Connective Constants on Nested Fractal Graphs

What the math gives to ML

The transferable contribution is a finite-dimensional boundary-state renormalization for recursively assembled graphs: global self-avoiding connectivity statistics are represented by a small vector and updated by a fixed nonnegative polynomial map. This is more structured than ordinary message passing because it explicitly enumerates admissible acyclic degree-constrained combinations and preserves global path constraints across many scales. A practical neural use is a differentiable hierarchical graph module whose local state space is derived once from the cell-incidence pattern and reused at every scale with shared parameters. The construction is most promising for graph data with known recursive or multiscale structure rather than unstructured graphs.