OUTPUT of run 3 of at most 100: ``` L0 OV spectra 0 [8.0675 3.3266 2.0965 0.6725 0.5605 0.3138 0.2573 0.1923 0.1454 0.1409 0.1155 0.1128 0.1006 0.0849 0.0811 0.0724 0.0712 0.0656 0.0612 0.0571 0.0528 0.0489 0.047 0.0456 0.043 0.0395 0.0389 0.0361 0.0352 0.0335 0.0316 0.0304] 1 [5.6578 3.8262 1.0639 0.5023 0.4283 0.2699 0.2168 0.1662 0.1512 0.112 0.0944 0.0923 0.0829 0.0769 0.0712 0.0676 0.0621 0.0566 0.0552 0.0525 0.0499 0.0447 0.0435 0.0419 0.0384 0.0362 0.0357 0.0323 0.0321 0.031 0.0302 0.0285] 2 [0.7872 0.718 0.682 0.6712 0.6362 0.6009 0.5687 0.5579 0.55 0.5221 0.5148 0.4858 0.4799 0.4694 0.4386 0.4206 0.4004 0.3928 0.3466 0.3042 0.2771 0.2754 0.2554 0.2285 0.2179 0.2048 0.1813 0.1699 0.1626 0.1591 0.1313 0.1181] 3 [1.0317 0.964 0.6167 0.5045 0.4475 0.2267 0.2014 0.1834 0.1719 0.1475 0.1364 0.117 0.1057 0.093 0.0874 0.0833 0.0765 0.065 0.0612 0.0591 0.0545 0.0495 0.0465 0.0458 0.0394 0.0382 0.0359 0.0322 0.0315 0.0298 0.0284 0.0259] 4 [3.3943 1.6416 1.0818 0.6072 0.3784 0.3273 0.2313 0.2045 0.1705 0.1412 0.1263 0.1156 0.1029 0.1003 0.0812 0.0771 0.0741 0.0648 0.0593 0.0572 0.0538 0.0494 0.0464 0.0439 0.0401 0.0383 0.0367 0.0346 0.0334 0.0312 0.0306 0.0295] 5 [8.3281 3.6039 1.6786 0.7676 0.5104 0.3903 0.3443 0.3045 0.2473 0.1927 0.1667 0.1265 0.1142 0.1088 0.0982 0.0936 0.0851 0.0714 0.0675 0.0611 0.06 0.0574 0.0562 0.0517 0.0493 0.0461 0.0436 0.0403 0.0381 0.0364 0.0343 0.032 ] L0 OV pairwise cosines [[1. 0.885 0.008 0.164 0.903 0.724] [0.885 1. 0.006 0.195 0.889 0.802] [0.008 0.006 1. 0.012 0.006 0.017] [0.164 0.195 0.012 1. 0.195 0.156] [0.903 0.889 0.006 0.195 1. 0.728] [0.724 0.802 0.017 0.156 0.728 1. ]] Joint broad-head output spectrum [11.9885 8.4303 3.3621 1.3104 0.9989 0.8608 0.73 0.6052 0.566 0.54 0.4823 0.4356 0.3927 0.3667 0.3463 0.3207 0.3058 0.2952 0.262 0.246 0.2384 0.215 0.2062 0.1875 0.1871 0.1741 0.171 0.1613 0.1555 0.153 0.1481 0.1405 0.1331 0.1328 0.125 ] Broad-output subspace dimension 2 layer 1 Q/K/both energy [[0.061 0.575 0.047] [0.065 0.537 0.052] [0.06 0.549 0.049] [0.059 0.555 0.046] [0.057 0.603 0.046] [0.068 0.549 0.053]] layer 2 Q/K/both energy [[0.028 0.092 0.022] [0.008 0.044 0.007] [0.02 0.177 0.016] [0.038 0.092 0.031] [0.03 0.092 0.025] [0.031 0.088 0.025]] layer 3 Q/K/both energy [[0.001 0.013 0.001] [0.001 0.002 0. ] [0.012 0.069 0.008] [0.016 0.065 0.011] [0.005 0.044 0.003] [0.003 0.008 0. ]] Broad-output subspace dimension 4 layer 1 Q/K/both energy [[0.099 0.65 0.08 ] [0.092 0.607 0.075] [0.086 0.642 0.076] [0.09 0.644 0.076] [0.091 0.701 0.078] [0.142 0.636 0.117]] layer 2 Q/K/both energy [[0.037 0.101 0.026] [0.015 0.055 0.009] [0.042 0.2 0.031] [0.048 0.1 0.036] [0.039 0.102 0.029] [0.04 0.097 0.028]] layer 3 Q/K/both energy [[0.005 0.017 0.001] [0.006 0.007 0.001] [0.02 0.076 0.009] [0.021 0.071 0.012] [0.012 0.048 0.004] [0.016 0.014 0.001]] Broad-output subspace dimension 8 layer 1 Q/K/both energy [[0.214 0.658 0.176] [0.216 0.614 0.183] [0.235 0.649 0.211] [0.229 0.653 0.199] [0.244 0.711 0.215] [0.27 0.644 0.228]] layer 