When Are Nearby Experts Composable? Cross-Task Model Merging in Neural Thickets

Random perturbations around a shared checkpoint can produce experts for distinct tasks, but shared origin does not ensure that their gains survive composition. We formulate expert-pair selection for joint base-relative retention, measured by strict joint success and worst-task gain with unconditional abstention accounting. An exact finite-difference decomposition and an arbitrarily small orthogonal counterexample show why proximity and orthogonality alone are insufficient. We instantiate this formulation with quality-constrained spectral selection, a fixed-budget framework combining cross-task screening, layerwise pair geometry, separate validation, and Base fallback. Across six checkpoints, 21 task pairs, and five independent perturbation pools, the procedure improves strict joint success over Top-1 averaging throughout and leads the four-method model-scale comparison on four of six checkpoints. For the five models with at least 1.5B parameters, matched quality-only, global-cosine, and spectral ranking attain 49.1%, 50.5%, and 53.1% joint success. Under this matched protocol, the spectral selector also yields the highest worst-task gain and Weak Pareto rate and the lowest regression rate. Mean worst-task gain reaches +0.61 percentage points, while 17.1% regression and 13.0% abstention show that composability remains conditional. Project page: https://anonymous.4open.science/r/Thickets-Merge/.