{"abstract":"Exponential decay raises the base rate to a power.","category":"Learning rate schedules","checks":6,"contract":"Return base*gamma**step for nonnegative step; negative steps clamp to zero.","contract_signature":"step, base, gamma","evaluation_group":"lr-schedule-exponential-decay","failed_approach":"Replacing the exponent with a linear step multiplier creates a linear curve, not geometric decay.","family":"w3-learning-rate-schedules-exponential-decay","id":"FA-99056","implementations":{"attempt":{"sha256":"160c76a7de7f938e8fad3975d8d173786dc08f0482150819607cb0caec3c9729","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(step, base, gamma):\n    return base*gamma*max(0,step)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('two steps',solve(2,8,0.5),2); check('start',solve(0,7,0.4),7); check('one',solve(1,10,0.8),8); check('zero factor',solve(3,5,0),0); check('negative step',solve(-2,9,0.5),9); check('growth factor',solve(2,2,2),8)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"},"broken":{"sha256":"8847efec541f8641a4482ecc51c6fd384d91c21906bd52ce67014e3e8a58af47","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(step, base, gamma):\n    return (base*gamma)**max(0,step)\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('two steps',solve(2,8,0.5),2); check('start',solve(0,7,0.4),7); check('one',solve(1,10,0.8),8); check('zero factor',solve(3,5,0),0); check('negative step',solve(-2,9,0.5),9); check('growth factor',solve(2,2,2),8)\nprint(json.dumps({\"observations\": observations, \"passed\": all(x[\"passed\"] for x in observations)}, ensure_ascii=False))\nraise SystemExit(0 if all(x[\"passed\"] for x in observations) else 1)\n"}},"limitations":"These are toy scalar contracts with integer steps and finite parameters; they do not model framework defaults or optimizer state. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.","method":"Deterministic executable model with adversarial boundary fixtures.","provenance":{"created_by":"Failure Map","dependencies":"Python standard library","family":"w3-learning-rate-schedules-exponential-decay","generated_at":"2026-09-30T16:48:19.909547+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"A deterministic scalar schedule makes step-to-rate mapping explicit for a small training loop.","root_cause":"The base is multiplied by gamma before the whole product is exponentiated.","sha256":"ecd40065094f6e7d00377863c4c5d7d414356e29732b95d899a451c7a4719fdd","title":"Exponential decay raises the base rate to a power · case 01","variant":1,"variant_policy":"The same explicitly authored fixtures repeat across all five numbered records; runtime N is unused. These records share one mechanism and must remain together in evaluation splits.","verified":true,"visibility":"public","verification":{"attempt":{"elapsed_ms":28.826,"exit_code":1,"observations":[{"actual":8.0,"check":"two steps","expected":2,"passed":false},{"actual":0.0,"check":"start","expected":7,"passed":false},{"actual":8.0,"check":"one","expected":8,"passed":true},{"actual":0,"check":"zero factor","expected":0,"passed":true},{"actual":0.0,"check":"negative step","expected":9,"passed":false},{"actual":8,"check":"growth factor","expected":8,"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"two steps\", \"actual\": 8.0, \"expected\": 2, \"passed\": false}, {\"check\": \"start\", \"actual\": 0.0, \"expected\": 7, \"passed\": false}, {\"check\": \"one\", \"actual\": 8.0, \"expected\": 8, \"passed\": true}, {\"check\": \"zero factor\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"negative step\", \"actual\": 0.0, \"expected\": 9, \"passed\": false}, {\"check\": \"growth factor\", \"actual\": 8, \"expected\": 8, \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":28.769,"exit_code":1,"observations":[{"actual":16.0,"check":"two steps","expected":2,"passed":false},{"actual":1.0,"check":"start","expected":7,"passed":false},{"actual":8.0,"check":"one","expected":8,"passed":true},{"actual":0,"check":"zero factor","expected":0,"passed":true},{"actual":1.0,"check":"negative step","expected":9,"passed":false},{"actual":16,"check":"growth factor","expected":8,"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"two steps\", \"actual\": 16.0, \"expected\": 2, \"passed\": false}, {\"check\": \"start\", \"actual\": 1.0, \"expected\": 7, \"passed\": false}, {\"check\": \"one\", \"actual\": 8.0, \"expected\": 8, \"passed\": true}, {\"check\": \"zero factor\", \"actual\": 0, \"expected\": 0, \"passed\": true}, {\"check\": \"negative step\", \"actual\": 1.0, \"expected\": 9, \"passed\": false}, {\"check\": \"growth factor\", \"actual\": 16, \"expected\": 8, \"passed\": false}], \"passed\": false}\n"}},"member_only":{"stages":["fixed"],"fields":["implementations.fixed","verification.fixed","harness","repair"],"note":"The verified repair, its recorded checks, the repair description, and the scoring harness are available to members."}}