Unsupervised Topological Alignment Between Neural and Phenomenal Spaces via GromovWasserstein Transport

A fundamental challenge in computational neuroscience lies in quantifying the structural correspondence between high-dimensional neural representations and the low-dimensional phenomenal space of subjective experience. Current approaches lack a principled metric framework that can compare these disparate spaces without requiring coordinate alignment. We introduce a novel computational pipeline combining Gromov–Wasserstein (GW) optimal transport with topological data analysis (TDA) to establish unsupervised alignment between neural activity patterns and phenomenal structure. Our framework defines a hybrid phenomenal metric incorporating information-geometric and dynamical components, with a rigorous derivation connecting temporal synchronization (Kuramoto coherence) to spatial curvature. We validate our approach on two systems: (1) a synthetic “Color Ring” model demonstrating recovery of circular topology (β1 = 1) with alignment GW = 0.042 ± 0.005, and (2) a recurrent neural network (RNN) trained on spatial navigation, where emergent manifold structure aligns with task geometry (GW = 0.078 ± 0.012) without explicit topological supervision. Both show significant improvement over shuffled controls (GW = 0.350±0.020, p < 0.001). Sensitivity analysis reveals critical thresholds in metric parameters corresponding to phase transitions in alignment quality. We propose three falsification protocols targeting anesthesia-induced topological collapse, crossmodal geometric isometry, and adversarial validation. This work provides a mathematically rigorous framework for investigating the geometric relationship between neural computation and phenomenal experience.