OUTPUT of run 21 of at most 60:
```
=== TASK-ASSOCIATED WRITING SUBSPACES ===
Ranks: {'digits': 9, 'colors': 7, 'regions': 5, 'cities': 12, 'languages': 9} union rank: 42
Enrichment compares captured squared weight difference with eight
matched-rank vocabulary contrast subspaces.
Relative change compares projected A/B output matrices, not activations.
Neither quantity is causal importance.

=== ALL MLPs ===
L | union fraction raw/diag | minimum raw/diag enrichment by domain
Domain order: ['digits', 'colors', 'regions', 'cities', 'languages']
 0 | 0.074/0.038 |   0.86   0.82   0.63   0.81   0.77
 1 | 0.077/0.026 |   1.00   1.00   0.87   1.11   1.12
 2 | 0.079/0.053 |   1.17   0.82   1.06   0.94   0.99
 3 | 0.067/0.050 |   0.90   0.91   0.83   0.87   0.85
 4 | 0.065/0.049 |   0.86   0.82   0.74   0.85   0.84
 5 | 0.065/0.044 |   0.76   0.75   0.72   0.89   0.82
 6 | 0.067/0.048 |   0.79   0.76   0.79   1.00   0.89
 7 | 0.066/0.048 |   0.74   0.73   0.83   0.90   0.86
 8 | 0.067/0.050 |   0.75   0.85   0.84   1.00   0.87
 9 | 0.065/0.048 |   0.76   0.79   0.85   0.90   0.77
10 | 0.069/0.051 |   0.82   0.85   0.80   1.01   0.97
11 | 0.073/0.077 |   1.43   1.23   1.06   1.00   0.97
12 | 0.090/0.100 |   2.05   1.28   1.22   1.10   0.92
13 | 0.106/0.114 |   2.86   1.38   1.41   1.09   0.95
14 | 0.151/0.140 |   5.66   1.68   1.71   1.04   0.98
15 | 0.228/0.206 |   9.70   1.98   2.29   1.07   1.00
16 | 0.369/0.326 |  15.97   2.93   3.11   1.28   1.14
17 | 0.552/0.441 |  13.24   2.98   3.44   1.98   1.45

=== ATTENTION HEADS: TOP SIX PER DOMAIN BY ROBUST ENRICHMENT ===
digits
 L17H3: enrichment=21.39/22.71; captured=33.90%/31.75%; projected-relative-change=5.623%/6.315%
 L16H3: enrichment=13.11/12.10; captured=20.53%/15.94%; projected-relative-change=4.050%/4.805%
 L16H1: enrichment=11.59/10.31; captured=18.16%/13.91%; projected-relative-change=4.029%/5.347%
 L16H2: enrichment=11.43/10.21; captured=17.78%/13.63%; projected-relative-change=3.102%/3.589%
 L16H0: enrichment=10.10/8.95; captured=15.40%/12.17%; projected-relative-change=2.926%/3.514%
 L17H0: enrichment=6.24/6.61; captured=11.16%/10.34%; projected-relative-change=2.468%/2.564%
colors
 L17H2: enrichment=9.83/10.11; captured=14.19%/12.83%; projected-relative-change=2.357%/2.450%
 L17H0: enrichment=5.09/5.28; captured=7.16%/6.62%; projected-relative-change=1.233%/1.270%
 L17H1: enrichment=3.94/3.95; captured=5.89%/5.21%; projected-relative-change=1.994%/2.122%
 L15H0: enrichment=2.86/4.02; captured=3.43%/3.52%; projected-relative-change=1.286%/1.488%
 L16H2: enrichment=2.42/2.20; captured=2.96%/2.40%; projected-relative-change=1.658%/1.914%
 L14H2: enrichment=2.39/2.18; captured=2.89%/2.32%; projected-relative-change=1.024%/1.282%
regions
 L17H2: enrichment=4.34/4.29; captured=4.51%/3.93%; projected-relative-change=1.496%/1.449%
 L17H1: enrichment=4.07/4.03; captured=4.42%/3.84%; projected-relative-change=2.018%/2.154%
 L17H0: enrichment=3.12/3.08; captured=3.24%/2.85%; projected-relative-change=0.879%/0.856%
 L12H2: enrichment=2.37/4.38; captured=2.14%/2.60%; projected-relative-change=0.930%/0.998%
 L16H0: enrichment=2.58/2.30; captured=2.20%/1.75%; projected-relative-change=1.783%/1.853%
 L15H0: enrichment=2.23/3.39; captured=2.07%/2.30%; projected-relative-change=1.337%/1.554%
cities
 L17H1: enrichment=1.62/1.75; captured=3.92%/3.62%; projected-relative-change=1.258%/1.353%
 L17H3: enrichment=1.46/1.67; captured=3.35%/3.43%; projected-relative-change=1.335%/1.650%
 L17H2: enrichment=1.44/1.56; captured=3.54%/3.31%; projected-relative-change=0.843%/0.845%
 L17H0: enrichment=1.42/1.58; captured=3.33%/3.24%; projected-relative-change=0.563%/0.568%
 L11H1: enrichment=1.21/2.26; captured=2.30%/2.74%; projected-relative-change=1.031%/1.771%
 L12H2: enrichment=1.20/2.01; captured=2.47%/2.83%; projected-relative-change=0.636%/0.632%
languages
 L17H1: enrichment=1.42/1.46; captured=2.72%/2.45%; projected-relative-change=1.179%/1.233%
 L17H3: enrichment=1.27/1.43; captured=2.35%/2.38%; projected-relative-change=1.353%/1.625%
 L17H2: enrichment=1.16/1.24; captured=2.22%/2.07%; projected-relative-change=0.701%/0.696%
 L11H1: enrichment=1.14/2.18; captured=1.66%/2.13%; projected-relative-change=1.040%/1.768%
 L14H0: enrichment=1.13/1.13; captured=1.66%/1.49%; projected-relative-change=0.831%/1.000%
 L17H0: enrichment=1.09/1.15; captured=2.19%/2.04%; projected-relative-change=0.492%/0.477%

=== WITHIN-LAYER HEAD SHARES OF TASK-ASSOCIATED OUTPUT-WEIGHT CHANGE ===
These shares decompose squared output-matrix change, not head activity.
