| # Threshold-conversion reproduction: raw summary | |
| - generated: 2026-10-20T21:42:39.043724+00:00 | |
| - upstream repo: https://github.com/isllabres/python-multiagent-system | |
| - execution fork: https://github.com/jomasego/python-multiagent-system | |
| - branch: `orx/threshold-conversion-baseline-theory-and-simplex` | |
| - commit: `9aa1d7906cd301302adda9e77fd167694f7263e5` | |
| - device: auto (text=cpu, vision=mps if available, digits=cpu) | |
| ## Theory | |
| - whiteboard example: `{"argmax": 1, "dot": 0.41400000000000003, "dot_threshold_pred": 0, "hadamard_argmax": 1, "p": [0.07, 0.93], "renormalized": [0.10144927536231883, 0.8985507246376813], "renormalized_argmax": 1, "w": [0.6, 0.4]}` | |
| - binary conversion max decision mismatch: 0 | |
| - binary conversion max AUC difference: 0 | |
| - uniform-simplex closed form: `{"10": 0.98046875, "2": 0.0, "20": 0.9999618530273438, "3": 0.25, "4": 0.5, "5": 0.6875, "6": 0.8125}` | |
| | C | delta_0.5 | coverage | ambiguous | adaptive decision match | | |
| |---:|---:|---:|---:|---:| | |
| | 2 | 0.0000 | 1.0000 | 0.0000 | 1.0000 | | |
| | 3 | 0.2486 | 0.7514 | 0.0000 | 1.0000 | | |
| | 4 | 0.4945 | 0.5054 | 0.0000 | 1.0000 | | |
| | 5 | 0.6862 | 0.3139 | 0.0000 | 1.0000 | | |
| | 6 | 0.8090 | 0.1910 | 0.0000 | 1.0000 | | |
| | 10 | 0.9806 | 0.0194 | 0.0000 | 1.0000 | | |
| | 20 | 1.0000 | 0.0001 | 0.0000 | 1.0000 | | |
| Counterexamples to `argmax = max_c p_c >= 0.5`: | |
| - p=[0.4, 0.35, 0.25], max=0.40, argmax=0, classes>=0.5: 0, adaptive q=[0.5, 0.437, 0.312] | |
| - p=[0.34, 0.33, 0.33], max=0.34, argmax=0, classes>=0.5: 0, adaptive q=[0.5, 0.485, 0.485] | |
| - p=[0.3, 0.3, 0.2, 0.1, 0.1], max=0.30, argmax=0, classes>=0.5: 0, adaptive q=[0.5, 0.5, 0.333, 0.167, 0.167] | |
| - p=[0.25, 0.2, 0.2, 0.2, 0.15], max=0.25, argmax=0, classes>=0.5: 0, adaptive q=[0.5, 0.4, 0.4, 0.4, 0.3] | |
| ## Models | |
| | model | C | n | argmax acc | delta_0.5 | coverage | selective acc | ECE | exact adaptive | | |
| |---|---:|---:|---:|---:|---:|---:|---:|---:| | |
| | 10-class tabular: logistic regression on sklearn digits | 10 | 540 | 97.22% | 0.74% | 99.26% | 97.76% | 0.0222 | True | | |
| ### Temperature sweep | |
| | model | T | delta_0.5 | argmax acc | ECE | | |
| |---|---:|---:|---:|---:| | |
| ### Per-class ROC operating points (0.5 vs best F1) | |
| | model | class | AUC | TPR@0.5 | FPR@0.5 | best F1 thr | best F1 | | |
| |---|---|---:|---:|---:|---:|---:| | |
| | 10-class tabular: logistic regression on sklearn digits | 0 | 1.000 | 1.000 | 0.000 | 0.727 | 1.000 | | |
| | 10-class tabular: logistic regression on sklearn digits | 1 | 0.997 | 0.982 | 0.012 | 0.552 | 0.939 | | |
| | 10-class tabular: logistic regression on sklearn digits | 2 | 1.000 | 0.981 | 0.000 | 0.593 | 0.990 | | |
| | 10-class tabular: logistic regression on sklearn digits | 3 | 1.000 | 0.964 | 0.002 | 0.445 | 0.982 | | |
| | 10-class tabular: logistic regression on sklearn digits | 4 | 1.000 | 0.963 | 0.000 | 0.546 | 0.981 | | |
| | 10-class tabular: logistic regression on sklearn digits | 5 | 1.000 | 0.964 | 0.004 | 0.298 | 0.973 | | |
| | 10-class tabular: logistic regression on sklearn digits | 6 | 1.000 | 0.981 | 0.000 | 0.554 | 0.991 | | |
| | 10-class tabular: logistic regression on sklearn digits | 7 | 1.000 | 1.000 | 0.002 | 0.569 | 0.991 | | |
| | 10-class tabular: logistic regression on sklearn digits | 8 | 0.997 | 0.904 | 0.004 | 0.232 | 0.953 | | |
| | 10-class tabular: logistic regression on sklearn digits | 9 | 0.999 | 0.963 | 0.002 | 0.595 | 0.981 | | |
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