1{
  2  "baseline": {
  3    "best_cfg": {
  4      "lr": 0.01
  5    },
  6    "full": {
  7      "mean": 0.0575008038431406,
  8      "n": 8,
  9      "per_seed": [
 10        0.06365571171045303,
 11        0.0492621511220932,
 12        0.07721881568431854,
 13        0.05750827118754387,
 14        0.04907004162669182,
 15        0.06700301915407181,
 16        0.03857070580124855,
 17        0.057717714458703995
 18      ],
 19      "std": 0.011260127917232875
 20    },
 21    "sweep": [
 22      {
 23        "cfg": {
 24          "lr": 0.001
 25        },
 26        "mean": 0.08882061671465635
 27      },
 28      {
 29        "cfg": {
 30          "lr": 0.003
 31        },
 32        "mean": 0.09223039448261261
 33      },
 34      {
 35        "cfg": {
 36          "lr": 0.01
 37        },
 38        "mean": 0.0575008038431406
 39      }
 40    ]
 41  },
 42  "bench_version": 1,
 43  "comparison": {
 44    "delta_mean": -0.05702371649658744,
 45    "idea_wins": 8,
 46    "mde": 0.010041533799026574,
 47    "mde_rel_pct": 17.46329290703377,
 48    "n_pairs": 8,
 49    "p_value": 0.0081,
 50    "per_seed_diffs": [
 51      -0.06314983440097421,
 52      -0.048904426948865876,
 53      -0.07662046700716019,
 54      -0.05741136383585399,
 55      -0.048732060997281224,
 56      -0.06664702549460344,
 57      -0.038038548082113266,
 58      -0.05668600520584732
 59    ],
 60    "system_worked": true,
 61    "verdict": "idea better (significant)"
 62  },
 63  "custom_track": {
 64    "domain": "graph-positional-encoding",
 65    "file": "cayley_graph_track.py",
 66    "name": "cayley_cycle_distance"
 67  },
 68  "idea": {
 69    "best_cfg": {
 70      "lr": 0.01
 71    },
 72    "mean": 0.0004770873465531622,
 73    "n": 8,
 74    "per_seed": [
 75      0.0005058773094788194,
 76      0.0003577241732273251,
 77      0.0005983486771583557,
 78      9.690735168987885e-05,
 79      0.0003379806294105947,
 80      0.0003559936594683677,
 81      0.0005321577191352844,
 82      0.0010317092528566718
 83    ],
 84    "std": 0.0002546983835343552,
 85    "sweep": [
 86      {
 87        "cfg": {
 88          "lr": 0.001
 89        },
 90        "mean": 0.02106541721150279
 91      },
 92      {
 93        "cfg": {
 94          "lr": 0.003
 95        },
 96        "mean": 0.0008379632126889192
 97      },
 98      {
 99        "cfg": {
100          "lr": 0.01
101        },
102        "mean": 0.0004770873465531622
103      }
104    ]
105  },
106  "math_check": {
107    "cycle_sum_mod_n": 0,
108    "group": "Z_32",
109    "max_edge_increment_error": 0,
110    "path_independence": true
111  },
112  "mechanism_signature": {
113    "baseline_mean_output_change": 0.2193981111049652,
114    "confirmed": true,
115    "idea_mean_output_change": 0.0,
116    "predicted_idea_change": 0.0,
117    "prediction": "relative group differences are invariant to simultaneous vertex translation"
118  },
119  "metric_direction": "lower is better",
120  "model": "mlp_tiny",
121  "n_seeds": 8,
122  "protocol_notes": {
123    "batch": 128,
124    "epochs": 18,
125    "grid_union": [
126      {
127        "lr": 0.001
128      },
129      {
130        "lr": 0.003
131      },
132      {
133        "lr": 0.01
134      }
135    ],
136    "paired_seeds": [
137      0,
138      1,
139      2,
140      3,
141      4,
142      5,
143      6,
144      7
145    ],
146    "structure_justification": "The custom task is a cyclic Cayley graph distance prediction problem, directly containing generator increments, cycle constraints, and relative group displacements."
147  },
148  "track": "cayley_cycle_distance"
149}