| Loading Freckles v40 + CIFAR-10... |
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| ====================================================================== |
| 1. FULL ROUND-TRIP β Per-patch reconstruction error |
| ====================================================================== |
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| Collecting per-patch reconstruction errors... |
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| Reconstructing: 0%| | 0/157 [00:00<?, ?it/s] |
| Reconstructing: 3%|β | 4/157 [00:00<00:03, 38.85it/s] |
| Reconstructing: 8%|β | 13/157 [00:00<00:02, 68.11it/s] |
| Reconstructing: 14%|ββ | 22/157 [00:00<00:01, 77.91it/s] |
| Reconstructing: 20%|ββ | 31/157 [00:00<00:01, 81.98it/s] |
| Reconstructing: 26%|βββ | 41/157 [00:00<00:01, 85.54it/s] |
| Reconstructing: 32%|ββββ | 51/157 [00:00<00:01, 87.75it/s] |
| Reconstructing: 39%|ββββ | 61/157 [00:00<00:01, 89.17it/s] |
| Reconstructing: 45%|βββββ | 71/157 [00:00<00:00, 89.94it/s] |
| Reconstructing: 52%|ββββββ | 81/157 [00:00<00:00, 90.52it/s] |
| Reconstructing: 58%|ββββββ | 91/157 [00:01<00:00, 90.89it/s] |
| Reconstructing: 64%|βββββββ | 101/157 [00:01<00:00, 91.03it/s] |
| Reconstructing: 71%|βββββββ | 111/157 [00:01<00:00, 91.05it/s] |
| Reconstructing: 77%|ββββββββ | 121/157 [00:01<00:00, 91.14it/s] |
| Reconstructing: 83%|βββββββββ | 131/157 [00:01<00:00, 91.22it/s] |
| Reconstructing: 90%|βββββββββ | 141/157 [00:01<00:00, 91.26it/s] |
| Reconstructing: 100%|ββββββββββ| 157/157 [00:01<00:00, 86.32it/s] |
| Collected 10000 images, 2000 individual maps |
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| ====================================================================== |
| 1a. SPATIAL STRUCTURE β Does recon error vary across patches? |
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| Per-image spatial CV of reconstruction error: |
| Mean CV: 0.3972 |
| Median CV: 0.3989 |
| Min CV: 0.0865 |
| Max CV: 0.7128 |
| VERDICT: HAS SPATIAL STRUCTURE |
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| 1b. PER-CLASS RECONSTRUCTION ERROR |
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| Class Mean MSE Std MSE Max patch |
| ------------------------------------------ |
| airplane 0.000000 0.000000 0.000000 |
| auto 0.000000 0.000000 0.000000 |
| bird 0.000000 0.000000 0.000000 |
| cat 0.000000 0.000000 0.000000 |
| deer 0.000000 0.000000 0.000000 |
| dog 0.000000 0.000000 0.000000 |
| frog 0.000000 0.000000 0.000000 |
| horse 0.000000 0.000000 0.000000 |
| ship 0.000000 0.000000 0.000000 |
| truck 0.000000 0.000000 0.000000 |
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| Mean inter-class cosine similarity: 0.996998 |
| Min inter-class cosine similarity: 0.991408 |
| VERDICT: SIMILAR PATTERNS |
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| ====================================================================== |
| 2. CENTER vs EDGE β Where does reconstruction fail? |
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| Class Center Edge Corner E/C ratio |
| ------------------------------------------------ |
| airplane 0.000000 0.000000 0.000000 0.9007 |
| auto 0.000000 0.000000 0.000000 0.9717 |
| bird 0.000000 0.000000 0.000000 0.9379 |
| cat 0.000000 0.000000 0.000000 0.9448 |
| deer 0.000000 0.000000 0.000000 0.9685 |
| dog 0.000000 0.000000 0.000000 1.0470 |
| frog 0.000000 0.000000 0.000000 0.9538 |
| horse 0.000000 0.000000 0.000000 0.9497 |
| ship 0.000000 0.000000 0.000000 1.0124 |
| truck 0.000000 0.000000 0.000000 0.9136 |
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| ====================================================================== |
| 3. PER-MODE RECONSTRUCTION β Ablating SVD modes |
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| Reconstructing with individual modes... |
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| Per-mode energy fraction (how much each mode contributes): |
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| Class Mode0 Mode1 Mode2 Mode3 FullMSE |
| -------------------------------------------------- |
| airplane 0.4242 0.3352 0.1705 0.0701 0.000000 |
| auto 0.4234 0.3359 0.1704 0.0703 0.000000 |
| bird 0.4237 0.3361 0.1700 0.0703 0.000000 |
| cat 0.4232 0.3363 0.1701 0.0704 0.000000 |
| deer 0.4236 0.3363 0.1700 0.0701 0.000000 |
| dog 0.4238 0.3358 0.1703 0.0701 0.000000 |
| frog 0.4229 0.3367 0.1698 0.0706 0.000000 |
| horse 0.4237 0.3358 0.1703 0.0702 0.000000 |
| ship 0.4243 0.3353 0.1706 0.0699 0.000000 |
| truck 0.4237 0.3358 0.1704 0.0701 0.000000 |
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| ====================================================================== |
| 4. LINEAR PROBE β Reconstruction error maps as features |
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| Ridge probe comparison: |
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| Recon error spatial map dims= 256 train=51.6% test=19.0% |
| Class Acc |
| ------------------ |
