| ================================================================================ |
| CONSTELLATION BOTTLENECK β FULL ANALYSIS |
| Params: 286,911,940 |
| Bottleneck: 281,845,505 |
| ================================================================================ |
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| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| TEST 1: Bottleneck Diagnostics |
| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| Patches: 16, Anchors/patch: 16, Patch dim: 16 |
| Drift: mean=0.171680 rad (9.84Β°) |
| std=0.053721 min=0.046172 max=0.353512 |
| max degrees: 20.25Β° |
| Skip gate: 0.1179 |
| Near 0.29154: 9.0% |
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| Per-patch drift: |
| P 0: mean=0.1744 (10.0Β°) max=0.2897 (16.6Β°) β MAX near 0.29 |
| P 1: mean=0.1470 (8.4Β°) max=0.2480 (14.2Β°) β MAX near 0.29 |
| P 2: mean=0.1465 (8.4Β°) max=0.2351 (13.5Β°) |
| P 3: mean=0.1497 (8.6Β°) max=0.2218 (12.7Β°) |
| P 4: mean=0.1327 (7.6Β°) max=0.2235 (12.8Β°) |
| P 5: mean=0.1639 (9.4Β°) max=0.2024 (11.6Β°) |
| P 6: mean=0.1369 (7.8Β°) max=0.1980 (11.3Β°) |
| P 7: mean=0.1643 (9.4Β°) max=0.2249 (12.9Β°) |
| P 8: mean=0.1752 (10.0Β°) max=0.2869 (16.4Β°) β MAX near 0.29 |
| P 9: mean=0.1797 (10.3Β°) max=0.2899 (16.6Β°) β MAX near 0.29 |
| P10: mean=0.1726 (9.9Β°) max=0.2314 (13.3Β°) |
| P11: mean=0.2548 (14.6Β°) max=0.3535 (20.3Β°) β 0.29 |
| P12: mean=0.2078 (11.9Β°) max=0.2778 (15.9Β°) β MAX near 0.29 |
| P13: mean=0.1867 (10.7Β°) max=0.2696 (15.4Β°) β MAX near 0.29 |
| P14: mean=0.1440 (8.3Β°) max=0.1875 (10.7Β°) |
| P15: mean=0.2105 (12.1Β°) max=0.2880 (16.5Β°) β MAX near 0.29 |
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| Anchor spread per patch: |
| P0: mean_cos=0.0030 max=0.6000 min=-0.7023 |
| P1: mean_cos=0.0238 max=0.5213 min=-0.5922 |
| P2: mean_cos=-0.0004 max=0.6274 min=-0.7749 |
| P3: mean_cos=0.0757 max=0.7292 min=-0.5168 |
| P4: mean_cos=0.0092 max=0.6820 min=-0.6667 |
| P5: mean_cos=0.0548 max=0.8025 min=-0.6882 |
| P6: mean_cos=-0.0070 max=0.6800 min=-0.6984 |
| P7: mean_cos=0.0219 max=0.7150 min=-0.5714 |
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| Anchor effective dimensionality: |
| P0: eff_dim=11.5 / 16 |
| P1: eff_dim=11.4 / 16 |
| P2: eff_dim=11.6 / 16 |
| P3: eff_dim=11.1 / 16 |
| P4: eff_dim=11.1 / 16 |
| P5: eff_dim=10.6 / 16 |
| P6: eff_dim=11.1 / 16 |
| P7: eff_dim=10.9 / 16 |
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| Drift distribution: |
| 0.00-0.05: 1 β |
| 0.05-0.10: 31 βββββββββββββββββββββββββββββββ |
| 0.10-0.15: 53 βββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| 0.15-0.20: 100 ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| 0.20-0.25: 51 βββββββββββββββββββββββββββββββββββββββββββββββββββ |
| 0.25-0.30: 19 βββββββββββββββββββ |
| 0.30-0.35: 0 |
| 0.35-0.40: 1 β |
