What question did this study set out to answer?

To develop a framework that aligns neural states and functional distinctions using Gromov-Wasserstein transport without assuming prior coordinate correspondence.

January 24, 2026Open Access

The Topological Signature of Consciousness: A Gromov-Wasserstein Framework for Neural-Phenomenal Alignment

Key Points

To develop a framework that aligns neural states and functional distinctions using Gromov-Wasserstein transport without assuming prior coordinate correspondence.
Utilized Gromov-Wasserstein Optimal Transport for alignment of metric spaces.
Applied Topological Data Analysis to extract invariant signatures across transformations.
Conducted quantitative comparisons of structural properties.
Demonstrated effective alignment of neural and functional metrics.
Showed invariant signatures that persist without coordinate assumptions.
Provided a new perspective on the structural properties of consciousness.

Abstract

We introduce a rigorous methodology using Gromov-Wasserstein (GW) Optimal Trans-port to align the metric space of neural states (N ) with the metric space of functionaldistinctions (Ψ) without assuming a priori coordinate correspondence. Topological DataAnalysis (TDA) provides invariant signatures that persist across coordinate transforma-tions. This framework enables quantitative comparison of structural properties withoutontological claims about the nature of internal representations.

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