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{
"title": "Held-Out Code & Math Test-Time Strategy Benchmark on Hugging Face A100-80GB",
"hardware": {
"platform": "Hugging Face Compute Jobs (a100-large)",
"gpu_name": "NVIDIA A100-SXM4-80GB",
"vram_total_gb": 79.25,
"elapsed_sec": 2050.32
},
"track1_competition_math_tir": {
"num_tasks": 35,
"base_passed": 27,
"base_pct": 77.14,
"polystep_passed": 30,
"polystep_pct": 85.71,
"gain_pct": 8.57,
"juncture_branches_switched": 10,
"tasks": [
{
"id": "AIME-HeldOut-01",
"category": "Number Theory (Modular Exponentiation)",
"gold_answer": "500",
"base_answer": "500",
"polystep_answer": "500",
"base_passed": true,
"polystep_passed": true,
"switched_branch": true,
"selected_source": "polystep_juncture_t1",
"elapsed_sec": 24.0
},
{
"id": "AIME-HeldOut-02",
"category": "Combinatorics (Digit DP)",
"gold_answer": "6923077",
"base_answer": "",
"polystep_answer": "6923265",
"base_passed": false,
"polystep_passed": false,
"switched_branch": true,
"selected_source": "polystep_pinned_self_repair",
"elapsed_sec": 84.9
},
{
"id": "AIME-HeldOut-03",
"category": "Number Theory (Chinese Remainder Theorem)",
"gold_answer": "3667381",
"base_answer": "",
"polystep_answer": "",
"base_passed": false,
"polystep_passed": false,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 157.45
},
{
"id": "AIME-HeldOut-04",
"category": "Algebra & Linear Recurrences",
"gold_answer": "23240118",
"base_answer": "23240118",
"polystep_answer": "23240118",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 12.37
},
{
"id": "AIME-HeldOut-05",
"category": "Counting & Probability (Dice Sum)",
"gold_answer": "25090131",
"base_answer": "25090131",
"polystep_answer": "25090131",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 91.1
},
{
"id": "AIME-HeldOut-06",
"category": "Combinatorics (Derangements)",
"gold_answer": "176214841",
"base_answer": "176214841",
"polystep_answer": "176214841",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 19.66
},
{
"id": "AIME-HeldOut-07",
"category": "Number Theory (Coprime Residues)",
"gold_answer": "2285",
"base_answer": "2285",
"polystep_answer": "2285",
"base_passed": true,
"polystep_passed": true,
"switched_branch": true,
"selected_source": "polystep_juncture_t2",
"elapsed_sec": 51.34
},
{
"id": "AIME-HeldOut-08",
"category": "Exact Rational Series (Telescoping Fraction)",
"gold_answer": "1076",
"base_answer": "1076",
"polystep_answer": "1076",
"base_passed": true,
"polystep_passed": true,
"switched_branch": true,
"selected_source": "polystep_juncture_t61",
"elapsed_sec": 38.1
},
{
"id": "AIME-HeldOut-09",
"category": "Number Theory (Divisor Sum)",
"gold_answer": "10584",
"base_answer": "10584",
"polystep_answer": "10584",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 34.06
},
{
"id": "AIME-HeldOut-10",
"category": "Combinatorics (Dyck Paths / Catalan)",
"gold_answer": "2674440",
"base_answer": "2674440",
"polystep_answer": "2674440",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 18.06
},
{
"id": "AIME-HeldOut-11",
"category": "Algebra (Polynomial Root Power Sums)",
"gold_answer": "851",
"base_answer": "851",
"polystep_answer": "-903",
"base_passed": true,
"polystep_passed": false,
"switched_branch": true,
"selected_source": "polystep_juncture_t60",
"elapsed_sec": 50.29
},
{
"id": "AIME-HeldOut-12",
"category": "Number Theory (p-adic Valuation)",
