Sparse, trainable subnetworks for multi-omics integration: a cross-validated evaluation of the Lottery Ticket Hypothesis across nutrigenomic, toxicogenomic, and oncogenomic datasets

Multi-omics integration, the joint analysis of two or more high-dimensional molecular data types collected on the same biological samples, is now a standard analytical approach across nutrigenomics, toxicogenomics, microbiome research, and disease genomics. Existing methods sit on a trade-off between expressiveness and interpretability: latent-variable methods such as MOFA and DIABLO yield compact, biologically interpretable signatures but assume a restrictive linear structure; tree ensembles such as Random Forests achieve strong predictive performance but resist mechanistic interpretation; deep neural networks combine the drawbacks of both, with large numbers of opaque weights and no built-in feature selection. I ask whether the Lottery Ticket Hypothesis (LTH), the conjecture that a randomly initialised dense network contains a sparse subnetwork that matches its accuracy when trained from the original initialisation, can help reconcile this trade-off in the multi-omics setting. I apply Iterative Magnitude Pruning with weight rewinding for 25 rounds (cumulative sparsity 99.6%) on a multi-input fused multi-layer perceptron across eight datasets spanning four biological domains (n=40 to n=1,492), with 5-fold outer cross-validation and inner-validation winning-ticket selection to avoid test-set leakage. On the largest task, TCGA Pan-Cancer (4-class tissue-of-origin, n=1,492), a 2,952-weight subnetwork (83% sparsity) reached 84% +/- 3% test accuracy compared with 86% +/- 2% for the dense network. Pruning improved test accuracy on two TCGA staging tasks (TCGA-LUAD: 51% +/- 1% vs 45% +/- 5%; TCGA-KIRC: 50% +/- 4% vs 48% +/- 7%). Networks compressed by 6x to 270x while retaining task-level signal on well-specified tasks. I suggest LTH as a domain-agnostic, prior-free option for sparse neural integration of multi-omics data, complementary to graph-based and pathway-constrained methods.