Blame for server/phase3/summarize_phase3.py

"""Validate exact fields and write a bounded scientific interpretation."""
import argparse
from fractions import Fraction as F
import json
from pathlib import Path


def exact(x):
    return F(x["rational"] if isinstance(x,dict) else x)


def main(run):
    cfg=json.loads((run/"phase3_config.json").read_text())
    s=json.loads((run/"schedules.json").read_text())
    b=json.loads((run/"biased_results.json").read_text())
    original=json.loads((run/"inputs"/"witnesses.json").read_text())["witnesses"]
    by_id={w["id"]:w for w in original}
    biased_origin=by_id[cfg["biased_source_id"]]
    assert cfg["biased_weights"]==biased_origin["weights"]
    assert cfg["biased_probabilities"]==biased_origin["probabilities"]
    assert cfg["biased_tau"]==biased_origin["tau"]
    assert s["status"]=="complete" and s["self_test"]["passed"]
    expected={(w["id"],k) for w in original for k in cfg["schedule_K"]}
    assert len(s["rows"])==len(expected) and {(r["id"],r["K"]) for r in s["rows"]}==expected
    assert len(original)==cfg["expected_schedule_models"]
    summary={"schedule_rows":len(s["rows"]),"schedule_evaluations":s["summary"]["schedule_evaluations"],
             "schedule_findings":[],"biased_findings":[],"failed_biased_cases":[],
             "scope":"Finite frozen models; no outer minimax or sharp-exponent experiment"}
    for r in s["rows"]:
        w=by_id[r["id"]]
        assert r["n"]==w["n"] and r["weights"]==w["weights"] and r["probabilities"]==w["probabilities"]
        lo,hi=map(exact,(r["all_policy"]["lower"],r["all_policy"]["upper"]))
        fixed=exact(r["best_fixed"]["tv_exact"])
        sym=exact(r["best_symmetrized"]["symmetrized_tv_exact"])
        assert fixed==min(exact(x["tv_exact"]) for x in r["enumeration"]["all_schedules"])
        assert sym==min(exact(x["symmetrized_tv_exact"]) for x in r["enumeration"]["all_schedules"])
        for x in r["enumeration"]["all_schedules"]:
            assert lo<=exact(x["symmetrized_tv_exact"])<=exact(x["tv_exact"])<=1
        summary["schedule_findings"].append({"id":r["id"],"K":r["K"],
            "best_fixed_minus_optimum_lower":str(max(F(0),fixed-hi)),
            "best_fixed_minus_optimum_upper":str(fixed-lo),
            "best_random_labels_minus_optimum_lower":str(max(F(0),sym-hi)),
            "best_random_labels_minus_optimum_upper":str(sym-lo),
            "equal_better_than_geometric":exact(r["equal"]["tv_exact"])<exact(r["geometric"]["tv_exact"])})
    assert b["selftest"]["status"]=="passed" and b["lp_selftests"]["status"]=="passed"
    assert b["config"]==cfg
    models={m["id"]:m for m in b["models"]}
    assert len(models)==len(b["models"])
    group_stats={}
    for m in b["models"]:
        d=m["diagnostics"]
        assert d["kl_budget_certified"] and exact(d["kl_upper"])<=exact(cfg["biased_budget"])
        assert 0<=exact(d["kl_lower"])<=exact(d["kl_upper"])
        assert exact(d["kl_width"])==exact(d["kl_upper"])-exact(d["kl_lower"])
        stats=tuple(exact(d[k]) for k in ("model_tv","kl_lower","kl_upper"))
        assert m["n"] not in group_stats or group_stats[m["n"]]==stats
        group_stats[m["n"]]=stats
    required={(n,a,k) for n in cfg["biased_required_n"] for a in cfg["biased_a"] for k in cfg["biased_required_K"]}
    expected_biased=set(required)
    if b.get("extension_gate",{}).get("passed"):
        expected_biased|={(cfg["biased_extension_n"],a,k) for a in cfg["biased_a"] for k in cfg["biased_extension_K"]}
    observed={(c["n"],c["a"],c["K"]) for c in b["cases"]}
    assert observed==expected_biased and len(observed)==len(b["cases"])
    cases={}
    for c in b["cases"]:
        if c["status"]!="certified":
            summary["failed_biased_cases"].append({k:c[k] for k in ("model_id","K","error")})
            continue
        v=c["certificate"]
        lo,hi=exact(v["tv_lower"]),exact(v["tv_upper"])
        mtv=exact(models[c["model_id"]]["diagnostics"]["model_tv"])
        assert 0<=lo<=hi<=1 and exact(v["interval_width"])==hi-lo
        assert exact(v["execution_gap_lower"])==lo-mtv
        if F(c["a"])==F(1,2):
            assert c["fair_three_state_crosscheck"]["status"]=="passed"
        cases[c["model_id"],c["K"]]=c
    for model_id in models:
        for k in (2,3):
            if (model_id,k) in cases and (model_id,k+1) in cases:
                margin=exact(cases[model_id,k]["certificate"]["tv_lower"])-exact(cases[model_id,k+1]["certificate"]["tv_upper"])
                summary["biased_findings"].append({"model_id":model_id,"from_K":k,"to_K":k+1,
                    "separation_lower_rational":str(margin),"separation_lower_display":float(margin),
                    "strict_separation_certified":margin>0})
    summary["certified_biased_cases"]=len(cases)
    summary["extension_gate"]=b.get("extension_gate")
    summary["validation"]="PASS"
    (run/"validated_summary.json").write_text(json.dumps(summary,indent=2)+"\n")

