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"""
SenseMath v2 Inference + Analysis Pipeline — OpenAI API version.
Runs Use-level inference on the v2 item-family benchmark using the OpenAI API
with async concurrent requests for speed.
Usage:
# Inference (API key required)
python run_sensemath_v2_api.py --step inference --model gpt-5-mini --scale 2
# With higher concurrency
python run_sensemath_v2_api.py --step inference --model gpt-5-mini --scale 2 --concurrency 40
# Analyze (no API key needed)
python run_sensemath_v2_api.py --step analyze --scale 2
"""
import os
import re
import json
import asyncio
import argparse
import numpy as np
from pathlib import Path
from typing import List, Dict
from collections import defaultdict, Counter
SCRIPT_DIR = Path(__file__).parent
V2_DATA_DIR = SCRIPT_DIR.parent / "benchmark"
if not V2_DATA_DIR.exists():
V2_DATA_DIR = SCRIPT_DIR.parent / "data"
V2_RESULTS_DIR = SCRIPT_DIR.parent / "results" / json.loads((V2_DATA_DIR / "manifest.json").read_text())["release_id"]
COT_TEMPLATE = (
"Please solve the following multiple-choice problem. "
"Show your step-by-step reasoning, then provide your final answer as "
"a single capital letter (A, B, C, or D) inside \\boxed{{}}.\n\n"
"{problem_block}\n\n"
"Put your final answer in \\boxed{{}}."
)
NC_TEMPLATE = (
"Please solve the following multiple-choice problem WITHOUT performing precise calculations. "
"Rely on your mathematical intuition, number sense, and estimation. "
"Show brief reasoning, then provide your final answer as "
"a single capital letter (A, B, C, or D) inside \\boxed{{}}.\n\n"
"{problem_block}\n\n"
"Put your final answer in \\boxed{{}}."
)
STRICT_TEMPLATE = (
"Please solve the following multiple-choice problem using strict sequential computation. "
"You MUST perform every arithmetic operation digit by digit in order. "
"Do NOT use shortcuts, estimation, rounding, algebraic identities, "
"or any mental math tricks. Do NOT skip any intermediate steps. "
"Show each computation fully, then provide your final answer as "
"a single capital letter (A, B, C, or D) inside \\boxed{{}}.\n\n"
"{problem_block}\n\n"
"Put your final answer in \\boxed{{}}."
)
# ── Helpers (same as run_sensemath_v2.py) ────────────────────────────────────
def safe_model_name(model: str) -> str:
return re.sub(r"[/: ]", "_", model)
def load_json(path: Path) -> List[Dict]:
with open(path) as f:
return json.load(f)
def save_json(data, path: Path):
path.parent.mkdir(parents=True, exist_ok=True)
with open(path, "w") as f:
json.dump(data, f, indent=2, ensure_ascii=False)
def build_mc_block(question: str, options: List[str]) -> str:
labels = ["A", "B", "C", "D"]
lines = [f"Question: {question}", "Options:"]
for i, opt in enumerate(options[:4]):
lines.append(f"{labels[i]}. {opt}")
return "\n".join(lines)
def find_correct_letter(options: List[str], answer: str) -> str:
labels = ["A", "B", "C", "D"]
for i, opt in enumerate(options[:4]):
if str(opt).strip().lower() == str(answer).strip().lower():
return labels[i]
return "A"
def extract_mc_answer(response: str) -> str:
response = re.sub(r"<think>.*?</think>", "", response, flags=re.DOTALL).strip()
# 1. Try \boxed{X}
m = re.search(r"\\boxed\{([A-D])\}", response)
if m:
return m.group(1).upper()
# 2. Try "final answer" / "answer" (skip template like (A/B/C/D))
m = re.search(r"(?:final answer|answer)\s*(?:\([A-D/]+\))?\s*[:\s]\s*([A-D])", response, re.IGNORECASE)
if m:
return m.group(1).upper()
# 3. Last standalone letter on its own line
m = re.search(r"(?:^|\n)\s*([A-D])\s*$", response)
if m:
return m.group(1).upper()
# 4. Last occurrence of standalone A-D
matches = re.findall(r"\b([A-D])\b", response)
if matches:
return matches[-1].upper()
return ""
# ── Async API inference ──────────────────────────────────────────────────────
async def call_openai(client, model: str, prompt: str, max_tokens: int, semaphore: asyncio.Semaphore):
"""Make a single OpenAI chat completion call with concurrency control."""
async with semaphore:
try:
kwargs = dict(
model=model,
messages=[{"role": "user", "content": prompt}],
max_completion_tokens=max_tokens,
)
# Some models (e.g. gpt-5-mini) don't support temperature=0
if "5-mini" not in model and "o1" not in model and "o3" not in model and "o4" not in model:
kwargs["temperature"] = 0
response = await client.chat.completions.create(**kwargs)
text = response.choices[0].message.content or ""
token_count = response.usage.completion_tokens if response.usage else 0
return text.strip(), token_count
except Exception as e:
print(f" API error: {e}")
return "", 0
async def run_inference_async(args):
from openai import AsyncOpenAI
api_key = os.environ.get("OPENAI_API_KEY")
if not api_key:
print("Error: OPENAI_API_KEY environment variable is not set.")
