GS-Net: Multi-Domain Network Frameworks

• GS-Net is a suite of network frameworks that leverage deep learning and graph models to address specialized tasks in medical imaging, 3D scene rendering, and neuroanatomy.
• It integrates innovative modules such as global self-attention for glaucoma staging, plug-and-play dense ellipsoid prediction for scene representation, and graph-based cortical folding analysis.
• Each instantiation of GS-Net demonstrates improved performance metrics and enhanced interpretability through tailored architectures and rigorous experimental validation.

GS-Net refers to several independent frameworks across different subfields, each leveraging network representations and/or deep learning for domain-specific tasks. Notably, the designation “GS-Net” has been used for: (1) a global self-attention guided CNN for multi-stage glaucoma classification; (2) a plug-and-play module for generalizable 3D Gaussian Splatting; (3) an integrated network model for representing gyral and sulcal folding patterns in the brain. Each instantiation of GS-Net is distinct in its underlying methodology, application domain, and technical contributions.

1. GS-Net for Multi-Stage Glaucoma Classification

GS-Net (Das et al., 2024) is a deep learning framework designed for classifying glaucoma severity (normal, early, advanced) from retinal fundus images. It addresses challenges such as minute lesion size variation and high inter-class similarity.

Architecture Overview:

• Input: RGB fundus image, resized to $224 \times 224 \times 3$.
• Backbone: ImageNet-pretrained CNN (e.g., ResNet-50, InceptionV3, MobileNet, EfficientNetB1, DenseNet-121). DenseNet-121 was empirically superior, outputting a $H \times W \times K$ feature map ($H=W=7$ or $14$, $K=1024$).
• Global Self-Attention Module (GSAM): Placed after the backbone's feature map. Enhances feature discrimination via dual attention branches.
• Classifier: Global average pooling, a fully connected layer with three outputs, softmax activation.

GSAM Details:

• Parallel Branches:
  • Channel Attention Module (CAM): Learns inter-channel dependencies. Constructs query, key, value via global max/average pooling and $1\times1$ convolutions, yielding $K\times K$ attention weights to reweight channels.
  • Spatial Attention Module (SAM): Learns long-range spatial relationships. Utilizes $1\times1$ convolutions and reshaping to compute $(HW)\times(HW)$ spatial attention.
• Fusion and Residuals: The outputs of CAM ($F_{ch}$), SAM ($H \times W \times K$0), and the input feature map ($H \times W \times K$1) are fused:

$H \times W \times K$2

with learnable scalars $H \times W \times K$3 and elementwise sum $H \times W \times K$4.

Training:

• Loss: Categorical cross-entropy.
• Optimizer: Adam (lr=0.005).
• Data Augmentation: Random rotation, scaling, horizontal/vertical flip.
• Dataset: Harvard Dataverse V1 [Ahn et al. 2018], 1,524 images across “normal,” “early,” and “advanced” grades; split 754/324/464 for train/val/test.

Performance:

• DenseNet-121 + GSAM yielded Accuracy = 84.91%, F1 = 84.55%, AUC = 0.9454.
• Outperformed prior SOTA by 2–9% across metrics and all tested backbones. Ablation confirmed complementary strength: both CAM and SAM are required for best results.

Backbone (+ GSAM)	Accuracy (%)	F1 (%)	AUC
DenseNet-121	83.18	83.13	0.9357
DenseNet-121 + GSAM	84.91	84.55	0.9454

Table: Key results for the glaucoma staging task; see (Das et al., 2024) Table 1.

2. GS-Net for Plug-and-Play 3D Gaussian Splatting

GS-Net (Zhang et al., 2024) is the first published generalizable, plug-and-play network module for 3D Gaussian Splatting (3DGS) scene representation, aimed at closing the gap between scene-conditioned initialization and cross-scene priors.

Background:

3DGS represents a scene as a set of anisotropic Gaussian ellipsoids, each defined by center $H \times W \times K$5, covariance $H \times W \times K$6, opacity $H \times W \times K$7, and color $H \times W \times K$8, composited via rasterization for real-time view synthesis.

Motivation:

• Standard 3DGS pipelines initialize splats with Structure-from-Motion (SfM) point clouds, which, if sparse, hinder optimization and detail recovery.
• Scene-specific overfitting and computationally intensive Multiview Stereo (MVS) limits scalability.

