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