| airplane 25.9% βββββ |
| auto 19.4% βββ |
| bird 9.1% β |
| cat 12.2% ββ |
| deer 7.9% β |
| dog 31.4% ββββββ |
| frog 22.7% ββββ |
| horse 14.3% ββ |
| ship 36.6% βββββββ |
| truck 15.6% βββ |
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| ====================================================================== |
| 5. FULL CONDUIT β Release error + eigenvalues + friction |
| ====================================================================== |
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| Full conduit: 0%| | 0/157 [00:00<?, ?it/s] |
| Full conduit: 2%|β | 3/157 [00:00<00:06, 25.60it/s] |
| Full conduit: 6%|β | 9/157 [00:00<00:03, 42.69it/s] |
| Full conduit: 10%|β | 15/157 [00:00<00:02, 48.80it/s] |
| Full conduit: 13%|ββ | 21/157 [00:00<00:02, 51.60it/s] |
| Full conduit: 20%|ββ | 32/157 [00:00<00:02, 47.18it/s] |
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| Comparative linear probes: |
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| Release error only dims= 256 train=51.6% test=16.0% |
| Class Acc |
| ------------------ |
| airplane 27.8% βββββ |
| auto 18.2% βββ |
| bird 14.6% ββ |
| cat 5.4% β |
| deer 8.3% β |
| dog 21.6% ββββ |
| frog 18.9% βββ |
| horse 17.1% βββ |
| ship 11.6% ββ |
| truck 20.0% ββββ |
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| Eigenvalues (S) only dims= 1024 train=91.6% test=20.7% |
| Class Acc |
| ------------------ |
| airplane 16.7% βββ |
| auto 24.2% ββββ |
| bird 18.8% βββ |
| cat 21.6% ββββ |
| deer 14.6% ββ |
| dog 16.2% βββ |
| frog 24.3% ββββ |
| horse 17.1% βββ |
| ship 32.6% ββββββ |
| truck 22.5% ββββ |
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| Friction only dims= 1024 train=92.4% test=22.5% |
| Class Acc |
| ------------------ |
| airplane 19.4% βββ |
| auto 21.2% ββββ |
| bird 18.8% βββ |
| cat 21.6% ββββ |
| deer 14.6% ββ |
| dog 16.2% βββ |
| frog 27.0% βββββ |
| horse 22.0% ββββ |
| ship 34.9% ββββββ |
| truck 30.0% ββββββ |
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| Combinations: |
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| Release + Eigenvalues dims= 1280 train=98.4% test=18.5% |
| Class Acc |
| ------------------ |
| airplane 2.8% |
| auto 21.2% ββββ |
| bird 18.8% βββ |
| cat 2.7% |
| deer 18.8% βββ |
| dog 16.2% βββ |
| frog 21.6% ββββ |
| horse 26.8% βββββ |
| ship 25.6% βββββ |
| truck 27.5% βββββ |
| Release + Friction dims= 1280 train=98.3% test=15.3% |
| Class Acc |
| ------------------ |
| airplane 8.3% β |
| auto 18.2% βββ |
| bird 16.7% βββ |
| cat 5.4% β |
| deer 12.5% ββ |
| dog 16.2% βββ |
| frog 13.5% ββ |
| horse 19.5% βββ |
| ship 23.3% ββββ |
| truck 17.5% βββ |
| Release + Eigenvalues + Friction dims= 2304 train=99.9% test=17.0% |
| Class Acc |
| ------------------ |
| airplane 13.9% ββ |
| auto 3.0% |
| bird 16.7% βββ |
| cat 10.8% ββ |
| deer 12.5% ββ |
| dog 21.6% ββββ |
| frog 27.0% βββββ |
| horse 22.0% ββββ |
| ship 23.3% ββββ |
| truck 17.5% βββ |
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| ====================================================================== |
| 6. HIGH-ERROR PATCHES β Where does reconstruction fail? |
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| Top error positions per class (patch coordinates): |
| Class Top 3 positions (row, col) Error ratio |
| ---------------------------------------------------------------- |
| airplane (10,8), (9,8), (10,7) 1.19x |
| auto (11,14), (11,7), (10,1) 1.12x |
| bird (8,9), (7,9), (10,8) 1.11x |
| cat (5,8), (5,7), (6,5) 1.08x |
| deer (5,7), (5,5), (7,6) 1.06x |
| dog (15,15), (14,15), (9,15) 1.07x |
| frog (5,4), (4,7), (4,6) 1.07x |
| horse (10,9), (9,7), (9,9) 1.11x |
| ship (14,13), (14,12), (15,9) 1.20x |
| truck (10,14), (10,13), (10,1) 1.16x |
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| Overall error map: |
| Mean: 0.000000 |
| Std: 0.000000 |
| Hot patches (>2Ο): 0/256 |
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| ====================================================================== |
| THEOREM 3: RELEASE FIDELITY β SUMMARY |
| ====================================================================== |
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| SPATIAL STRUCTURE: |
| Recon error spatial CV: 0.3972 |
| (Friction spatial CV was: 0.0137) |
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| CLASSIFICATION (ridge probe, test accuracy): |
| Chance: 10.0% |
| Friction maps: 24.3% (from Cell 3) |
| Eigenvalue (S) maps: 21.0% (from Cell 3) |
| Release error maps: 19.0% |
| Release + Eigenvalues: 18.5% |
| Release + Friction: 15.3% |
| FULL CONDUIT (all three): 17.0% |
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| THE QUESTION ANSWERED: |
| Does the release signal carry class-discriminative information |
| that eigenvalues and friction do not? |
| Lift from release over eigenvalues: -4.7pp |
| Lift from full conduit over eigenvalues: -3.7pp |
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