    lines=["# 第三轮实验：简单调度与偏置稳健性\n",
        "实验只使用 CPU，未修改论文和投稿文件。所有模型参数、筛选范围和资源门槛见 PROTOCOL.md。\n",
        "## 1. 固定模型上的统一策略比较\n",
        f"9 个既有模型、K=3/4，共 {len(s['rows'])} 组；穷举 {s['summary']['schedule_evaluations']} 个有序批大小配置。概率与 TV 使用精确有理数。\n",
        "固定标签策略的完整输出 TV 由各批失配计数向量计算；随机标签策略边缘化其私有置换后，才使用总失配计数 TV。两者不混同。\n",
        "| n | B | K | 几何/固定标签 | 等分/固定标签 | 最佳固定标签批次 | 最佳随机标签批次 | all-policy 下界 | 上界 |",
        "|---:|---:|---:|---:|---:|---:|---:|---:|---:|"]
    for r in sorted(s["rows"],key=lambda r:(r["n"],F(r["budget"]),r["K"])):
        vals=[exact(r[k]["tv_exact"]) for k in ("geometric","equal","best_fixed")]
        vals += [exact(r["best_symmetrized"]["symmetrized_tv_exact"]),exact(r["all_policy"]["lower"]),exact(r["all_policy"]["upper"])]
        lines.append(f"| {r['n']} | {float(F(r['budget'])):.2f} | {r['K']} | "+" | ".join(f"{float(v):.8f}" for v in vals)+" |")
    k3=[r for r in summary["schedule_findings"] if r["K"]==3]
    k4=[r for r in summary["schedule_findings"] if r["K"]==4]
    lines += ["\n### 解释\n",
        f"三轮下，最佳随机标签批次族距 all-policy 最优的认证误差上限最大为 {float(max(F(r['best_random_labels_minus_optimum_upper']) for r in k3)):.3g}。这表明这些实例中的三轮最优值可以由非常简单的策略逼近，不需要宣称复杂自适应策略一定必要。\n",
        f"四轮下，该族距 all-policy 最优的认证差距下界范围为 {float(min(F(r['best_random_labels_minus_optimum_lower']) for r in k4)):.8f} 至 {float(max(F(r['best_random_labels_minus_optimum_lower']) for r in k4)):.8f}。\n",
        f"四轮时，等分固定标签调度在 {sum(r['equal_better_than_geometric'] for r in k4)}/{len(k4)} 个模型上优于几何固定标签调度。几何调度的理论贡献是对整个模型类的渐近统一保证，不是已知某个模型后的有限维最优。\n",
        "最佳随机标签批次只优化一个预设批大小向量再随机排列标签，不允许事先混合多个不同批大小向量；也不等于最优的所有非自适应策略。因此其差距不能单独解释为自适应能力的价值。\n",
        "等分使用累计 floor(j*n/(K-1))；这是本轮明确固定的约定，不与此前采用另一种取整顺序的调度混作同一策略。\n",
        "## 2. 固定偏置稳健性\n",
        "只改变 P 与 R 中相同的代表位偏置 a，保持失配混合权重和分量概率不变。同一 n 下的实际 joint KL 和模型 TV 在所有偏置间完全相同；n 改变后不重新匹配预算。\n",
        "采用新的九类 pair-state 转移核。终态指标是四种完整 pair 类型计数的 TV，不能仅用总失配计数。\n",
        "| n | a | 实际 KL 认证上界 | 模型 TV | 最坏 head TV | 是否 <= 1/4 |",
        "|---:|---:|---:|---:|---:|:---:|"]
    for m in sorted(b["models"],key=lambda m:(m["n"],-F(m["a"]))):
        d=m["diagnostics"]
        lines.append(f"| {m['n']} | {float(F(m['a'])):.2f} | {float(exact(d['kl_upper'])):.8f} | {float(exact(d['model_tv'])):.8f} | {float(exact(d['all_context_head_error'])):.8f} | {d['head_bound_1_over_4_satisfied']} |")