return
scale = args.scale
model = args.model
model_safe = safe_model_name(model)
V2_RESULTS_DIR.mkdir(parents=True, exist_ok=True)
# Load dataset
ds_path = V2_DATA_DIR / f"sensemath_v2_d{scale}.json"
if not ds_path.exists():
print(f"Dataset not found: {ds_path}")
return
families = load_json(ds_path)
print(f"Loaded {len(families)} families from {ds_path}")
# Load existing results for resumption
out_path = V2_RESULTS_DIR / f"use_{model_safe}_d{scale}.json"
existing = load_json(out_path) if out_path.exists() else []
done = {(r["family_id"], r["variant"], r["condition"]) for r in existing}
# Build prompts: each family x 3 variants x 2 conditions (CoT, NC) = 6 prompts
tasks = [] # list of (prompt_text, meta_dict)
for fam in families:
fid = fam["family_id"]
cat = fam["category"]
for var_name in ("strong_shortcut", "weak_shortcut", "control"):
task = fam[var_name]
pm = task["pure_math"]
options = pm.get("options", [])
question = pm["question"]
answer = pm["answer"]
correct_letter = find_correct_letter(options, answer)
for cond, template in [("CoT", COT_TEMPLATE), ("NC", NC_TEMPLATE), ("Strict", STRICT_TEMPLATE)]:
if (fid, var_name, cond) in done:
continue
block = build_mc_block(question, options)
prompt = template.format(problem_block=block)
meta = {
"family_id": fid,
"category": cat,
"variant": var_name,
"condition": cond,
"model": model,
"problem": question,
"ground_truth": answer,
"ground_truth_letter": correct_letter,
"shortcut_strength": task.get("shortcut_strength", 0),
}
tasks.append((prompt, meta))
if not tasks:
print("All conditions already done.")
return
print(f"To infer: {len(tasks)} prompts ({len(tasks)//6} families x 6)")
# Create async client and semaphore for concurrency control
client = AsyncOpenAI(api_key=api_key)
semaphore = asyncio.Semaphore(args.concurrency)
# Launch all requests concurrently (bounded by semaphore)
async_tasks = [
call_openai(client, model, prompt, args.max_tokens, semaphore)
for prompt, _ in tasks
]
print(f"Running {len(async_tasks)} API calls with concurrency={args.concurrency}...")
results = await asyncio.gather(*async_tasks)
# Build records
new_records = []
for (prompt, meta), (response_text, token_count) in zip(tasks, results):
rec = dict(meta)
rec["raw_response"] = response_text
rec["response_token_count"] = token_count
new_records.append(rec)
all_records = existing + new_records
save_json(all_records, out_path)
print(f"Saved {len(all_records)} records -> {out_path}")
# Summary
cond_counts = Counter((r["variant"], r["condition"]) for r in all_records)
print(f"\nRecords by variant x condition:")
for k, v in sorted(cond_counts.items()):
print(f" {k[0]:>20} x {k[1]:<4}: {v}")
await client.close()
def step_inference(args):
asyncio.run(run_inference_async(args))
# ── Analysis (identical to run_sensemath_v2.py) ─────────────────────────────
def step_analyze(args):
scale = args.scale
# Load all model results for this scale
all_records = []
for f in sorted(V2_RESULTS_DIR.glob(f"use_*_d{scale}.json")):
records = load_json(f)
all_records.extend(records)
if not all_records:
print(f"No results found for d={scale}")
return
# Score correctness
for r in all_records:
predicted = extract_mc_answer(r["raw_response"])
r["predicted"] = predicted
r["is_correct"] = (predicted == r.get("ground_truth_letter", ""))
models = sorted(set(r["model"] for r in all_records))
categories = sorted(set(r["category"] for r in all_records))
print(f"\n{'='*90}")
print(f" SenseMath v2 Analysis — d={scale}")
print(f" {len(all_records)} records, {len(models)} models, {len(categories)} categories")
print(f"{'='*90}")
results = {}
for model in models:
model_recs = [r for r in all_records if r["model"] == model]
model_short = model.split("/")[-1][:30]
# Per variant x condition accuracy
print(f"\n Model: {model_short}")
print(f" {'Variant':<20} {'Cond':<5} {'N':>5} {'Acc%':>7} {'AvgTok':>7}")
print(f" {'-'*50}")
for var in ("strong_shortcut", "weak_shortcut", "control"):