"gold_answer": "335",
"base_answer": "335",
"polystep_answer": "335",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 33.49
},
{
"id": "AIME-HeldOut-13",
"category": "Combinatorics (Pattern-Avoiding Binary Strings)",
"gold_answer": "2555757",
"base_answer": "2555757",
"polystep_answer": "2555757",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 41.8
},
{
"id": "AIME-HeldOut-14",
"category": "Graph Theory (Closed Walks on K_4)",
"gold_answer": "10761681",
"base_answer": "10761681",
"polystep_answer": "10761681",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 38.79
},
{
"id": "AIME-HeldOut-15",
"category": "Number Theory (Integer Square Root Divisibility)",
"gold_answer": "352800",
"base_answer": "352800",
"polystep_answer": "352800",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 13.91
},
{
"id": "AIME-HeldOut-16",
"category": "Exact Rational Series (Harmonic Alternating)",
"gold_answer": "210631",
"base_answer": "210631",
"polystep_answer": "210631",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 20.8
},
{
"id": "AIME-HeldOut-17",
"category": "Linear Algebra (GCD Matrix Determinant)",
"gold_answer": "16",
"base_answer": "16",
"polystep_answer": "16",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 62.89
},
{
"id": "AIME-HeldOut-18",
"category": "Combinatorics (Odd Partitions / Compositions)",
"gold_answer": "2178309",
"base_answer": "",
"polystep_answer": "300540195",
"base_passed": false,
"polystep_passed": false,
"switched_branch": true,
"selected_source": "polystep_juncture_t41",
"elapsed_sec": 42.27
},
{
"id": "AIME-HeldOut-19",
"category": "Number Theory (Euler Totient Sum)",
"gold_answer": "12232",
"base_answer": "",
"polystep_answer": "12232",
"base_passed": false,
"polystep_passed": true,
"switched_branch": true,
"selected_source": "polystep_juncture_t1",
"elapsed_sec": 20.29
},
{
"id": "AIME-HeldOut-20",
"category": "Numerical Analysis (Barron Adaptive Robust Loss)",
"gold_answer": "118418",
"base_answer": "118418",
"polystep_answer": "118418",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 21.68
},
{
"id": "MATH500/test_prealgebra_1139.json",
"category": "MATH-500 L5 (Prealgebra)",
"gold_answer": "4",
"base_answer": "2",
"polystep_answer": "2",
"base_passed": false,
"polystep_passed": false,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 98.42
},
{
"id": "MATH500/test_number_theory_737.json",
"category": "MATH-500 L5 (Number Theory)",
"gold_answer": "284",
"base_answer": "284",
"polystep_answer": "284",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 42.92
},
{
"id": "MATH500/test_precalculus_1199.json",
"category": "MATH-500 L4 (Precalculus)",
"gold_answer": "3.1415927",
"base_answer": "3.1415927",
"polystep_answer": "3.1415927",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 19.79
},
{
"id": "MATH500/test_algebra_1837.json",
"category": "MATH-500 L5 (Algebra)",
"gold_answer": "5",
"base_answer": "5",
"polystep_answer": "5",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 104.66
},
{
"id": "MATH500/test_algebra_2427.json",
"category": "MATH-500 L5 (Algebra)",
"gold_answer": "10",
"base_answer": "10",
"polystep_answer": "10",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 104.61
},
{
"id": "MATH500/test_counting_and_probability_525.json",
"category": "MATH-500 L5 (Counting & Probability)",
"gold_answer": "144",
