Isometric tensor-network token mixer / results.json

Mechanism confirmed, baseline not beaten

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  1{
  2  "seed": 1620,
  3  "predictions": [
  4    "For every N=2^k, ||T x||/||x|| = 1 exactly up to floating point.",
  5    "T^*T-I is at machine precision and does not grow materially with N.",
  6    "If every local gate is scaled by 1+eps, repeated-pass norm drift is (1+eps)^(k*r), k=log2(N)."
  7  ],
  8  "unitarity_sweep": [
  9    {
 10      "N": 4,
 11      "levels": 2,
 12      "unitarity_fro_error": 6.518129683673256e-16,
 13      "norm_ratio": 1.0,
 14      "predicted_norm_ratio": 1.0
 15    },
 16    {
 17      "N": 8,
 18      "levels": 3,
 19      "unitarity_fro_error": 1.4324005761866033e-15,
 20      "norm_ratio": 1.0,
 21      "predicted_norm_ratio": 1.0
 22    },
 23    {
 24      "N": 16,
 25      "levels": 4,
 26      "unitarity_fro_error": 3.1637566171101538e-15,
 27      "norm_ratio": 0.9999999999999998,
 28      "predicted_norm_ratio": 1.0
 29    },
 30    {
 31      "N": 32,
 32      "levels": 5,
 33      "unitarity_fro_error": 3.95486773296341e-15,
 34      "norm_ratio": 0.9999999999999998,
 35      "predicted_norm_ratio": 1.0
 36    },
 37    {
 38      "N": 64,
 39      "levels": 6,
 40      "unitarity_fro_error": 7.607348859942032e-15,
 41      "norm_ratio": 0.9999999999999999,
 42      "predicted_norm_ratio": 1.0
 43    }
 44  ],
 45  "controlled_drift": [
 46    {
 47      "epsilon": 0.0,
 48      "repetitions": 1,
 49      "observed": 0.9999999999999998,
 50      "predicted": 1.0,
 51      "relative_error": 2.220446049250313e-16
 52    },
 53    {
 54      "epsilon": 0.0,
 55      "repetitions": 4,
 56      "observed": 0.9999999999999989,
 57      "predicted": 1.0,
 58      "relative_error": 1.1102230246251565e-15
 59    },
 60    {
 61      "epsilon": 0.0,
 62      "repetitions": 8,
 63      "observed": 0.9999999999999986,
 64      "predicted": 1.0,
 65      "relative_error": 1.4432899320127035e-15
 66    },
 67    {
 68      "epsilon": 0.001,
 69      "repetitions": 1,
 70      "observed": 1.0050100100050003,
 71      "predicted": 1.0050100100050003,
 72      "relative_error": 0.0
 73    },
 74    {
 75      "epsilon": 0.001,
 76      "repetitions": 4,
 77      "observed": 1.0201911448605396,
 78      "predicted": 1.0201911448605405,
 79      "relative_error": 8.706000088067209e-16
 80    },
 81    {
 82      "epsilon": 0.001,
 83      "repetitions": 8,
 84      "observed": 1.0407899720518592,
 85      "predicted": 1.0407899720518605,
 86      "relative_error": 1.2800542523711052e-15
 87    },
 88    {
 89      "epsilon": 0.01,
 90      "repetitions": 1,
 91      "observed": 1.0510100500999997,
 92      "predicted": 1.0510100501000001,
 93      "relative_error": 4.2253564540872753e-16
 94    },
 95    {
 96      "epsilon": 0.01,
 97      "repetitions": 4,
 98      "observed": 1.2201900399479657,
 99      "predicted": 1.220190039947967,
100      "relative_error": 1.0918525688072328e-15
101    },
102    {
103      "epsilon": 0.01,
104      "repetitions": 8,
105      "observed": 1.4888637335882187,
106      "predicted": 1.4888637335882213,
107      "relative_error": 1.7896434703790782e-15
108    },
109    {
110      "epsilon": 0.05,
111      "repetitions": 1,
112      "observed": 1.2762815625,
113      "predicted": 1.2762815625000004,
114      "relative_error": 3.479555161638265e-16
115    },
116    {
117      "epsilon": 0.05,
118      "repetitions": 4,
119      "observed": 2.6532977051444195,
120      "predicted": 2.653297705144422,
121      "relative_error": 1.0042353158992168e-15
122    },
123    {
124      "epsilon": 0.05,
125      "repetitions": 8,
126      "observed": 7.039988712124649,
127      "predicted": 7.039988712124658,
128      "relative_error": 1.2616190963068666e-15
129    }
130  ],
131  "inverse_reconstruction_error": 3.935883022631844e-15,
132  "toy_fit": {
133    "N": 16,
134    "samples": 256,
135    "steps": 300,
136    "structured_params": 128,
137    "dense_complex_params": 256,
138    "structured_final_mse": 2.6289821430935945e-09,
139    "dense_final_mse": 6.717594010349423e-14,
140    "structured_curve": [
141      1.7592724561691284,
142      0.0034636000636965036,
143      1.7555914382683113e-05,
144      4.507657536123588e-08,
145      2.6289821430935945e-09
146    ],
147    "dense_curve": [
148      2.1629297733306885,
149      0.004571008030325174,
150      3.12544361804612e-05,
151      7.688760739199552e-10,
152      6.717594010349423e-14
153    ],
154    "seconds": 15.026386260986328,
155    "device": "cuda"
156  }
157}