for cond in ("CoT", "NC"):
recs = [r for r in model_recs if r["variant"] == var and r["condition"] == cond]
if not recs:
continue
n = len(recs)
acc = sum(1 for r in recs if r["is_correct"]) / n
avg_tok = sum(r.get("response_token_count", 0) for r in recs) / n
print(f" {var:<20} {cond:<5} {n:>5} {acc:>6.1%} {avg_tok:>7.0f}")
key = f"{safe_model_name(model)}|{var}|{cond}"
results[key] = {
"model": model, "variant": var, "condition": cond,
"n": n, "accuracy": round(acc, 4),
"avg_tokens": round(avg_tok, 1),
}
# Interaction effect: (NS advantage on strong_shortcut) - (NS advantage on control)
# Per family
by_family = defaultdict(dict)
for r in model_recs:
by_family[(r["family_id"], r["variant"], r["condition"])] = r
family_ids = sorted(set(r["family_id"] for r in model_recs))
Y = []
for fid in family_ids:
ns_strong = by_family.get((fid, "strong_shortcut", "NC"))
cot_strong = by_family.get((fid, "strong_shortcut", "CoT"))
ns_ctrl = by_family.get((fid, "control", "NC"))
cot_ctrl = by_family.get((fid, "control", "CoT"))
if not all([ns_strong, cot_strong, ns_ctrl, cot_ctrl]):
continue
y = (int(ns_strong["is_correct"]) - int(cot_strong["is_correct"])) - \
(int(ns_ctrl["is_correct"]) - int(cot_ctrl["is_correct"]))
Y.append(y)
if Y:
Y = np.array(Y, dtype=float)
mean_Y = float(np.mean(Y))
# Permutation test (sign-flip)
rng = np.random.RandomState(42)
n_perm = 10000
perm_means = np.zeros(n_perm)
for p in range(n_perm):
signs = rng.choice([-1, 1], size=len(Y))
perm_means[p] = np.mean(Y * signs)
p_value = float(np.mean(np.abs(perm_means) >= np.abs(mean_Y)))
# Bootstrap CI
boot_means = np.zeros(n_perm)
for b in range(n_perm):
idx = rng.randint(0, len(Y), size=len(Y))
boot_means[b] = np.mean(Y[idx])
ci_lo = float(np.percentile(boot_means, 2.5))
ci_hi = float(np.percentile(boot_means, 97.5))
wins = int(np.sum(Y > 0))
losses = int(np.sum(Y < 0))
ties = int(np.sum(Y == 0))
sig = "***" if p_value < 0.0042 else "" # Bonferroni
print(f"\n Interaction (NS vs CoT, strong vs control):")
print(f" mean(Y) = {mean_Y:+.4f} [{ci_lo:+.4f}, {ci_hi:+.4f}] p={p_value:.6f} {sig}")
print(f" W/L/T = {wins}/{losses}/{ties} (n={len(Y)} families)")
results[f"{safe_model_name(model)}|interaction"] = {
"model": model, "n_families": len(Y),
"mean_Y": round(mean_Y, 4),
"ci_lo": round(ci_lo, 4), "ci_hi": round(ci_hi, 4),
"p_value": round(p_value, 6),
"significant": p_value < 0.0042,
"wins": wins, "losses": losses, "ties": ties,
}
# Per-category breakdown
print(f"\n Per-category accuracy (NC, strong vs control):")
for cat in categories:
cat_strong = [r for r in model_recs if r["category"] == cat and r["variant"] == "strong_shortcut" and r["condition"] == "NC"]
cat_ctrl = [r for r in model_recs if r["category"] == cat and r["variant"] == "control" and r["condition"] == "NC"]
if cat_strong and cat_ctrl:
acc_s = sum(1 for r in cat_strong if r["is_correct"]) / len(cat_strong)
acc_c = sum(1 for r in cat_ctrl if r["is_correct"]) / len(cat_ctrl)
delta = acc_s - acc_c
print(f" {cat:<25} strong={acc_s:.1%} ctrl={acc_c:.1%} delta={delta:+.1%}")
# Save
out_path = V2_RESULTS_DIR / f"analysis_d{scale}.json"
save_json(results, out_path)
print(f"\nSaved analysis -> {out_path}")
# ── Main ─────────────────────────────────────────────────────────────────────
def main():
parser = argparse.ArgumentParser(
description="SenseMath v2 inference via OpenAI API")
parser.add_argument("--step", required=True,
choices=["inference", "analyze"])
parser.add_argument("--model", default="gpt-5-mini")
parser.add_argument("--scale", type=int, default=2, choices=[2, 4, 8, 16])
parser.add_argument("--max-tokens", type=int, default=512)
parser.add_argument("--concurrency", type=int, default=20,
help="Max concurrent API requests")
args = parser.parse_args()
if args.step == "inference":
step_inference(args)
elif args.step == "analyze":
step_analyze(args)
if __name__ == "__main__":
main()
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