"base_answer": "",
"polystep_answer": "144",
"base_passed": false,
"polystep_passed": true,
"switched_branch": true,
"selected_source": "polystep_juncture_t26",
"elapsed_sec": 146.59
},
{
"id": "MATH500/test_counting_and_probability_134.json",
"category": "MATH-500 L4 (Counting & Probability)",
"gold_answer": "720",
"base_answer": "720",
"polystep_answer": "720",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 25.94
},
{
"id": "MATH500/test_counting_and_probability_119.json",
"category": "MATH-500 L4 (Counting & Probability)",
"gold_answer": "-125",
"base_answer": "-125",
"polystep_answer": "-125",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 43.88
},
{
"id": "MATH500/test_geometry_627.json",
"category": "MATH-500 L4 (Geometry)",
"gold_answer": "17",
"base_answer": "",
"polystep_answer": "17",
"base_passed": false,
"polystep_passed": true,
"switched_branch": true,
"selected_source": "polystep_juncture_t509",
"elapsed_sec": 114.16
},
{
"id": "MATH500/test_prealgebra_1558.json",
"category": "MATH-500 L5 (Prealgebra)",
"gold_answer": "1.25",
"base_answer": "1.25",
"polystep_answer": "1.25",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 22.74
},
{
"id": "MATH500/test_algebra_305.json",
"category": "MATH-500 L5 (Algebra)",
"gold_answer": "5",
"base_answer": "5",
"polystep_answer": "5",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 27.88
},
{
"id": "MATH500/test_prealgebra_1388.json",
"category": "MATH-500 L4 (Prealgebra)",
"gold_answer": "83",
"base_answer": "83",
"polystep_answer": "83",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 16.11
},
{
"id": "MATH500/test_number_theory_1055.json",
"category": "MATH-500 L5 (Number Theory)",
"gold_answer": "203",
"base_answer": "203",
"polystep_answer": "203",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 74.49
},
{
"id": "MATH500/test_prealgebra_951.json",
"category": "MATH-500 L5 (Prealgebra)",
"gold_answer": "12",
"base_answer": "12",
"polystep_answer": "12",
"base_passed": true,
"polystep_passed": true,
"switched_branch": false,
"selected_source": "base_greedy",
"elapsed_sec": 80.43
},
{
"id": "MATH500/test_algebra_187.json",
"category": "MATH-500 L4 (Algebra)",
"gold_answer": "3",
"base_answer": "",
"polystep_answer": "3",
"base_passed": false,
"polystep_passed": true,
"switched_branch": true,
"selected_source": "polystep_juncture_t100",
"elapsed_sec": 130.81
}
]
},
"track2_algorithmic_code_math_fuzz": {
"num_tasks": 10,
"base_passed": 9,
"base_pct": 90.0,
"polystep_passed": 10,
"polystep_pct": 100.0,
"gain_pct": 10.0,
"tasks": [
{
"task_id": "HeldOut-CodeMath/01_rolling_geometric_max",
"entry_point": "rolling_max_product_pair",
"base_passed": true,
"polystep_passed": true,
"base_probe_passed": true,
"polystep_probe_passed": true,
"switched_branch": false,
"base_completion": "if not nums:\n return []\n max_so_far = nums[0]\n result = [max_so_far]\n for num in nums[1:]:\n max_so_far = max(max_so_far, num)\n result.append(max_so_far)\n return result",
"polystep_completion": "if not nums:\n return []\n max_so_far = nums[0]\n result = [max_so_far]\n for num in nums[1:]:\n max_so_far = max(max_so_far, num)\n result.append(max_so_far)\n return result",
"elapsed_sec": 10.19
},
{
"task_id": "HeldOut-CodeMath/02_circular_digit_shift",
"entry_point": "circular_shift_digits",
"base_passed": true,
"polystep_passed": true,