GS-Net Module:

• Input: Sparse SfM point clouds $H \times W \times K$9, where $H=W=7$0 is position and $H=W=7$1 is RGB color.
• Output: For each input point, predict $H=W=7$2 dense ellipsoids with $H=W=7$3, $H=W=7$4, $H=W=7$5, $H=W=7$6, yielding $H=W=7$7 total ellipsoids per scene.
• Architecture:
  • Encoder: Pointwise MLP to 16-d features, 3-NN fusion ($H=W=7$8), second MLP to 128-d.
  • Decoder: 3-layer FC stack to predict ellipsoid parameters ($H=W=7$9: 3, $14$0: 7, $14$1: 1, $14$2: 3).
  • Regularization: Scaled and normalized (tanh for $14$3, sigmoid for $14$4 scales, quaternion normalization for rotations).
  • Supervision: MSE loss on deltas with respect to input points (benefits over absolute value learning).

Efficiency and Results:

• Trained on CARLA-NVS dataset (urban/rural static and dynamic scenes, 12 cameras, LiDAR, weather variants).
• Improves PSNR by +2.08 dB (cv) / +1.86 dB (novel), with faster preprocessing (58 min vs. 153 min for MVS).
• Qualitative gains: reduced holes in textureless regions, sharper structure, less “bleed” behind occlusions.

Method	PSNR (CV)	SSIM (CV)	LPIPS (CV)	PSNR (NV)	SSIM (NV)	LPIPS (NV)
3DGS	25.6	0.917	0.184	21.8	0.854	0.262
GS-Net+3DGS	27.7	0.936	0.153	23.7	0.869	0.232

Table: Rendering metrics for conventional (CV) and novel (NV) viewpoints on CARLA-NVS (Zhang et al., 2024).

3. GS-Net for Network Representation of Brain Folding Patterns

Gyral-Sulcal-Net (GS-Net) (Cao et al., 13 Jan 2026) is a formal graph-theoretic framework for analyzing the organization of brain cortical folding patterns, specifically integrating both gyri and sulci landmarks into a unified anatomical network.

Pipeline and Definitions:

• Input: T1-weighted MRI, processed via FreeSurfer to yield a triangular mesh $14$5.
• Gyral Altitude Function: $14$6 assigns each vertex $14$7 its signed distance from the mid-cortical surface ($14$8 for gyri, $14$9 for sulci).
• Graph Construction:
  • Extract crest-line skeletons of gyri (GyralNet $K=1024$0).
  • Extract sulcal valley-line skeletons (SulcalNet $K=1024$1).
  • Build cross-pattern edges $K=1024$2 (sulcal ends $K=1024$3 gyral junctions).
  • Unified network: $K=1024$4, $K=1024$5, $K=1024$6.

Landmark Types:

• GC: Gyral conjunctions (degree $K=1024$7 3 in $K=1024$8, not incident to $K=1024$9).
• SGC: Sulci–gyri conjunctions (degree $1\times1$0 3 in $1\times1$1 + at least one $1\times1$2).
• SC: Sulci conjunctions (degree $1\times1$3 3 in $1\times1$4).

Network Metrics:

• Adjacency $1\times1$5, degrees, clustering coefficient $1\times1$6, modularity $1\times1$7, betweenness centrality BC, defined according to standard graph theory.

Datasets and Evaluation:

• Applied to datasets covering >1,600 brain scans spanning gestational week 34 to elderly adults, across healthy and pathological cohorts.

Significance:

• GS-Net provides a rigorous combinatorial model of cortical folding, facilitating integration with structural and functional brain networks. The approach enables quantification of topological properties and network motifs specific to folding patterns (Cao et al., 13 Jan 2026).

4. Technical Comparison and Domain Applications

Instantiation	Domain	Core Methodology	Application
GS-Net (Glaucoma)	Medical imaging	Self-attention augmented CNN	Fundus image staging
GS-Net (3DGS)	Computer vision	Plug-and-play dense splat net	3D scene rendering
GS-Net (Gyral-Sulcal)	Brain connectomics	Graph-based mesh skeletonization	Cortical folding analysis

All three frameworks employ network principles, either in neural attention, point cloud mapping, or explicit graph models. However, there is no methodological overlap beyond this abstraction. Each GS-Net is specific to its respective data type and scientific question.

5. Limitations and Future Directions

• GS-Net (Glaucoma): Evaluation is limited to public fundus datasets; cross-modality generalization and clinical validation remain open.
• GS-Net (3DGS): Current form only supports static point sets; extensions to dynamic Gaussians and domain adaptation to noisy, real-world sensors are ongoing.
• GS-Net (Gyral-Sulcal): The toolbox will extend to larger cross-cohort analyses and facilitate integration with multimodal neuroimaging.

Ongoing work in each subfield aims to broaden the generalization, scalability, and biological or physical interpretability of GS-Net architectures (Das et al., 2024, Zhang et al., 2024, Cao et al., 13 Jan 2026).