Higher-Order Interactions in Financial Networks: An Ablation Study with Simplicial Complexes

Abstract

This paper investigates whether explicitly modeling higher-order interactions improves prediction in financial-network settings when the data-generating mechanism depends on group synergy. We formally define the prediction problem over a known simplicial complex and conduct a controlled ablation study across three topological levels: (i) a 0-simplex baseline using only node-level history, (ii) a 1-simplex graph model using self-history and neighbor aggregation, and (iii) a 2-simplex simplicial model that incorporates a triangle-face interaction term. Using synthetic data in which a target node depends on the multiplicative synergy between two other nodes, we show that the simplicial model consistently outperforms pairwise baselines. At the target node, the reduction in MSE reaches 96.1% in the main scenario and 95.7% ± 0.6% across 20 random seeds, with strong statistical significance (Wilcoxon signed-rank test, p ≈ 1.9 × 10⁻⁶; paired t-test, p ≈ 4.4 × 10⁻¹⁸). Additional analyses using MAE, R², correlation, sensitivity to interaction strength, noise and lag depth, a second 2-simplex, a nonlinear MLP baseline and a one-layer GCN baseline indicate that the performance gain is localized in higher-order structures and attributable to the simplicial topology rather than to generic nonlinear capacity. A set of fair pair-identification baselines,  including a linear model with the trigger units as separate features, an MLP that can learn the interaction, and a model with products of all unit pairs shows that the 2-simplex provides both the identification of the relevant interaction and a substantial parsimony advantage (7 features versus 409 for comparable error). A semi-synthetic experiment using real quarterly US macroeconomic series as triggers reproduces the same pattern (99.9% MSE reduction at the target, Wilcoxon p ≈ 1.9 × 10⁻⁶). The full experimental pipeline, including code, data generation and figures, is publicly available for reproduction. These results provide quantitative evidence for the use of Topological Deep Learning and simplicial complexes in network problems where systemic propagation depends on group-level effects.