\section{Discussion}
\paragraph{Statistically Coherent Network:}
This study introduces the Statistically Coherent Network (SCN), a multi-modal framework designed to encode DICOM images $\mathbf{x}_{\text{img}}$, radiomic descriptors $\mathbf{x}_{\text{rad}}$, and patient metadata $\mathbf{x}_{\text{meta}}$ into a structured latent representation $\mathbf{Z}(\mathbf{x}) \in \mathbb{R}^{k \times d}$. Unlike single-vector embeddings, SCN employs a multi-space latent architecture that facilitates group-level alignment while preserving inter-class separability. Empirical results confirm that SCN achieves consistently high performance across four diverse clinical tasks. The SCN model is trained with a composite objective ($\mathcal{L}_{\text{total}} = \mathcal{L}_{\text{sup}} + \lambda_1 \mathcal{L}_{\text{T-stochastic}} + \lambda_2 \mathcal{L}_{\text{triplet}}$), where $\mathcal{L}_{\text{sup}}$ supervises classification, $\mathcal{L}_{\text{T-stochastic}}$ aligns latent distributions of similar patient groups via statistical testing, and $\mathcal{L}_{\text{triplet}}$ enforces pairwise geometric consistency. Ablation analysis (Table~\ref{tab:unified_f1}) reveals that removing $\mathcal{L}_{\text{T-stochastic}}$ degrades performance by an average of $3.70\%$, greater than the $1.83\%$ drop from removing the triplet term, validating the dominant contribution of statistical regularization.

To further analyze class-wise structural properties, we computed intra-class variance $\sigma^2_{\text{intra}}$ and inter-class divergence $\sigma^2_{\text{inter}}$ within the latent space. Across all datasets, we observed $\sigma^2_{\text{inter}} > \sigma^2_{\text{intra}}$ with clear margin (Table~\ref{tab:latent-consistency}), indicating that SCN clusters samples from the same class into compact and distinguishable regions. This behavior supports the claim that $\mathbf{Z}(\mathbf{x})$ not only encodes task-relevant information but also preserves statistical semantics over subpopulations.

\vspace{-0.8em}
\paragraph{Limitations and Future Directions:}
One limitation is the reliance on hard-threshold grouping (e.g., discrete bins for age or BMI), which may poorly approximate the underlying continuous variation. Replacing this with a learnable stratification function $g(\mathbf{x}_{\text{meta}})$ may yield smoother population-level modeling. SCN also assumes access to radiomics and structured metadata, which may be unavailable in certain real-world settings; extending SCN to handle missing or noisy clinical modalities remains an open challenge. The current formulation is designed for classification. Extending SCN to segmentation, detection, or temporal modeling (e.g., in longitudinal studies) would broaden its utility. Additionally, loss balancing via sample-aware dynamic coefficients $\lambda_i(\mathbf{x})$ could improve learning stability under subgroup imbalance. Finally, future work will explore real-world deployment in federated or streaming environments, where statistical heterogeneity and domain shift are intrinsic to clinical workflows.