    lines += ["\n| n | a | K | 认证下界 L | 可行上界 U | L - 模型 TV |",
              "|---:|---:|---:|---:|---:|---:|"]
    for c in sorted(b["cases"],key=lambda c:(c["n"],-F(c["a"]),c["K"])):
        if c["status"]=="certified":
            v=c["certificate"]
            lines.append(f"| {c['n']} | {float(F(c['a'])):.2f} | {c['K']} | "+" | ".join(f"{float(exact(v[k])):.8f}" for k in ("tv_lower","tv_upper","execution_gap_lower"))+" |")
        else:
            lines.append(f"| {c['n']} | {float(F(c['a'])):.2f} | {c['K']} | 未完成 | 未完成 | 不作结论 |")
    lines += ["\n### 已认证的相邻轮数分离\n",
        "| 模型 | 轮数 | L_K - U_(K+1) | 严格为正 |",
        "|---|---|---:|:---:|"]
    for r in summary["biased_findings"]:
        lines.append(f"| {r['model_id']} | {r['from_K']} -> {r['to_K']} | {r['separation_lower_display']:.8f} | {r['strict_separation_certified']} |")
    lines += ["\n### 限制与核验\n",
        "偏置会使单独可见的 B 提供潜在分量信息，也可能放大反向 A|B 条件头误差。这里逐上下文检查实际误差，不声称这些点满足完全相同的 head 误差预算。\n",
        "模型 TV 是串行生成 R 的可行基线，不是无限轮数最优值。L-TV(P,R)<0 只表示这个下界没有证得正额外代价；如 U<TV(P,R)，才证得某个策略优于该基线。\n",
        "计算证书独立于浮点 LP 的可行性判断，但共享经过 literal-head/kernel 交叉检查的精确转移公式。它不是 Lean 形式化证明，也不代表固定偏置的 sharp 指数已解决。\n",
        "解析证明和实验对照分别见 docs/。原始 policies、terminal tests、LP diagnostics、有理数端点和失败记录保存在 biased_results.json。\n",
        f"资源门槛结果：{json.dumps(b.get('extension_gate',{}),ensure_ascii=False)}\n",
        f"未完成 cases：{json.dumps(summary['failed_biased_cases'],ensure_ascii=False)}\n",
        "## 3. 图片与复现\n",
        "figures/fixed_schedule_benchmark.pdf：n=16，固定模型的不同策略完整输出 TV。\n",
        "figures/geometric_schedule_overhead.pdf：全部9个模型的几何固定标签调度相对最优值的认证额外误差。\n",
        "figures/biased_depth_sensitivity.pdf：固定偏置敏感性，图中区间为算术认证区间而非统计置信区间。\n",
        "绘图参考 https://github.com/ChenLiu-1996/figures4papers/ ，标签22pt、图例/刻度至少18pt；PDF和300dpi PNG同存。\n"]
    (run/"RESULTS_PHASE3.md").write_text("\n".join(lines)+"\n")
    print(json.dumps({k:v for k,v in summary.items() if k not in ("schedule_findings","biased_findings")},indent=2))


if __name__=="__main__":
    parser=argparse.ArgumentParser()
    parser.add_argument("--run-dir",type=Path,required=True)
    main(parser.parse_args().run_dir)