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## CIFAR-10 depth scaling
| depth | method | n | test acc (%) | early-third alignment | wall (s) |
|---:|:---|---:|---:|---:|---:|
| 5 | BP | 5 | 41.546 ± 0.422 | — | 6.9 ± 0.3 |
| 5 | FA | 5 | 38.924 ± 0.729 | 0.630 ± 0.022 | 5.7 ± 1.0 |
| 5 | DFA | 5 | 37.768 ± 0.654 | 0.514 ± 0.032 | 5.0 ± 0.2 |
| 5 | SDIL | 5 | 41.460 ± 0.226 | 0.797 ± 0.018 | 9.8 ± 1.9 |
| 10 | BP | 5 | 41.702 ± 0.730 | — | 11.7 ± 0.3 |
| 10 | FA | 5 | 39.056 ± 0.557 | 0.610 ± 0.022 | 10.0 ± 2.1 |
| 10 | DFA | 5 | 36.716 ± 0.363 | 0.231 ± 0.030 | 9.4 ± 1.7 |
| 10 | SDIL | 5 | 41.046 ± 0.222 | 0.496 ± 0.024 | 19.6 ± 4.4 |
| 20 | BP | 5 | 41.910 ± 0.560 | — | 20.2 ± 1.1 |
| 20 | FA | 5 | 37.448 ± 0.603 | 0.569 ± 0.025 | 18.8 ± 3.6 |
| 20 | DFA | 5 | 37.106 ± 0.710 | 0.126 ± 0.023 | 17.9 ± 3.5 |
| 20 | SDIL | 5 | 41.288 ± 0.606 | 0.403 ± 0.020 | 31.2 ± 1.5 |
| 30 | BP | 5 | 41.908 ± 0.697 | — | 29.8 ± 1.3 |
| 30 | FA | 5 | 38.158 ± 0.517 | 0.593 ± 0.014 | 26.9 ± 1.9 |
| 30 | DFA | 5 | 36.988 ± 0.524 | 0.087 ± 0.007 | 23.4 ± 0.8 |
| 30 | SDIL | 5 | 41.198 ± 0.523 | 0.366 ± 0.007 | 47.8 ± 1.4 |
| 60 | BP | 5 | 41.624 ± 0.781 | — | 58.4 ± 1.0 |
| 60 | FA | 5 | 38.428 ± 0.387 | 0.577 ± 0.011 | 49.8 ± 1.8 |
| 60 | DFA | 5 | 36.898 ± 0.444 | 0.047 ± 0.005 | 47.6 ± 5.6 |
| 60 | SDIL | 5 | 41.246 ± 0.323 | 0.336 ± 0.013 | 96.4 ± 12.4 |
Paired SDIL−DFA gap at d5: 3.692 ± 0.625 points (n=5).
Paired SDIL−DFA gap at d10: 4.330 ± 0.501 points (n=5).
Paired SDIL−DFA gap at d20: 4.182 ± 0.907 points (n=5).
Paired SDIL−DFA gap at d30: 4.210 ± 0.426 points (n=5).
Paired SDIL−DFA gap at d60: 4.348 ± 0.554 points (n=5).
## Somato-dendritic nuisance control
| rho | signal | n | test acc (%) |
|---:|:---|---:|---:|
| 0 | raw | 5 | 97.450 ± 0.046 |
| 0 | matched raw | 5 | 97.450 ± 0.046 |
| 0 | residual | 5 | 97.450 ± 0.046 |
| 0.05 | raw | 5 | 96.438 ± 0.077 |
| 0.05 | matched raw | 5 | 96.980 ± 0.148 |
| 0.05 | residual | 5 | 97.382 ± 0.154 |
| 0.2 | raw | 5 | 95.512 ± 0.150 |
| 0.2 | matched raw | 5 | 95.974 ± 0.144 |
| 0.2 | residual | 5 | 97.370 ± 0.083 |
| 0.5 | raw | 5 | 10.380 ± 0.548 |
| 0.5 | matched raw | 5 | 10.310 ± 0.633 |
| 0.5 | residual | 5 | 97.348 ± 0.133 |
## Native-protocol local baselines
| method | dataset | depth × width | budget | n | test acc (%) | wall (s) |
|:---|:---|:---|:---|---:|---:|---:|
| EP | mnist | 1 × 500 | 25 | 5 | 96.926 ± 0.238 | 800.5 ± 53.3 |
| EP | mnist | 2 × 500 | 60 | 5 | 89.526 ± 4.461 | 17530.4 ± 613.6 |
| FF | mnist | 3 × 256 | 15/layer | 5 | 93.558 ± 0.232 | 68.2 ± 0.8 |
| PEPITA | mnist | 3 × 256 | 60 | 5 | 91.094 ± 0.214 | 89.2 ± 3.5 |
## EP near-parameter-matched comparison
| method | depth × width | forward params | epochs | n | last acc (%) | best acc (%) | wall (s) |
|:---|:---|---:|---:|---:|---:|---:|---:|
| BP | 1 × 500 | 397,510 | 25 | 5 | 98.240 ± 0.073 | 98.272 ± 0.080 | 15.0 ± 0.5 |
| BP | 2 × 500 | 648,010 | 60 | 5 | 98.288 ± 0.030 | 98.326 ± 0.036 | 45.1 ± 0.8 |
| BP | 3 × 256 | 335,114 | 25 | 2 | 98.295 ± 0.078 | 98.320 ± 0.071 | 22.4 ± 0.3 |
| DFA | 1 × 500 | 397,510 | 25 | 5 | 97.662 ± 0.078 | 97.700 ± 0.074 | 10.6 ± 1.6 |
| DFA | 2 × 500 | 648,010 | 60 | 5 | 97.590 ± 0.046 | 97.622 ± 0.036 | 34.6 ± 2.8 |
| DFA | 3 × 256 | 335,114 | 25 | 2 | 97.160 ± 0.085 | 97.200 ± 0.141 | 17.4 ± 0.4 |
| EP | 1 × 500 | 397,510 | 25 | 5 | 96.926 ± 0.238 | 97.198 ± 0.147 | 800.5 ± 53.3 |
| EP | 2 × 500 | 648,010 | 60 | 5 | 89.526 ± 4.461 | 90.028 ± 4.272 | 17530.4 ± 613.6 |
| SDIL | 1 × 500 | 397,510 | 25 | 5 | 97.596 ± 0.089 | 97.638 ± 0.075 | 15.5 ± 0.2 |
| SDIL | 2 × 500 | 648,010 | 60 | 5 | 97.516 ± 0.067 | 97.562 ± 0.058 | 58.5 ± 4.0 |
| SDIL | 3 × 256 | 335,114 | 25 | 2 | 97.130 ± 0.042 | 97.170 ± 0.028 | 32.7 ± 5.0 |
Provenance: 216 files audited; 0 dirty or unknown.
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