SCOPE: Spectral-Conditioned Omic-Pathology Encoder for Interpretable Multimodal Cancer Survival Analysis

Predicting patient survival from cancer biopsies is a multimodal learning problem in which whole-slide images (WSI) and gene expression must be fused effectively. The state of the art relies almost exclusively on flattened bag of patch tokens, discarding the 2D structure of tissue and yielding fusion mechanisms that are difficult to interpret biologically. We introduce SCOPE (Spectral-Conditioned Omic-Pathology Encoder), the first spectral-conditioned multimodal architecture for joint pathology-genomics survival modeling. The core primitive is the Gene-Modulated Convolution: a global 2D convolution whose kernel is generated with FiLM modulations driven by pathway-level gene embeddings. Stacking these modules across a multi-scale Haar wavelet pyramid delivers a global receptive field at each spatial-frequency band at log-linear cost. A mask-aware differentiable Top-$K$ predictor then selects the most prognostic spatial positions for the discrete-time negative-log-likelihood survival head. On 10 TCGA cohorts, SCOPE raises the mean C-index to $0.744$ ($+3.3\%$ relative) over the strongest baseline while using $1.9\times$ lower peak memory and running $1.6\times$ faster, and it remains the top method in both the pathology-only and missing-omics settings. SCOPE further exposes three complementary axes of intrinsic interpretability (Top-$K$ spatial saliency, wavelet sub-band allocation, and pathway attention) that bridge molecular biology and observable tissue architecture. Our code/models will be publicly available.