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| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| TEST 2: Sphere Representation β CV of bottleneck embeddings |
| These live on S^15. Does CV approach 0.20? |
| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
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| t CV_sphere CV_tri eff_d_sph eff_d_tri sph_norm |
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| Per-patch CV at t=0 (should be β0.20 if d=16): |
| Patch 0: CV=0.6609 |
| Patch 1: CV=0.8585 |
| Patch 2: CV=0.9021 |
| Patch 3: CV=0.8482 |
| Patch 4: CV=0.7948 |
| Patch 5: CV=0.8473 |
| Patch 6: CV=0.8640 |
| Patch 7: CV=1.1050 |
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| 0.00 0.4321 0.4884 57.9 35.8 4.0000 |
| 0.10 0.3555 0.4503 68.9 41.9 4.0000 |
| 0.25 0.3288 0.4592 70.5 43.8 4.0000 |
| 0.50 0.3436 0.4650 69.5 43.6 4.0000 |
| 0.75 0.3845 0.5050 59.4 37.5 4.0000 |
| 0.90 0.4392 0.5671 45.6 29.1 4.0000 |
| 1.00 0.5039 0.5428 28.9 20.2 4.0000 |
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| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| TEST 3: Per-Class Anchor Routing |
| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
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| Patch 0 β nearest anchor per class: |
| class 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
| plane 23%β 0% 0% 0% 0% 0% 0% 1% 43%β 0% 7%β 10%β 0% 2% 0% 14%β |
| auto 19%β 0% 0% 0% 0% 0% 1% 0% 31%β 0% 14%β 26%β 0% 1% 0% 9%β |
| bird 23%β 0% 0% 0% 0% 1% 1% 0% 36%β 0% 7%β 20%β 0% 1% 0% 10%β |
| cat 14%β 0% 0% 0% 0% 1% 0% 0% 27%β 0% 19%β 21%β 0% 0% 1% 16%β |
| deer 15%β 1% 1% 0% 0% 2% 1% 2% 24%β 0% 16%β 21%β 0% 2% 1% 14%β |
| dog 14%β 0% 0% 0% 0% 0% 1% 0% 31%β 0% 13%β 25%β 0% 0% 1% 14%β |
| frog 11%β 0% 0% 0% 0% 1% 2% 0% 23%β 0% 18%β 27%β 0% 0% 0% 17%β |
| horse 18%β 0% 1% 0% 0% 2% 2% 1% 43%β 0% 11%β 10%β 1% 0% 0% 11%β |
| ship 13%β 1% 0% 0% 0% 1% 0% 0% 50%β 0% 10%β 7%β 0% 1% 0% 16%β |
| truck 22%β 0% 0% 0% 0% 1% 1% 0% 47%β 0% 5%β 14%β 0% 1% 0% 7%β |
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| Patch 1 β nearest anchor per class: |
| class 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
| plane 0% 0% 1% 0% 0% 0% 5%β 0% 93%β 0% 0% 0% 0% 0% 0% 0% |
| auto 0% 0% 2% 0% 0% 1% 4% 1% 92%β 0% 0% 0% 0% 0% 0% 0% |
| bird 0% 0% 0% 0% 0% 0% 7%β 0% 93%β 0% 0% 0% 0% 0% 0% 0% |
| cat 0% 0% 1% 0% 0% 1% 4% 0% 94%β 0% 0% 0% 0% 0% 0% 0% |
| deer 0% 0% 2% 0% 0% 0% 5% 0% 92%β 0% 0% 0% 0% 0% 0% 0% |
| dog 0% 0% 0% 0% 0% 1% 6%β 0% 93%β 0% 0% 0% 0% 0% 0% 0% |
| frog 0% 0% 0% 0% 0% 0% 5%β 0% 94%β 0% 0% 0% 0% 0% 0% 0% |
| horse 0% 0% 1% 0% 0% 2% 5%β 0% 92%β 0% 0% 0% 0% 0% 0% 0% |
| ship 0% 0% 1% 0% 0% 1% 5% 0% 93%β 0% 0% 0% 0% 0% 0% 0% |
| truck 1% 0% 1% 0% 0% 0% 12%β 0% 86%β 0% 0% 0% 0% 0% 0% 0% |
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| Patch 2 β nearest anchor per class: |
| class 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
| plane 0% 0% 0% 0% 4% 0% 0% 0% 0% 0% 0% 91%β 1% 0% 0% 5%β |
