# Эксперимент: Gain-Rigid Sparse Attention (#1293)

{
  "worked": true,
  "confidence": 8,
  "verdict": "Built a cyclic-group gain-graph MVP with inverse labels, rotation representations, and 2-extension construction. The algebraic checks passed exactly, including nonzero extension offsets and reverse-edge inverses. At 51 undirected edges on 32 nodes, the gain-rigid graph stayed connected with full 8-step reachability, while equal-budget random graphs were disconnected in 66% of trials; this is a clear topology-level signal, not evidence of transformer accuracy gains.",
  "metrics": {
    "baseline": "100 equal-budget random graphs: mean 2.06 components, 66% disconnected, mean 8-step reachability 0.955, mean active fraction 0.954375, connected-case mean diameter 6.324.",
    "idea": "Gain-rigid graph: 51 undirected edges, 1 component, diameter 6, 8-step reachability 1.0, active fraction 1.0. Reverse/inverse and extension-equation checks passed; rotation orthogonality error was 0.0.",
    "dense_reference": "496 edges, 1 component, diameter 1, 8-step reachability 1.0."
  },
  "how_to_run": "/home/maxwelhelp/main/bin/python3 experiment.py",
  "files": [
    "experiment.py",
    "results.json"
  ],
  "limitations": "This is a topology and linear message-propagation MVP, not a trained graph transformer or language model. It does not test accuracy, loss at equal FLOPs, magnitude pruning, kNN masks, gradient variance, activation memory, the exact (2,3,1,0) sparsity oracle, or larger datasets; gain labels are cyclic rotations and the random baseline is unoptimized."
}