Aligning latent space with graph Laplacian eigenvectors yields commute-time distance
hisspikeness · x · 2026-10-05
Graph theory says yes: if the latent space is aligned with the eigenvectors of the environment's graph Laplacian and correctly scaled (i.e., the right metric), straight-line distance in that space equals commute-time distance — how long a random walker takes to reach the goal and back, capturing bottlenecks and shortcuts relevant for planning.
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