| auto 0% 0% 0% 0% 14%β 0% 0% 0% 0% 0% 0% 73%β 2% 0% 0% 10%β |
| bird 0% 0% 0% 0% 8%β 0% 0% 0% 0% 0% 0% 75%β 3% 0% 0% 12%β |
| cat 0% 2% 0% 0% 19%β 0% 0% 0% 0% 0% 0% 63%β 2% 0% 0% 14%β |
| deer 0% 1% 0% 0% 9%β 0% 0% 0% 0% 0% 0% 60%β 7%β 0% 0% 22%β |
| dog 0% 1% 0% 0% 21%β 0% 0% 0% 0% 0% 0% 63%β 1% 0% 0% 12%β |
| frog 0% 1% 0% 0% 18%β 0% 0% 0% 0% 0% 0% 64%β 4% 0% 0% 13%β |
| horse 0% 1% 0% 0% 8%β 0% 0% 0% 0% 0% 0% 72%β 4% 0% 0% 14%β |
| ship 0% 0% 0% 0% 2% 0% 0% 0% 0% 0% 0% 87%β 2% 0% 0% 9%β |
| truck 0% 0% 0% 0% 3% 0% 0% 0% 0% 0% 0% 86%β 3% 0% 0% 7%β |
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| Patch 3 β nearest anchor per class: |
| class 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 |
| plane 0% 0% 0% 1% 0% 0% 74%β 0% 0% 0% 0% 4% 5%β 14%β 1% 0% |
| auto 0% 0% 0% 0% 0% 0% 50%β 1% 0% 0% 0% 26%β 8%β 13%β 1% 0% |
| bird 0% 0% 0% 0% 0% 0% 70%β 2% 0% 0% 0% 12%β 4% 9%β 2% 0% |
| cat 0% 0% 0% 0% 0% 0% 60%β 1% 0% 1% 0% 20%β 7%β 10%β 1% 1% |
| deer 0% 0% 0% 0% 0% 0% 67%β 1% 1% 0% 0% 16%β 5%β 8%β 1% 0% |
| dog 0% 0% 0% 0% 0% 0% 59%β 2% 0% 0% 0% 19%β 6%β 13%β 1% 0% |
| frog 0% 0% 0% 0% 0% 0% 64%β 2% 0% 0% 0% 21%β 4% 8%β 1% 0% |
| horse 0% 0% 0% 0% 0% 0% 73%β 0% 0% 0% 0% 9%β 5%β 11%β 1% 1% |
| ship 0% 0% 0% 1% 0% 0% 70%β 1% 0% 0% 0% 2% 2% 20%β 3% 0% |
| truck 0% 0% 0% 1% 0% 0% 58%β 1% 0% 0% 0% 5%β 7%β 23%β 4% 0% |
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| Anchor routing entropy per class (lower = more concentrated): |
| plane: H=1.203 / 2.773 (43.4% of max) |
| auto: H=1.284 / 2.773 (46.3% of max) |
| bird: H=1.123 / 2.773 (40.5% of max) |
| cat: H=1.121 / 2.773 (40.4% of max) |
| deer: H=1.247 / 2.773 (45.0% of max) |
| dog: H=1.189 / 2.773 (42.9% of max) |
| frog: H=1.106 / 2.773 (39.9% of max) |
| horse: H=1.217 / 2.773 (43.9% of max) |
| ship: H=1.202 / 2.773 (43.4% of max) |
| truck: H=1.212 / 2.773 (43.7% of max) |
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| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| TEST 4: Skip Gate β how much goes through constellation vs skip? |
| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| Skip gate value: 0.1179 |
| Skip path: 11.8% |
| Constellation path: 88.2% |
| Skip proj params: 268,451,840 |
| Patchwork params: 9,194,496 |
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| β skip_proj is Linear(16384, 16384) = 268,435,456 params |
| β This single layer is 268M params β larger than the rest of the model combined |
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| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| TEST 5: Generation Quality |
| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| class intra_cos std CV norm |
| plane 0.8908 0.0565 0.5620 33.59 |
| auto 0.7927 0.0750 0.4022 27.18 |
| bird 0.8655 0.0650 0.5689 28.36 |
| cat 0.8152 0.0754 0.4562 27.54 |
| deer 0.8810 0.0495 0.4669 27.55 |
| dog 0.7997 0.0946 0.4984 27.54 |