"base_probe_passed": true,
"polystep_probe_passed": true,
"switched_branch": false,
"base_completion": "x = str(x)\n if shift > len(x):\n return x[::-1]\n else:\n return x[-shift:] + x[:-shift]",
"polystep_completion": "x = str(x)\n if shift > len(x):\n return x[::-1]\n else:\n return x[-shift:] + x[:-shift]",
"elapsed_sec": 5.71
},
{
"task_id": "HeldOut-CodeMath/03_caesar_double_two",
"entry_point": "encrypt_shift_four",
"base_passed": true,
"polystep_passed": true,
"base_probe_passed": true,
"polystep_probe_passed": true,
"switched_branch": false,
"base_completion": "result = []\n for char in s:\n if char.isalpha():\n # Determine the base ASCII value for the case of the character\n base = ord('a') if char.islower() else ord('A')\n # Shift by 4 (2 * 2) and wrap around within the 26-letter alphabet\n shifted = (ord(char) - base + 4) % 26 + base\n result.append(chr(shifted))\n else:\n # Non-alphabetic characters remain unchanged\n result.append(char)\n return ''.join(result)",
"polystep_completion": "result = []\n for char in s:\n if char.isalpha():\n # Determine the base ASCII value for the case of the character\n base = ord('a') if char.islower() else ord('A')\n # Shift by 4 (2 * 2) and wrap around within the 26-letter alphabet\n shifted = (ord(char) - base + 4) % 26 + base\n result.append(chr(shifted))\n else:\n # Non-alphabetic characters remain unchanged\n result.append(char)\n return ''.join(result)",
"elapsed_sec": 22.15
},
{
"task_id": "HeldOut-CodeMath/04_balanced_concat_parens",
"entry_point": "match_parens_pair",
"base_passed": true,
"polystep_passed": true,
"base_probe_passed": true,
"polystep_probe_passed": true,
"switched_branch": false,
"base_completion": "def is_good(s: str) -> bool:\n balance = 0\n for char in s:\n if char == '(':\n balance += 1\n else:\n balance -= 1\n if balance < 0:\n return False\n return balance == 0\n\n return 'Yes' if is_good(lst[0] + lst[1]) or is_good(lst[1] + lst[0]) else 'No'",
"polystep_completion": "def is_good(s: str) -> bool:\n balance = 0\n for char in s:\n if char == '(':\n balance += 1\n else:\n balance -= 1\n if balance < 0:\n return False\n return balance == 0\n\n return 'Yes' if is_good(lst[0] + lst[1]) or is_good(lst[1] + lst[0]) else 'No'",
"elapsed_sec": 12.94
},
{
"task_id": "HeldOut-CodeMath/05_sum_two_digit_prefix",
"entry_point": "add_two_digit_elements",
"base_passed": true,
"polystep_passed": true,
"base_probe_passed": true,
"polystep_probe_passed": true,
"switched_branch": false,
"base_completion": "return sum(x for x in arr[:k] if abs(x) < 100)",
"polystep_completion": "return sum(x for x in arr[:k] if abs(x) < 100)",
"elapsed_sec": 1.63
},
{
"task_id": "HeldOut-CodeMath/06_sorted_at_most_two_dups",
"entry_point": "is_sorted_max_two_dups",
"base_passed": true,
"polystep_passed": true,
"base_probe_passed": true,
"polystep_probe_passed": true,
"switched_branch": false,
"base_completion": "for i in range(len(lst) - 1):\n if lst[i] > lst[i + 1]:\n return False\n if i < len(lst) - 2 and lst[i] == lst[i + 1] == lst[i + 2]:\n return False\n return True",
"polystep_completion": "for i in range(len(lst) - 1):\n if lst[i] > lst[i + 1]:\n return False\n if i < len(lst) - 2 and lst[i] == lst[i + 1] == lst[i + 2]:\n return False\n return True",
"elapsed_sec": 10.32
},
{
"task_id": "HeldOut-CodeMath/07_sum_of_four_positive_evens",
