OUTPUT of run 7 of at most 100:
```
Final MLP output weights after linear regression on input weights.
This is weight-space regression only, not evaluation of an MLP.
Best scalar cancellation coefficient 0.1226
scalar first 55 singular values [28.283 20.308 19.323 19.114 18.692 18.549 18.137 17.786 17.483 16.527 15.894 15.6   14.962 14.885 14.406 14.312 13.34  12.985 12.591 12.374 12.256
 12.037 11.345 11.107 10.768  9.222  8.598  7.927  6.518  5.299  3.919  3.262  2.783  2.656  2.402  2.166  2.125  1.959  1.933  1.864  1.809  1.786
  1.757  1.74   1.704  1.659  1.646  1.626  1.579  1.576  1.56   1.535  1.513  1.502  1.49 ]
gaps [(30, 1.352), (29, 1.23), (28, 1.216), (31, 1.201), (32, 1.172), (25, 1.168), (35, 1.109), (34, 1.106)]
regress first 55 singular values [18.909 18.247 17.385 16.993 16.749 16.475 16.143 15.907 15.758 14.826 14.425 14.017 13.553 13.176 12.916 12.74  11.888 11.44  11.079 10.939 10.762
 10.254  9.966  9.931  9.492  8.276  7.586  7.012  4.48   3.376  2.688  2.222  1.946  1.805  1.713  1.473  1.43   1.362  1.343  1.332  1.314  1.303
  1.276  1.239  1.228  1.205  1.187  1.181  1.172  1.163  1.155  1.15   1.141  1.13   1.119]
gaps [(28, 1.565), (29, 1.327), (30, 1.256), (31, 1.21), (35, 1.163), (25, 1.147), (32, 1.141), (26, 1.091)]

Shared QK subspace: congruence-invariant phase diagnostics.
rank 8
H1 versus transpose [(1.721, 1.0), (2.465, 1.0)]
H5 versus transpose [(1.281, 1.0), (1.896, 1.0), (2.669, 1.0)]
H1 versus H5 [(1.138, 0.121), (2.248, 1.244)]
rank 12
H1 versus transpose [(1.166, 1.0), (1.595, 1.0), (1.88, 0.795), (1.88, 1.257)]
H5 versus transpose [(1.119, 1.0), (1.909, 1.0), (1.957, 1.0), (2.47, 1.135), (2.47, 0.881)]
H1 versus H5 [(0.748, 0.1), (1.525, 0.156), (2.197, 1.26), (2.834, 0.57)]
rank 16
H1 versus transpose [(0.134, 1.0), (0.828, 1.932), (0.828, 0.518), (1.476, 1.0), (1.8, 1.0), (1.993, 1.258), (1.993, 0.795)]
H5 versus transpose [(0.944, 1.0), (1.503, 1.0), (2.092, 1.0), (2.489, 0.779), (2.489, 1.284)]
H1 versus H5 [(0.478, 0.176), (0.823, 0.201), (1.357, 0.155), (1.611, 0.223), (2.133, 1.253), (2.637, 0.951)]
rank 20
H1 versus transpose [(0.067, 1.0), (0.819, 1.0), (1.214, 1.0), (1.627, 1.0), (1.937, 0.792), (1.937, 1.263), (1.94, 1.0)]
H5 versus transpose [(0.753, 1.0), (1.356, 1.0), (1.898, 1.0), (2.226, 1.038), (2.226, 0.963), (2.437, 1.0), (2.79, 1.0), (3.023, 1.0)]
H1 versus H5 [(0.678, 1.291), (0.716, 0.193), (0.925, 0.186), (1.349, 0.164), (1.654, 0.19), (1.995, 1.047), (2.123, 1.336), (2.171, 0.186)]
rank 24
H1 versus transpose [(0.024, 1.0), (0.333, 1.0), (0.958, 4.242), (0.958, 0.236), (1.368, 1.0), (1.563, 1.0), (1.854, 1.0), (1.982, 1.0), (2.652, 1.702), (2.652, 0.587), (2.924, 1.0)]
H5 versus transpose [(1.055, 1.0), (1.713, 1.0), (1.88, 1.0), (2.232, 1.227), (2.232, 0.815), (2.394, 1.0), (2.661, 0.978), (2.661, 1.023)]
H1 versus H5 [(0.114, 1.404), (0.126, 4.66), (0.299, 0.459), (0.823, 0.164), (0.892, 0.169), (1.455, 0.155), (1.584, 0.19), (1.899, 0.212), (2.021, 0.969), (2.132, 1.328), (2.209, 0.431)]
rank 28
H1 versus transpose [(0.084, 1.0), (0.426, 1.0), (0.978, 1.0), (1.517, 1.0), (1.714, 1.0), (1.926, 1.0), (2.355, 1.0), (2.82, 0.144), (2.82, 6.929), (2.933, 1.0)]
H5 versus transpose [(1.13, 1.0), (1.523, 0.136), (1.523, 7.341), (1.6, 1.0), (2.216, 0.603), (2.216, 1.658), (2.37, 1.0), (2.559, 0.908), (2.559, 1.101), (2.735, 0.868), (2.735, 1.152)]
H1 versus H5 [(0.671, 0.373), (0.693, 0.209), (0.915, 0.33), (1.347, 0.142), (1.374, 0.102), (1.58, 0.244), (1.644, 0.135), (2.013, 1.369), (2.014, 0.208), (2.112, 0.49), (2.469, 1.38)]

```