Fractal Graph Rewriting Framework (FGRF) v3.0.0
Version 3 transitions FGRF from a proposed diagnostic to a validated one. Version 2 reframed the framework from an optimizer into a structural probe for weight matrices. Version 3 tests that reframing empirically.
Key improvements:
- De-saturated estimators. The topological complexity C, the interdependence exponent I, and the Hausdorff dimension D no longer sit at their clip floors. The scale k is now derived from each matrix's own singular-value spectrum, and the finite-difference windows used to estimate C and I adapt to real transitions in the spectral counting function.
- Trained-vs-untrained experiment. Across five random seeds and three architectures (Qwen2.5-0.5B, SmolLM2-360M, GPT-2-medium), the probe shows a reproducible signature: key and value projections of trained models have systematically lower C and higher D than the same matrices in an untrained model of the same architecture.
- Ablation invariance. The probe table under full is byte-identical to the one under no_thermo, and no_fractal and plain_gd produce identical flat tables. The probe reads the matrix before any update; the update has no effect on the measurement.
- Thermodynamic gate as a second readout. The gate is silent on the heavily optimized Qwen2.5-0.5B, fires once on SmolLM2-360M, and fires nine times on GPT-2-medium — on matrices that the geometric probe independently flags as structurally ordered.
Full details: see the Version 3 paper (paper/fgrf_v3_paper.pdf) and the README.
DOI: 10.6084/m9.figshare.33440932