts from hair occlusion or specular highlights). This mechanism is fully differentiable and trained end-to-end, with no fixed thresholds or hard masking.
• Preservation and Enhancement of Boundaries: Given that aggressive gating may suppress true boundary information, the residual connection $i$9 ensures that low-level spatial details, essential for precise contour delineation, are continuously reinforced.

All convolutional parameters within the gating branch are learnable and jointly optimized with the rest of HyM-UNet.

5. Integration within HyM-UNet and Training Configuration

MGF-Skip is instantiated at each of the four encoder–decoder transition stages. Inputs are drawn from a hybrid encoder: early stages utilize CNN blocks for local texture modeling, while deeper stages employ Visual Mamba modules for long-range context. The training protocol for HyM-UNet with MGF-Skip includes:

• Optimizer: AdamW (weight decay $$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$0, $$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$1, $$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$2)
• Initial learning rate: $$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$3, cosine-annealed to $$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$4 over 200 epochs
• Batch size: 24
• Input resolution: $$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$5
• Loss:

$$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$6

combining Dice, binary cross-entropy, and boundary-aware edge loss.

6. Empirical Performance and Comparative Analysis

Table 1 of (Chen et al., 22 Nov 2025) demonstrates that HyM-UNet incorporating MGF-Skip achieves superior results on the ISIC 2018 test set:

• Intersection over Union (IoU): $$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$7
• Dice Similarity Coefficient (DSC): $$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$8
• 95th percentile Hausdorff Distance (HD95): $$D_i \in \mathbb{R}^{H_{i+1} \times W_{i+1} \times C_d}$$9 mm
• Precision: $D_i$0

These scores surpass those of U-Net, CE-Net, and Attention U-Net. Table 2 presents an ablation: integrating MGF-Skip into a U-Net baseline increases IoU by $D_i$1 (from $D_i$2 to $D_i$3) and DSC by $D_i$4 (from $D_i$5 to $D_i$6), outperforming SE and CBAM attention modules in the same positions.

MGF-Skip's design results in minimal additional parameter overhead relative to standard skip connections or spatial/channel attention modules, while maintaining inference latency ($D_i$7 ms per $D_i$8 image on RTX 3090) competitive with or lower than ViT-based architectures.

7. Distinctions from Prior Skip Connection Mechanisms

MGF-Skip contrasts with alternative strategies as follows:

Skip Module	Gating Source	Residual Path	Attention Dimension
Standard concat	None	None	None
SE	Encoder/Decoder	None	Channel
CBAM	Encoder/Decoder	None	Channel + Spatial
MGF-Skip	Decoder (deep)	Encoder	Spatial (decoder-guided)

Standard concatenation indiscriminately propagates all encoder features, including noise. SE and CBAM introduce channel/spatial attention but lack explicit residual renormalization and do not leverage decoder semantics for gating. MGF-Skip’s use of the decoder as a gating source, with end-to-end-learned dynamic suppression and explicit residual addition, is unique in enhancing ambiguous boundary regions and suppressing artifacts, as shown by empirical evaluation (Chen et al., 22 Nov 2025).