2 Q/K/both energy [[0.052 0.111 0.031] [0.029 0.067 0.01 ] [0.069 0.215 0.044] [0.064 0.11 0.042] [0.057 0.113 0.037] [0.057 0.107 0.035]] layer 3 Q/K/both energy [[0.015 0.027 0.002] [0.019 0.021 0.002] [0.04 0.091 0.014] [0.039 0.082 0.015] [0.026 0.062 0.006] [0.048 0.031 0.004]] Broad-output subspace dimension 16 layer 1 Q/K/both energy [[0.258 0.672 0.204] [0.263 0.626 0.209] [0.278 0.662 0.241] [0.28 0.666 0.23 ] [0.303 0.726 0.259] [0.324 0.666 0.262]] layer 2 Q/K/both energy [[0.081 0.137 0.041] [0.056 0.089 0.014] [0.098 0.244 0.058] [0.095 0.133 0.051] [0.087 0.134 0.047] [0.088 0.132 0.043]] layer 3 Q/K/both energy [[0.037 0.051 0.004] [0.047 0.052 0.007] [0.067 0.111 0.019] [0.065 0.104 0.021] [0.054 0.083 0.01 ] [0.081 0.061 0.008]] Key-bias vector cosines within layers 0 [[ 1. 0.259 0.055 0.18 -0.119 -0.169] [ 0.259 1. -0.169 0.089 -0.058 -0.425] [ 0.055 -0.169 1. 0.451 -0.225 0.019] [ 0.18 0.089 0.451 1. -0.446 -0.3 ] [-0.119 -0.058 -0.225 -0.446 1. 0.374] [-0.169 -0.425 0.019 -0.3 0.374 1. ]] 1 [[1. 0.967 0.961 0.961 0.945 0.959] [0.967 1. 0.976 0.963 0.967 0.962] [0.961 0.976 1. 0.969 0.971 0.966] [0.961 0.963 0.969 1. 0.964 0.967] [0.945 0.967 0.971 0.964 1. 0.972] [0.959 0.962 0.966 0.967 0.972 1. ]] 2 [[1. 0.839 0.875 0.909 0.926 0.907] [0.839 1. 0.858 0.845 0.849 0.832] [0.875 0.858 1. 0.863 0.88 0.851] [0.909 0.845 0.863 1. 0.925 0.914] [0.926 0.849 0.88 0.925 1. 0.904] [0.907 0.832 0.851 0.914 0.904 1. ]] 3 [[ 1. 0.08 0.403 0.336 0.361 0.192] [ 0.08 1. -0.049 -0.173 -0.013 -0.028] [ 0.403 -0.049 1. 0.7 0.649 0.201] [ 0.336 -0.173 0.7 1. 0.628 0.258] [ 0.361 -0.013 0.649 0.628 1. 0.228] [ 0.192 -0.028 0.201 0.258 0.228 1. ]] L0H2 nonzero effective QK eigenvalues, sorted by phase (positive imaginary part) magnitude, phase [[0.5123 0.0533] [0.7691 0.5616] [0.0324 0.655 ] [1.0295 0.9098] [0.6117 0.9859] [0.9325 1.2064] [0.1356 1.4186] [0.9555 1.8152] [0.0438 2.2779] [0.3409 2.3246] [0.3192 2.7337] [0.846 2.7354]] L0H2 effective V singular values [0.4305 0.4155 0.3844 0.3695 0.3615 0.3482 0.3276 0.3153 0.3091 0.3019 0.3002 0.2964 0.2916 0.2741 0.2653 0.2643 0.2597 0.2535 0.2471 0.2447 0.235 0.2317 0.23 0.2235 0.2159 0.2131 0.2056 0.1984 0.1913 0.1877 0.1848 0.181 0.1727 0.1611 0.1575 0.1521 0.1505 0.1366 0.1268 0.123 0.1143 0.1138 0.1063 0.1011 0.0968 0.0929 0.0898 0.0875 0.0852 0.0845 0.0816 0.0744 0.0733 0.0701 0.0672 0.0649 0.0628 0.0596 0.0582 0.0561 0.0545 0.0502 0.0469 0.0451] V-input subspace dimension 16 layer 1 composition trace/F, symmetry, positive-symmetric-mass [[-0.014 -0.007 0.496] [-0.11 0.257 0.474] [ 0.73 0.145 0.661] [ 0.589 0.225 0.624] [ 0.708 0.067 0.658] [-0.055 -0. 