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
