Effective Dimensionality from Fisher Information Rank: Operational Validation on Tori, Fractals, Random Graphs, and Coarse-Grained Lattices

Key Points

• This research aims to validate Fisher Information Matrix rank as a reliable metric for determining effective spatial dimensions.
• Evaluated the rank of Fisher Information Matrix on flat tori up to d=4.
• Assessed Hausdorff dimension in fractals using the matrix rank.
• Investigated a new disorder direction in random geometric graphs.
• Confirmed an exact integer dimension for flat tori up to d=4.
• Determined Hausdorff dimension values for various fractals.
• Identified a unique disorder direction associated with random geometric graphs.