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8815366 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | {
"paper": "Positive Distribution Shift as a Framework for Understanding Tractable Learning",
"openreview_id": "DkLQ40hTlt",
"claim": "Appendix-B printed decoder threshold for Theorem 3.2",
"exact_identity": "K~Binomial(m,3/(5r)); printed success=P[K>=ceil(3m/(5r))]",
"logical_consequence": "All-bit success for an all-ones code is at most this one-bit marginal. For r=1 the bound is exact, so the printed decoder cannot attain the usual >=2/3 success probability as epsilon decreases.",
"rows": 25,
"all_printed_probabilities_below_two_thirds": true,
"r1_smallest_epsilon": {
"r": 1,
"epsilon": 1e-12,
"samples_m": 1133,
"p_one": 0.6,
"p_zero": 0.4,
"printed_threshold": 0.6,
"midpoint_threshold": 0.5,
"printed_one_bit_success_exact": 0.5080632831256272,
"midpoint_one_bit_success_exact": 0.9999999999948532,
"printed_zero_bit_success_exact": 1.0,
"midpoint_zero_bit_success_exact": 0.9999999999948532,
"all_ones_success_upper_bound_printed": 0.5080632831256272,
"printed_exceeds_two_thirds": 0
},
"maximum_printed_one_bit_success": 0.5395430622999275,
"minimum_midpoint_one_bit_success": 0.9895403809911729,
"asymptotic_limit_printed_one_bit": 0.5,
"scope": "Exact audit of the printed decoder, not a disproof of a repaired midpoint decoder or of every possible f-PDS universality theorem.",
"execution": {
"started_at_utc": "2026-07-22T09:49:56.127198+00:00",
"completed_at_utc": "2026-07-22T09:49:56.135377+00:00",
"elapsed_seconds": 0.008177252486348152,
"python": "3.10.12",
"platform": "Linux-5.15.0-139-generic-x86_64-with-glibc2.35",
"packages": {
"numpy": "2.2.6",
"scipy": "1.14.0",
"matplotlib": "3.10.3"
}
}
}
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