L00 digits     raw=[0.208 0.243 0.243 0.307] diag=[0.216 0.269 0.239 0.276]
L00 colors     raw=[0.195 0.272 0.253 0.28 ] diag=[0.255 0.234 0.247 0.264]
L00 regions    raw=[0.228 0.263 0.219 0.29 ] diag=[0.234 0.255 0.238 0.273]
L00 cities     raw=[0.211 0.275 0.22  0.295] diag=[0.235 0.235 0.274 0.256]
L00 languages  raw=[0.194 0.267 0.261 0.278] diag=[0.238 0.269 0.2   0.293]
L14 digits     raw=[0.24  0.213 0.287 0.26 ] diag=[0.242 0.21  0.289 0.258]
L14 colors     raw=[0.187 0.268 0.364 0.181] diag=[0.19  0.255 0.371 0.184]
L14 regions    raw=[0.18  0.269 0.332 0.219] diag=[0.183 0.267 0.32  0.23 ]
L14 cities     raw=[0.218 0.256 0.25  0.276] diag=[0.233 0.258 0.248 0.261]
L14 languages  raw=[0.236 0.258 0.26  0.246] diag=[0.248 0.253 0.264 0.235]
L15 digits     raw=[0.151 0.288 0.314 0.247] diag=[0.149 0.29  0.31  0.251]
L15 colors     raw=[0.322 0.201 0.248 0.23 ] diag=[0.315 0.205 0.25  0.229]
L15 regions    raw=[0.306 0.24  0.216 0.238] diag=[0.298 0.248 0.217 0.237]
L15 cities     raw=[0.231 0.264 0.237 0.268] diag=[0.216 0.279 0.249 0.257]
L15 languages  raw=[0.227 0.261 0.252 0.26 ] diag=[0.212 0.281 0.253 0.254]
L16 digits     raw=[0.208 0.244 0.247 0.3  ] diag=[0.209 0.244 0.246 0.301]
L16 colors     raw=[0.239 0.23  0.299 0.232] diag=[0.239 0.232 0.298 0.232]
L16 regions    raw=[0.317 0.237 0.259 0.187] diag=[0.32  0.235 0.261 0.184]
L16 cities     raw=[0.254 0.239 0.241 0.266] diag=[0.254 0.245 0.244 0.257]
L16 languages  raw=[0.246 0.247 0.261 0.247] diag=[0.249 0.252 0.259 0.24 ]
L17 digits     raw=[0.157 0.132 0.098 0.613] diag=[0.157 0.132 0.097 0.614]
L17 colors     raw=[0.222 0.222 0.454 0.102] diag=[0.22  0.219 0.452 0.109]
L17 regions    raw=[0.213 0.354 0.307 0.126] diag=[0.212 0.359 0.309 0.121]
L17 cities     raw=[0.207 0.297 0.228 0.268] diag=[0.207 0.291 0.223 0.279]
L17 languages  raw=[0.203 0.306 0.212 0.279] diag=[0.197 0.298 0.211 0.293]

=== MLP UNIT CONCENTRATION IN THE UNION ANSWER SUBSPACE ===
L geometry | top1 top10 top100 shares | effective number of contributing columns
14 raw  | 0.168% 1.440% 10.232% | 1758.4
14 diag | 0.170% 1.466% 10.321% | 1749.6
15 raw  | 0.151% 1.352% 10.677% | 1713.5
15 diag | 0.150% 1.343% 10.708% | 1715.2
16 raw  | 0.232% 1.693% 11.572% | 1645.9
16 diag | 0.230% 1.693% 11.524% | 1646.6
17 raw  | 0.250% 1.688% 12.089% | 1600.0
17 diag | 0.258% 1.748% 12.292% | 1583.9

=== L17 MLP: FIVE LARGEST CONDITIONAL WRITING-CHANGE COLUMNS PER DOMAIN ===
raw digits [(956, 0.322), (1751, 0.225), (1149, 0.221), (18, 0.203), (1470, 0.203)]
raw colors [(343, 0.372), (450, 0.348), (1666, 0.266), (626, 0.252), (425, 0.25)]
raw regions [(1664, 0.475), (1641, 0.372), (1779, 0.352), (1722, 0.338), (717, 0.321)]
raw cities [(1779, 0.353), (425, 0.308), (1613, 0.303), (1643, 0.289), (457, 0.234)]
raw languages [(1389, 0.356), (425, 0.319), (1455, 0.313), (343, 0.278), (48, 0.278)]
diag digits [(956, 0.334), (1149, 0.251), (1751, 0.223), (1470, 0.215), (1940, 0.205)]
diag colors [(343, 0.402), (450, 0.364), (935, 0.329), (425, 0.284), (24, 0.279)]
diag regions [(1664, 0.469), (1779, 0.377), (1641, 0.352), (1722, 0.345), (1509, 0.329)]
diag cities [(425, 0.388), (1643, 0.375), (1779, 0.361), (1613, 0.333), (1455, 0.33)]
diag languages [(1455, 0.485), (1389, 0.421), (425, 0.421), (1643, 0.368), (48, 0.346)]
Percentages above do not justify assuming positive or nonzero unit coefficients.

```