COGENT: Counterfactual Gaussian Explanations for Volumetric Medical Images

Technical Summary: COGENT

Problem Statement
The deployment of deep learning models in high-stakes medical applications, particularly volumetric imaging like CT and MRI, requires robust explainability. While modern models achieve state-of-the-art performance, their decision-making processes often remain opaque. Existing explainability methods for volumetric data predominantly operate in the pixel or voxel space (image space). These approaches often fail to explicitly model the underlying three-dimensional structure of the scene, leading to explanations that are difficult to interpret anatomically or that obscure complex spatial dependencies. Furthermore, many techniques are applied slice-by-slice, failing to capture coherent 3D object structures. There is a need for explainability frameworks that operate directly within structured 3D representations to preserve anatomical consistency and provide clinically meaningful insights.

Methodology
The paper introduces COGENT (Counterfactual Gaussian Explanations for Volumetric Medical Images), a framework that generates counterfactual explanations directly in the parameter space of Gaussian-based volumetric representations, rather than in raw image space. The methodology integrates three core components:

1. Representation Layer (MedGS): The framework utilizes MedGS (Medical Gaussian Splatting), which extends 3D Gaussian Splatting to multi-modal medical imaging. MedGS represents volumetric medical data as a collection of explicit, differentiable Gaussian primitives. Each primitive is defined by parameters including spatial position ($x_i$), appearance coefficients ($f_i$), opacity ($o_i$), scale ($s_i$), and rotation ($r_i$). This creates a fully differentiable bridge between the Gaussian parameters and the rendered imaging slices.
2. Downstream Predictor (Sybil): The framework employs Sybil, a deep learning model designed to predict future lung cancer risk directly from low-dose chest CT scans. In COGENT, Sybil acts as a fixed, frozen classifier. Its output (risk logits) serves as the optimization signal.
3. Counterfactual Optimization:
   • Formulation: Explainability is framed as a constrained counterfactual optimization problem. The goal is to identify which Gaussian primitives, when modified, would alter the model's prediction (e.g., shifting a high-risk prediction to low-risk).
   • Process: The system selects a subset of Gaussians (often those intersecting anatomical masks or specific regions of interest). Using Projected Gradient Descent (PGD), the framework optimizes the parameters of these selected Gaussians.
   • Gradient Flow: Gradients are propagated backward from the frozen Sybil classifier, through the differentiable rendering pipeline, to the Gaussian parameters.
   • Constraints: The optimization is constrained by an $L_\infty$ bound ($\epsilon$) and global clipping intervals to ensure the perturbed volume remains anatomically close to the original, preventing unrealistic artifacts.
   • Objective: The loss function ($L_{cf}$) is defined based on the counterfactual goal, either untargeted (maximizing or minimizing a specific risk logit) or targeted (matching a specific logit value).
   • Extraction: After optimization, the framework identifies the top 10% of Gaussians that underwent the most significant parameter updates. These primitives constitute the explanation, representing the specific structural and textural regions driving the model's decision.

Key Contributions

• Representation-Space Framework: The authors introduce a novel framework that connects MedGS representations with a volumetric lung cancer risk prediction model, shifting explainability from image space to a structured 3D parameter space.
• Counterfactual Optimization in Parameter Space: The work formulates explainability as a counterfactual optimization problem directly within the parameter space of 3D Gaussian representations, a departure from conventional pixel/voxel perturbation methods.
• Clinically Meaningful Explanations: The paper demonstrates that Gaussian-space counterfactual explanations produce spatially localized, sparse, and anatomically consistent results that align with clinical expectations, validated through both quantitative metrics and expert assessment.

Results
The framework was evaluated on lung CT scans using the Sybil model, comparing COGENT against established baselines (GradCAM, Saliency, Integrated Gradients, Input $\times$ Gradient, Kernel SHAP) and a pixel-space counterfactual baseline.

• Quantitative Performance: COGENT achieved the highest localization scores, with RRA and RRA_abs values of 0.2837, significantly outperforming the strongest classical baseline, GradCAM (0.0805). This indicates a superior ability to identify the pathological regions driving the prediction.
• Sparsity and Compactness: COGENT maintained a high degree of sparsity (0.6550), producing focused explanations compared to the more diffuse Kernel SHAP (0.2083).
• Perturbation Stability: The method showed competitive Perturbation-AUC (0.0396) and Mean-Perturbation (0.0414) scores, indicating stable performance across evaluation criteria.
• Qualitative and Expert Evaluation: Visual comparisons showed that COGENT produces anatomically plausible, localized modifications (e.g., targeting specific nodules) whereas pixel-space baselines resulted in scattered, noisy patterns. An expert radiologist evaluation on a 5-point scale found that in 40% of cases, the counterfactual explanations corresponded to a positive mitigation of disease severity (attenuation of malignant traits), with another 40% showing a neutral impact. The explanations consistently localized to regions an expert would identify as suspicious.

Significance and Claims
The paper claims that COGENT provides a new perspective on interpreting volumetric deep learning models by embedding explainability within the explicit 3D scene representation. The significance lies in the ability to generate explanations that are not only technically effective in localizing the model's attention but are also clinically meaningful and anatomically consistent. By operating in the Gaussian parameter space, the method avoids the anatomical incoherence often found in voxel-level perturbations. The authors position COGENT as a general paradigm for representation-space explainability, demonstrating its potential to make volumetric AI models more transparent and trustworthy for medical decision-making. The work suggests that counterfactual parameter-space explanations can effectively reveal the structural and textural evidence underlying model predictions in a way that aligns with radiological understanding.