OUTPUT of run 4 of at most 100: ``` L0 OV input/output energy in candidate position space, dimension 16 0 total input/output [0.8579 0.216 ] top 5 input-vector overlaps [0.9539 0.5383 0.4343 0.0771 0.0913] top 5 output-vector overlaps [0.2457 0.0895 0.1317 0.0972 0.0261] 1 total input/output [0.8805 0.1878] top 5 input-vector overlaps [0.925 0.878 0.1423 0.0393 0.0678] top 5 output-vector overlaps [0.2379 0.0876 0.1431 0.0817 0.042 ] 2 total input/output [0.085 0.1071] top 5 input-vector overlaps [0.0367 0.0384 0.0507 0.0456 0.0534] top 5 output-vector overlaps [0.0753 0.0774 0.1159 0.0668 0.047 ] 3 total input/output [0.1107 0.0716] top 5 input-vector overlaps [0.1557 0.0964 0.0366 0.094 0.0347] top 5 output-vector overlaps [0.1296 0.0318 0.0227 0.0476 0.066 ] 4 total input/output [0.7985 0.1946] top 5 input-vector overlaps [0.9263 0.7577 0.1711 0.048 0.0472] top 5 output-vector overlaps [0.2369 0.0879 0.13 0.0363 0.059 ] 5 total input/output [0.8505 0.1501] top 5 input-vector overlaps [0.8973 0.8437 0.1056 0.152 0.069 ] top 5 output-vector overlaps [0.145 0.1923 0.1161 0.1198 0.0688] L0 head top QK and OV singular-direction pairwise alignments Q vs Q [[ 1. -0.77 0.434 0.797 -0.129 -0.24 ] [-0.77 1. -0.528 -0.738 0.229 0.048] [ 0.434 -0.528 1. 0.492 -0.113 0.07 ] [ 0.797 -0.738 0.492 1. 0.064 0.033] [-0.129 0.229 -0.113 0.064 1. 0.326] [-0.24 0.048 0.07 0.033 0.326 1. ]] K vs K [[ 1. -0.264 -0.057 -0.003 -0.38 -0.098] [-0.264 1. 0.02 0.124 0.258 -0.143] [-0.057 0.02 1. 0.529 0.019 0.13 ] [-0.003 0.124 0.529 1. -0.101 0.012] [-0.38 0.258 0.019 -0.101 1. 0.643] [-0.098 -0.143 0.13 0.012 0.643 1. ]] V vs V [[ 1. 0.945 0.066 -0.044 0.962 -0.692] [ 0.945 1. 0.076 0.181 0.957 -0.639] [ 0.066 0.076 1. -0.005 0.037 -0.077] [-0.044 0.181 -0.005 1. 0.134 0.259] [ 0.962 0.957 0.037 0.134 1. -0.71 ] [-0.692 -0.639 -0.077 0.259 -0.71 1. ]] K vs V [[ 0.093 0.189 -0.417 0.262 0.156 0.075] [-0.011 -0.108 0.137 -0.175 -0.076 0.012] [-0.55 -0.535 -0.006 0.06 -0.531 0.509] [-0.81 -0.763 0.019 0.17 -0.826 0.926] [ 0.03 -0.198 -0.061 -0.471 -0.032 -0.166] [-0.211 -0.399 -0.244 -0.447 -0.243 -0.035]] Induction-candidate symmetric composition eigenvalues Largest 45 [0.1007 0.0826 0.0765 0.0738 0.0698 0.0647 0.0602 0.0561 0.0543 0.0525 0.0467 0.0417 0.039 0.035 0.0274 0.0252 0.0242 0.0186 0.0168 0.0127 0.0119 0.0111 0.0106 0.0089 0.0075 0.0063 0.006 0.0052 0.0046 0.0041 0.0035 0.0032 0.0031 0.0028 0.0024 0.0022 0.002 0.0018 0.0016 0.0014 0.0012 0.0011 0.001 0.0007 0.0007] Smallest 15 [-0.049 -0.0465 -0.0392 -0.039 -0.0354 -0.0339 -0.0308 -0.0297 -0.0291 -0.0285 -0.0249 -0.0234 -0.0228 -0.0192 -0.019 ] Positive composition-space overlap with position [0.028 0.027 0.027 0.027 0.026 0.05 0.034 0.029 0.028 0.017 0.022 0.029 0.02 0.024 0.059 0.07 0.049 0.095 0.063 0.18 0.157 0.235 0.132 0.274] current read SV [5.217 4.652 4.602 4.101 4.026 3.99 3.691 3.508 3.387 3.352 3.266 3.163 3.043 2.978 2.898 2.744 2.717 2.514 2.338 2.144 1.946 1.868 1.618 1.451] current read row-norm quantiles [0.04 0.074 0.085 0.104 0.308 0.752 1.332 2.341] previous-head read SV [3.087 2.192 2.091 1.913 1.84 1.665 1.595 1.526 1.441 1.306 1.235 1.122 1.046 0.97 0.901 0.861 0.767 0.661 0.503 0.333 0.266 0.23 0.189 0.165] previous-head read row-norm quantiles [0.014 0.024 0.028 0.034 0.085 0.339 0.579 0.937] First-MLP read composition strengths 0 F norm 15.046 top SV [13.942 4.323 2.45 1.777 1.434 0.975 0.637 0.548 0.342 0.273 0.22 0.186] 1 F norm 12.339 top SV [11.585 3.113 1.773 1.447 1.274 0.75 0.612 0.44 0.273 0.251 0.209 0.18 ] 2 F norm 8.418 top SV [3.742 2.715 2.602 2.407 2.33 1.984 1.953 1.904 1.774 1.624 1.61 1.404] 3 F norm 5.595 top SV [3.768 3.265 1.68 1.388 0.948 0.48 0.336 0.294 0.254 0.25 0.228 0.204] 4 F norm 7.0 top SV [6.275 2.011 1.433 1.046 0.894 0.781 0.52 0.497 0.357 0.326 0.272 0.188] 5 F norm 10.572 top SV [8.934 3.367 2.835 2.263 1.652 1.242 1.077 0.839 0.744 0.577 0.296 0.261] Final-MLP projection spectrum tail and consecutive ratios 16 13.4999 1.0156 17 13.2929 1.0608 18 12.5312 1.0105 19 12.4015 1.0371 20 11.9578 1.0185 21 11.7405 1.0126 22 11.5943 1.1184 23 10.3667 1.2414 24 8.3505 1.0356 25 8.0636 1.0189 26 7.9141 1.0607 27 7.461 1.0412 28 7.1656 1.2284 29 5.8331 1.4326 30 4.0718 1.2643 31 3.2206 1.0261 32 3.1387 1.1046 33 2.8415 1.0148 34 2.8001 1.0419 35 2.6874 1.0454 36 2.5707 1.0698 37 2.4029 1.0321 38 2.3282 1.0376 39 2.2438 1.0269 40 2.185 1.0019 ```