"entry_point": "is_sum_four_positive_even",
"base_passed": true,
"polystep_passed": true,
"base_probe_passed": true,
"polystep_probe_passed": true,
"switched_branch": false,
"base_completion": "return n >= 8 and n % 2 == 0",
"polystep_completion": "return n >= 8 and n % 2 == 0",
"elapsed_sec": 1.45
},
{
"task_id": "HeldOut-CodeMath/08_sum_squares_cubes_mod3_mod4",
"entry_point": "sum_squares_and_cubes",
"base_passed": true,
"polystep_passed": true,
"base_probe_passed": true,
"polystep_probe_passed": true,
"switched_branch": true,
"base_completion": "return sum(x**2 if i % 3 == 0 else x**3 if i % 4 == 0 else x for i, x in enumerate(lst))",
"polystep_completion": "return sum(x ** 3 if i % 4 == 0 and i % 3 != 0 else x ** 2 if i % 3 == 0 else x for i, x in enumerate(lst))",
"elapsed_sec": 5.78
},
{
"task_id": "HeldOut-CodeMath/09_snake_to_upper_camel",
"entry_point": "snake_to_camel_case",
"base_passed": false,
"polystep_passed": true,
"base_probe_passed": false,
"polystep_probe_passed": true,
"switched_branch": true,
"base_completion": "return ''.join([word[0].upper()] + [w[0].upper() + w[1:] for w in word.split('_')[1:]])",
"polystep_completion": "return ''.join([w.capitalize() for w in word.split('_')])",
"elapsed_sec": 4.12
},
{
"task_id": "HeldOut-CodeMath/10_modular_power_two",
"entry_point": "modp_fast",
"base_passed": true,
"polystep_passed": true,
"base_probe_passed": true,
"polystep_probe_passed": true,
"switched_branch": false,
"base_completion": "if n == 0:\n return 1\n if n % 2 == 0:\n return modp_fast(n // 2, p) ** 2 % p\n else:\n return 2 * modp_fast(n - 1, p) % p",
"polystep_completion": "if n == 0:\n return 1\n if n % 2 == 0:\n return modp_fast(n // 2, p) ** 2 % p\n else:\n return 2 * modp_fast(n - 1, p) % p",
"elapsed_sec": 7.9
}
]
},
"track3_heldout_competitions": {
"bigcodebench_hard": {
"num_tasks": 12,
"base_passed": 3,
"base_pass_at_1_pct": 25.0,
"polystep_passed": 12,
"polystep_pass_at_1_pct": 100.0,
"polystep_gain_pct": 75.0
},
"livecodebench": {
"num_tasks": 15,
"base_passed": 5,
"base_pass_at_1_pct": 33.33,
"polystep_passed": 15,
"polystep_pass_at_1_pct": 100.0,
"polystep_gain_pct": 66.67
},
"hf_private_competition": {
"num_tasks": 25,
"base_passed": 7,
"base_pass_at_1_pct": 28.0,
"polystep_passed": 22,
"polystep_pass_at_1_pct": 88.0,
"polystep_gain_pct": 60.0,
"tasks": [
{
"id": "HFComp/Blind-007_bisect_left_lower_bound_step",
"base_prediction": 0,
"polystep_prediction": 3,
"base_passed": false,
"polystep_passed": true
},
{
"id": "HFComp/Blind-010_fenwick_1_indexed_build",
"base_prediction": 3,
"polystep_prediction": 2,
"base_passed": false,
"polystep_passed": true
},
{
"id": "HFComp/Blind-016_levenshtein_dp_base_row",
"base_prediction": 2,
"polystep_prediction": 1,
"base_passed": false,
"polystep_passed": true
},
{
"id": "HFComp/Blind-022_circular_kadane_all_negative_guard",
"base_prediction": 0,
"polystep_prediction": 0,
"base_passed": true,
"polystep_passed": true
},
{
"id": "HFComp/Blind-027_kahn_toposort_cycle_guard",
"base_prediction": 0,
"polystep_prediction": 0,
"base_passed": false,
"polystep_passed": false
},
{
"id": "HFComp/Blind-033_welford_streaming_mean_update",
"base_prediction": 2,
"polystep_prediction": 2,
"base_passed": true,
"polystep_passed": true
},
{
"id": "HFComp/Blind-035_welford_bessel_sample_variance",
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