| frog 0.8504 0.0649 0.4737 25.12 |
| horse 0.8360 0.0747 0.4253 28.41 |
| ship 0.8957 0.0590 0.6958 32.40 |
| truck 0.8352 0.0535 0.3488 29.22 |
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| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| TEST 6: Ablation β Skip-only vs Constellation-only |
| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| skip_only: pixel_Ξ=0.430410 cos_sim=0.597844 max_Ξ=1.9629 |
| const_only: pixel_Ξ=0.111031 cos_sim=0.945127 max_Ξ=1.0788 |
| β Saved (top=full, mid=skip_only, bot=constellation_only) |
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| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| TEST 7: Velocity Field Quality |
| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| t v_norm vΒ·target mse |
| 0.05 52.96 0.8513 0.3386 |
| 0.10 55.94 0.8974 0.2402 |
| 0.25 58.35 0.9355 0.1554 |
| 0.50 59.08 0.9474 0.1284 |
| 0.75 58.68 0.9421 0.1423 |
| 0.90 57.26 0.9242 0.1869 |
| 0.95 56.64 0.9130 0.2168 |
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| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| TEST 8: ODE Trajectory β geometry through generation |
| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| step t x_norm x_std CV |
| 0 1.00 54.24 0.9787 0.0113 |
| 1 0.98 53.14 0.9589 0.0119 |
| 5 0.90 48.81 0.8807 0.0114 |
| 10 0.80 43.57 0.7860 0.0119 |
| 20 0.60 33.96 0.6124 0.0249 |
| 30 0.40 26.51 0.4790 0.0735 |
| 40 0.20 23.17 0.4245 0.1868 |
| 49 0.02 25.22 0.4671 0.2458 |
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| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| TEST 9: Inter vs Intra Class Separation |
| ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ |
| Intra-class cos: 0.8462 Β± 0.0350 |
| Inter-class cos: 0.8319 Β± 0.0244 |
| Separation ratio: 1.017Γ |
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| ================================================================================ |
| ANALYSIS COMPLETE |
| ================================================================================ |
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| Files in analysis_bn/: |
| class_*.png per-class samples |
| all_classes.png 4 per class grid |
| ablation_skip_vs_const.png top=full, mid=skip, bot=constellation |
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| Key questions answered: |
| 1. Does per-patch CV β 0.20? (Test 2) |
| β If yes, the bottleneck lives at the natural S^15 dimension |
| 2. Is anchor routing class-specific? (Test 3) |
| β If entropy varies by class, constellation routes differently |
| 3. Does the skip path dominate? (Tests 4 & 6) |
| β If skip_only β full, the 268M skip_proj IS the model |
| 4. Does constellation-only work at all? (Test 6) |
| β The real test of whether geometric encoding carries signal |
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| ================================================================================ |
