{"abstract":"Nesterov update uses the ordinary momentum direction.","category":"Optimizer update state","checks":6,"contract":"v_next=mu*v+g; p_next=p-lr*(g+mu*v_next).","contract_signature":"p, g, v, lr, mu","evaluation_group":"optimizer-toy-nesterov-lookahead","failed_approach":"Using g+mu*v uses the previous buffer rather than the newly updated one.","family":"w3-optimizer-update-state-nesterov-lookahead","id":"FA-98956","implementations":{"attempt":{"sha256":"c6a6f79d34ca7e7804ba456b2df775c83be8c874eb9e3441cc9f9a89781fae0a","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(p, g, v, lr, mu):\n    nv=mu*v+g\n    return [p-lr*(g+mu*v),nv]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('initial lookahead',solve(10,2,0,1,0.5),[7,2])\ncheck('existing velocity',solve(10,2,4,1,0.5),[6,4])\ncheck('negative gradient',solve(0,-2,4,0.5,0.5),[1,0])\ncheck('zero momentum',solve(5,3,7,2,0),[-1,3])\ncheck('zero rate',solve(3,4,2,0,0.9),[3,5.8])\ncheck('zero gradient with velocity',solve(6,0,4,1,0.5),[5,2])\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":"dc8e628f1ce57ae54d539544f3e27af8869876968b817e2260dc4dfcfd06da45","source":"\"\"\"Failure Map reference implementation. Python standard library only.\"\"\"\nimport json\n\nN = 1\nobservations = []\ndef solve(p, g, v, lr, mu):\n    nv=mu*v+g\n    return [p-lr*nv,nv]\ndef check(label, actual, expected):\n    observations.append({\"check\": label, \"actual\": actual, \"expected\": expected, \"passed\": actual == expected})\ncheck('initial lookahead',solve(10,2,0,1,0.5),[7,2])\ncheck('existing velocity',solve(10,2,4,1,0.5),[6,4])\ncheck('negative gradient',solve(0,-2,4,0.5,0.5),[1,0])\ncheck('zero momentum',solve(5,3,7,2,0),[-1,3])\ncheck('zero rate',solve(3,4,2,0,0.9),[3,5.8])\ncheck('zero gradient with velocity',solve(6,0,4,1,0.5),[5,2])\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-nesterov-lookahead","generated_at":"2026-09-30T16:48:18.534905+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 lookahead gradient is replaced by the accumulated buffer alone.","sha256":"5bfd2d3fd5bfdd53d7e2ed4445b83d5c8910c3fbef7c3c3e7e0fa7dffd3aad7e","title":"Nesterov update uses the ordinary momentum direction · 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":27.072,"exit_code":1,"observations":[{"actual":[8.0,2.0],"check":"initial lookahead","expected":[7,2],"passed":false},{"actual":[6.0,4.0],"check":"existing velocity","expected":[6,4],"passed":true},{"actual":[0.0,0.0],"check":"negative gradient","expected":[1,0],"passed":false},{"actual":[-1,3],"check":"zero momentum","expected":[-1,3],"passed":true},{"actual":[3.0,5.8],"check":"zero rate","expected":[3,5.8],"passed":true},{"actual":[4.0,2.0],"check":"zero gradient with velocity","expected":[5,2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"initial lookahead\", \"actual\": [8.0, 2.0], \"expected\": [7, 2], \"passed\": false}, {\"check\": \"existing velocity\", \"actual\": [6.0, 4.0], \"expected\": [6, 4], \"passed\": true}, {\"check\": \"negative gradient\", \"actual\": [0.0, 0.0], \"expected\": [1, 0], \"passed\": false}, {\"check\": \"zero momentum\", \"actual\": [-1, 3], \"expected\": [-1, 3], \"passed\": true}, {\"check\": \"zero rate\", \"actual\": [3.0, 5.8], \"expected\": [3, 5.8], \"passed\": true}, {\"check\": \"zero gradient with velocity\", \"actual\": [4.0, 2.0], \"expected\": [5, 2], \"passed\": false}], \"passed\": false}\n"},"broken":{"elapsed_ms":28.423,"exit_code":1,"observations":[{"actual":[8.0,2.0],"check":"initial lookahead","expected":[7,2],"passed":false},{"actual":[6.0,4.0],"check":"existing velocity","expected":[6,4],"passed":true},{"actual":[0.0,0.0],"check":"negative gradient","expected":[1,0],"passed":false},{"actual":[-1,3],"check":"zero momentum","expected":[-1,3],"passed":true},{"actual":[3.0,5.8],"check":"zero rate","expected":[3,5.8],"passed":true},{"actual":[4.0,2.0],"check":"zero gradient with velocity","expected":[5,2],"passed":false}],"passed":false,"stderr":"","stdout":"{\"observations\": [{\"check\": \"initial lookahead\", \"actual\": [8.0, 2.0], \"expected\": [7, 2], \"passed\": false}, {\"check\": \"existing velocity\", \"actual\": [6.0, 4.0], \"expected\": [6, 4], \"passed\": true}, {\"check\": \"negative gradient\", \"actual\": [0.0, 0.0], \"expected\": [1, 0], \"passed\": false}, {\"check\": \"zero momentum\", \"actual\": [-1, 3], \"expected\": [-1, 3], \"passed\": true}, {\"check\": \"zero rate\", \"actual\": [3.0, 5.8], \"expected\": [3, 5.8], \"passed\": true}, {\"check\": \"zero gradient with velocity\", \"actual\": [4.0, 2.0], \"expected\": [5, 2], \"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."}}