0.486]] layer 2 composition trace/F, symmetry, positive-symmetric-mass [[-0.435 -0.039 0.403] [-0.443 0.248 0.411] [-0.015 0.053 0.497] [ 0.394 -0.01 0.585] [-0.855 0.031 0.319] [-0.087 0.053 0.482]] layer 3 composition trace/F, symmetry, positive-symmetric-mass [[-0.269 0.032 0.445] [ 2.745 0.775 0.976] [ 0.39 0.054 0.578] [ 0.096 -0.064 0.521] [-0.372 0.205 0.426] [ 0.279 0.107 0.558]] V-input subspace dimension 24 layer 1 composition trace/F, symmetry, positive-symmetric-mass [[-0.266 0.022 0.435] [-0.025 0.224 0.495] [ 0.636 0.078 0.629] [ 0.674 0.128 0.629] [ 0.688 0.089 0.637] [ 0.201 0.022 0.545]] layer 2 composition trace/F, symmetry, positive-symmetric-mass [[-0.451 -0.014 0.417] [-0.5 0.118 0.412] [ 0.121 0.031 0.522] [ 0.266 -0.009 0.548] [-0.578 -0.019 0.395] [-0.019 0.013 0.497]] layer 3 composition trace/F, symmetry, positive-symmetric-mass [[-0.128 0.014 0.477] [ 2.907 0.649 0.95 ] [ 0.263 0.069 0.545] [-0.016 -0.083 0.497] [-0.296 0.166 0.45 ] [ 0.278 0.061 0.55 ]] V-input subspace dimension 28 layer 1 composition trace/F, symmetry, positive-symmetric-mass [[-0.308 0.048 0.431] [-0.022 0.209 0.496] [ 0.576 0.066 0.612] [ 0.711 0.118 0.633] [ 0.719 0.065 0.638] [ 0.189 0.013 0.54 ]] layer 2 composition trace/F, symmetry, positive-symmetric-mass [[-0.296 -0.013 0.447] [-0.419 0.11 0.431] [ 0.111 0.042 0.519] [ 0.207 -0.02 0.536] [-0.515 -0.006 0.414] [-0.018 0.009 0.497]] layer 3 composition trace/F, symmetry, positive-symmetric-mass [[-0.159 -0.003 0.473] [ 2.954 0.629 0.931] [ 0.238 0.012 0.539] [ 0.012 -0.08 0.502] [-0.328 0.124 0.448] [ 0.185 0.054 0.532]] V-input subspace dimension 40 layer 1 composition trace/F, symmetry, positive-symmetric-mass [[-0.263 0.057 0.444] [-0.009 0.185 0.498] [ 0.575 0.061 0.605] [ 0.582 0.089 0.605] [ 0.6 0.042 0.611] [ 0.18 0.022 0.537]] layer 2 composition trace/F, symmetry, positive-symmetric-mass [[-0.233 -0.009 0.462] [-0.306 0.063 0.455] [ 0.07 0.031 0.51 ] [ 0.18 -0.008 0.527] [-0.434 -0.006 0.436] [ 0.024 0.006 0.504]] layer 3 composition trace/F, symmetry, positive-symmetric-mass [[-0.127 0.008 0.482] [ 2.748 0.536 0.879] [ 0.182 0.001 0.526] [ 0.083 -0.044 0.512] [-0.302 0.074 0.457] [ 0.147 0.042 0.522]] MLP matrix-product spectra (not applying ReLU) 0 norm 182.075 trace 108.759 topSV [125.589 39.838 32.492 30.802 28.038 27.085 26.097 25.622 23.929 23.842 23.274 22.856 22.364 22.005 21.639 20.807 20.641 20.022 19.713 18.934 18.543 17.739 17.313 17.036 16.473 15.955 15.529 15.188 14.793 14.06 13.656 13.021 12.343 12.15 11.156] 1 norm 173.737 trace -379.418 topSV [76.145 32.918 27.909 26.868 25.244 24.417 24.076 23.193 23.072 22.428 22.228 22.016 21.36 21.149 21.061 20.413 20.317 19.89 19.459 19.177 18.917 18.702 18.598 18.15 18.072 17.965 17.612 17.442 17.182 16.847 16.777 16.276 16.127 16.003 15.684] 2 norm 207.809 trace -889.497 topSV [67.851 29.898 27.249 26.671 26.128 25.792 25.323 25.096 24.492 24.232 23.887 23.663 22.747 22.503 22.125 21.628 21.282 21.039 20.607 20.483 20.344 20.152 20.062 19.816 19.573 19.249 18.907 18.719 18.626 18.472 18.392 18.304 17.976 17.857 17.803] 3 norm 232.49 trace -926.657 topSV [133.224 55.432 48.819 45.113 38.683 38.229 37.439 36.181 35.707 35.113 33.956 33.208 31.855 30.777 29.986 29.814 29.384 28.138 26.731 25.424 25.262 24.435 24.105 23.314 22.456 21.569 20.308 19.311 18.704 18.259 17.235 16.782 16.385 15.897 15.172] ```