{"abstract":"Coupled decay is omitted from the gradient moments.","category":"Optimizer update state","checks":6,"contract":"This unit-coefficient toy step forms q=g+wd*p, then returns [p-lr*q,q,q*q]; it does not perform adaptive normalization.","contract_signature":"p, g, lr, wd","evaluation_group":"optimizer-toy-coupled-weight-decay","failed_approach":"Adding decay to the update direction skips its contribution to squared-gradient state.","family":"w3-optimizer-update-state-coupled-weight-decay","id":"FA-99001","implementations":{"attempt":{"sha256":"15b8b0f97813ee7bb83dc4df6caba3458e77d8769800b5a1f9096cd111af1ff6","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(p, g, lr, wd):\n    return [p-lr*(g+wd*p),g,g*g]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('decay-only',solve(2,0,1,0.5),[1,1,1])\ncheck('gradient plus decay',solve(2,1,0.5,0.5),[1,2,4])\ncheck('negative parameter',solve(-2,0,1,0.25),[-1.5,-0.5,0.25])\ncheck('zero decay',solve(3,-2,1,0),[5,-2,4])\ncheck('zero rate still moments',solve(2,1,0,0.5),[2,2,4])\ncheck('zero parameter',solve(0,3,1,2),[-3,3,9])\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":"30f15b3d7441ce0fd150be257e76f3a7a3b958702a0df24abdc6b422b079438c","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(p, g, lr, wd):\n    return [p-lr*g,g,g*g]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('decay-only',solve(2,0,1,0.5),[1,1,1])\ncheck('gradient plus decay',solve(2,1,0.5,0.5),[1,2,4])\ncheck('negative parameter',solve(-2,0,1,0.25),[-1.5,-0.5,0.25])\ncheck('zero decay',solve(3,-2,1,0),[5,-2,4])\ncheck('zero rate still moments',solve(2,1,0,0.5),[2,2,4])\ncheck('zero parameter',solve(0,3,1,2),[-3,3,9])\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 deterministic scalar or short-vector toy contracts, not claims about production optimizer APIs or training quality. 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-optimizer-update-state-coupled-weight-decay","generated_at":"2026-09-30T16:48:19.455849+00:00","license":"CC0-1.0","python":"3.12.14","seed":1,"split":"open-access"},"relevance":"Optimizer implementations must associate each parameter with its own mathematically specified update state.","root_cause":"The gradient and its squared-state summary omit the regularization contribution entirely.","sha256":"dd43898d6e8104b26977432f1461783b3fa5727067b260cf59a0d3df6df6e425","title":"Coupled decay is omitted from the gradient moments · 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":28.414,"exit_code":1,"observations":[{"actual":[1.0,0,0],"check":"decay-only","expected":[1,1,1],"passed":false},{"actual":[1.0,1,1],"check":"gradient plus decay","expected":[1,2,4],"passed":false},{"actual":[-1.5,0,0],"check":"negative parameter","expected":[-1.5,-0.5,0.25],"passed":false},{"actual":[5,-2,4],"check":"zero decay","expected":[5,-2,4],"passed":true},{"actual":[2.0,1,1],"check":"zero rate still moments","expected":[2,2,4],"passed":false},{"actual":[-3,3,9],"check":"zero parameter","expected":[-3,3,9],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"decay-only\", \"actual\": [1.0, 0, 0], \"expected\": [1, 1, 1], \"passed\": false}, {\"check\": \"gradient plus decay\", \"actual\": [1.0, 1, 1], \"expected\": [1, 2, 4], \"passed\": false}, {\"check\": \"negative parameter\", \"actual\": [-1.5, 0, 0], \"expected\": [-1.5, -0.5, 0.25], \"passed\": false}, {\"check\": \"zero decay\", \"actual\": [5, -2, 4], \"expected\": [5, -2, 4], \"passed\": true}, {\"check\": \"zero rate still moments\", \"actual\": [2.0, 1, 1], \"expected\": [2, 2, 4], \"passed\": false}, {\"check\": \"zero parameter\", \"actual\": [-3, 3, 9], \"expected\": [-3, 3, 9], \"passed\": true}], \"passed\": false}\n"},"broken":{"elapsed_ms":28.717,"exit_code":1,"observations":[{"actual":[2,0,0],"check":"decay-only","expected":[1,1,1],"passed":false},{"actual":[1.5,1,1],"check":"gradient plus decay","expected":[1,2,4],"passed":false},{"actual":[-2,0,0],"check":"negative parameter","expected":[-1.5,-0.5,0.25],"passed":false},{"actual":[5,-2,4],"check":"zero decay","expected":[5,-2,4],"passed":true},{"actual":[2,1,1],"check":"zero rate still moments","expected":[2,2,4],"passed":false},{"actual":[-3,3,9],"check":"zero parameter","expected":[-3,3,9],"passed":true}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"decay-only\", \"actual\": [2, 0, 0], \"expected\": [1, 1, 1], \"passed\": false}, {\"check\": \"gradient plus decay\", \"actual\": [1.5, 1, 1], \"expected\": [1, 2, 4], \"passed\": false}, {\"check\": \"negative parameter\", \"actual\": [-2, 0, 0], \"expected\": [-1.5, -0.5, 0.25], \"passed\": false}, {\"check\": \"zero decay\", \"actual\": [5, -2, 4], \"expected\": [5, -2, 4], \"passed\": true}, {\"check\": \"zero rate still moments\", \"actual\": [2, 1, 1], \"expected\": [2, 2, 4], \"passed\": false}, {\"check\": \"zero parameter\", \"actual\": [-3, 3, 9], \"expected\": [-3, 3, 9], \"passed\": true}], \"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."}}