Observer-Dependent Navigability in Swarm Intelligence: A Path-Theoretic Decomposition of Performance into Perception and Distortion

Abstract

Why do different swarm algorithms achieve different performance on the same fitness landscape? This paper proposes that navigability—the structural capacity to find improving paths—is observer-dependent: different algorithms perceive different navigability on the same landscape, and this difference is irreducible to landscape properties alone. We formalise this through the decomposition F = P/D, where Perception (P) measures an algorithm's differentiation capacity and Distortion (D) measures structural resistance. Three claims are advanced and tested at scale on the Deucalion supercomputer. First, D is confirmed as multiplicative (geometric), not additive (R² = 0.993 vs 0.643, 10,000 simulations). Second, P is observer-dependent: six different strategies on the same graph yield six different P values, with hidden variable reconstruction achieving only R² = 0.069 (57,518 trials across 10,000 graphs). Third, step-wise alignment—the fraction of moves that reduce distance to the optimum—is the dominant predictor of navigation efficiency (R² = 0.82), outperforming all tested graphtheoretic and landscape metrics (maximum R² = 0.03). Complementarity is demonstrated: system-level and agent-level Perception are anti-correlated (ρ = −0.393), meaning that increasing the number of available paths decreases the fraction of improving paths per step. Eight counterfactual tests, mediation analysis, and cross-domain validation (graph navigation, 2D continuous landscapes, PSO, ACO) support the framework. All results are simulationbased. Falsification criteria are specified. The framework is a hypothesis under test, not a proven law. Author ORCID: 0009-0008-6255-7724. License: Creative Commons Attribution 4.0 International.