| Loading Freckles v40 + CIFAR-10... |
| Collecting spatial friction maps (full test set)... |
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| Collected 10000 images, 2000 individual maps |
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| ====================================================================== |
| 1. SPATIAL STRUCTURE — Do friction maps have spatial variance? |
| ====================================================================== |
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| Per-image spatial friction variance (across 256 patches): |
| Mode 0 (S₀): mean=0.0359 std=0.0196 |
| Mode 1 (S₁): mean=0.0207 std=0.0143 |
| Mode 2 (S₂): mean=0.3235 std=0.1607 |
| Mode 3 (S₃): mean=0.0000 std=0.0000 |
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| Per-image spatial CV (std/mean): |
| Mode 0: CV mean=0.0145 median=0.0145 max=0.0300 |
| Mode 1: CV mean=0.0109 median=0.0106 max=0.0272 |
| Mode 2: CV mean=0.0294 median=0.0297 max=0.0533 |
| Mode 3: CV mean=0.0000 median=0.0000 max=0.0000 |
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| VERDICT: SPATIALLY UNIFORM (mean CV = 0.0137) |
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| ====================================================================== |
| 2. PER-CLASS SPATIAL PATTERNS — Do classes have different friction maps? |
| ====================================================================== |
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| Inter-class friction map L2 distances: |
| airpl auto bird cat deer dog frog horse ship truck |
| airplane 0.000 5.791 5.016 6.309 6.924 5.982 7.640 5.202 3.186 4.733 |
| auto 5.791 0.000 3.181 3.194 3.779 3.585 3.552 3.158 3.951 2.838 |
| bird 5.016 3.181 0.000 2.093 2.065 2.115 2.931 1.535 4.403 4.120 |
| cat 6.309 3.194 2.093 0.000 1.806 1.493 1.996 2.043 5.563 4.821 |
| deer 6.924 3.779 2.065 1.806 0.000 2.135 1.485 2.355 6.168 5.364 |
| dog 5.982 3.585 2.115 1.493 2.135 0.000 2.682 2.474 5.349 5.220 |
| frog 7.640 3.552 2.931 1.996 1.485 2.682 0.000 3.063 6.488 5.457 |
| horse 5.202 3.158 1.535 2.043 2.355 2.474 3.063 0.000 4.650 3.783 |
| ship 3.186 3.951 4.403 5.563 6.168 5.349 6.488 4.650 0.000 3.010 |
| truck 4.733 2.838 4.120 4.821 5.364 5.220 5.457 3.783 3.010 0.000 |
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| Mean inter-class distance: 3.8820 |
| Mean cosine similarity: 0.999958 |
| Min cosine similarity: 0.999881 |
| VERDICT: NEARLY IDENTICAL PATTERNS |
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| ====================================================================== |
| 3. CENTER vs EDGE — Do boundary patches have higher friction? |
| ====================================================================== |
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| Class Center Edge Edge/Center |
| ---------------------------------------- |
| airplane 12.155 12.126 0.9975 |
| auto 12.203 12.219 1.0013 |
| bird 12.193 12.177 0.9987 |
| cat 12.206 12.212 1.0005 |
| deer 12.207 12.198 0.9993 |
| dog 12.179 12.200 1.0017 |
| frog 12.201 12.222 1.0018 |
| horse 12.214 12.183 0.9974 |
| ship 12.147 12.166 1.0015 |
| truck 12.210 12.185 0.9980 |
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| ====================================================================== |
| 4. PER-PATCH-POSITION DISCRIMINABILITY |
| ====================================================================== |
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| F-statistic (inter-class var / intra-class var) per mode: |
| Mode 0: mean=0.054267 max=0.113004 top 5% threshold=0.096192 |
| Mode 1: mean=0.165008 max=0.262047 top 5% threshold=0.254798 |
| Mode 2: mean=0.069616 max=0.170688 top 5% threshold=0.149573 |
| Mode 3: mean=0.000000 max=0.000000 top 5% threshold=0.000000 |
| Mode 0 best position: (1, 15) F=0.113004 |
| Mode 1 best position: (1, 13) F=0.262047 |
| Mode 2 best position: (0, 14) F=0.170688 |
| Mode 3 best position: (0, 0) F=0.000000 |
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| Overall best discriminative patch position: 0, 14 F=0.133089 |
| Overall mean F-statistic: 0.072223 |
| VERDICT: POSITIONALLY DISCRIMINATIVE |
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| ====================================================================== |
