baseline/summary.md

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