| 5. PER-MODE SPATIAL VARIANCE — Which mode has the most structure? |
| ====================================================================== |
| Mode 0: map_mean=12.5844 map_var=0.000355 map_cv=0.0015 |
| Mode 1: map_mean=12.4741 map_var=0.000701 map_cv=0.0021 |
| Mode 2: map_mean=18.6994 map_var=0.004943 map_cv=0.0038 |
| Mode 3: map_mean=5.0000 map_var=0.000000 map_cv=0.0000 |
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| ====================================================================== |
| 6. SAMPLE FRICTION MAPS — Individual images |
| ====================================================================== |
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| Class Img Mean Std Max Entropy HotSpots |
| ------------------------------------------------------- |
| airplane 0 12.11 0.22 19.60 1.000 0 |
| airplane 1 12.09 0.11 19.89 1.000 0 |
| auto 0 12.35 0.26 20.45 1.000 0 |
| auto 1 12.15 0.24 20.03 1.000 0 |
| bird 0 12.18 0.23 20.62 1.000 0 |
| bird 1 12.30 0.26 20.28 1.000 0 |
| cat 0 12.19 0.20 19.87 1.000 0 |
| cat 1 12.07 0.18 20.44 1.000 0 |
| deer 0 12.30 0.09 19.88 1.000 0 |
| deer 1 12.26 0.24 20.43 1.000 0 |
| dog 0 12.26 0.23 20.28 1.000 0 |
| dog 1 12.19 0.30 20.55 1.000 0 |
| frog 0 12.18 0.19 20.18 1.000 0 |
| frog 1 12.23 0.17 20.43 1.000 0 |
| horse 0 12.38 0.34 20.69 1.000 0 |
| horse 1 12.15 0.21 19.89 1.000 0 |
| ship 0 12.16 0.29 20.76 1.000 0 |
| ship 1 12.17 0.23 20.06 1.000 0 |
| truck 0 12.17 0.26 20.30 1.000 0 |
| truck 1 12.21 0.23 20.33 1.000 0 |
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| ====================================================================== |
| 7. LINEAR PROBE — Can flattened friction maps classify? |
| ====================================================================== |
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| Features: flattened friction map (1024 dims) |
| Train: 1600, Test: 400 |
| Train accuracy: 92.6% |
| Test accuracy: 24.3% |
| Chance: 10.0% |
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| Class Acc |
| ------------------ |
| airplane 32.6% ██████ |
| auto 24.4% ████ |
| bird 20.6% ████ |
| cat 15.7% ███ |
| deer 10.3% ██ |
| dog 21.9% ████ |
| frog 37.8% ███████ |
| horse 22.9% ████ |
| ship 24.1% ████ |
| truck 27.8% █████ |
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| VERDICT: DISCRIMINATIVE spatial friction signal |
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| ====================================================================== |
| 8. SETTLE MAP — Spatial convergence patterns |
| ====================================================================== |
| Settle map linear probe: |
| Test accuracy: 10.5% |
| VERDICT: NOT DISCRIMINATIVE |
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| ====================================================================== |
| 9. COMBINED CONDUIT — All evidence stacked |
| ====================================================================== |
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| Collecting eigenvalue spatial maps... |
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| Linear probe comparison (all use same train/test split): |
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| Eigenvalues (S) spatial dims= 1024 test_acc=21.0% |
| Friction spatial dims= 1024 test_acc=24.3% |
| Settle spatial dims= 1024 test_acc=10.5% |
| Combined (S+fric+settle) dims= 3072 test_acc=22.0% |
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| Chance: 10.0% |
| VERDICT: Combined vs eigenvalues-only lift = +1.0 percentage points |
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| ====================================================================== |
| SPATIAL FRICTION ANALYSIS — SUMMARY |
| ====================================================================== |
| 1. Spatial structure within images: CV = 0.0137 |
| 2. Inter-class pattern distance: cos_min = 0.999881 |
| 3. Center vs edge asymmetry: (see table above) |
| 4. Per-position F-statistic: max = 0.133089 |
| 5. Friction map linear probe: 24.3% |
| 6. Settle map linear probe: 10.5% |
| 7. Eigenvalue map linear probe: 21.0% |
| 8. Combined conduit linear probe: 22.0% |
| 9. Conduit lift over eigenvalues: +1.0pp |
