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ac2. Checkpoint saved
after training step 27 (0-indexed). Strict upstream eval parity:
1100s hard kill, verbatim prompts/entrypoints, group 64x8, T=1.0, kl 0.1.1{
2 "step": 27,
3 "progress/batch": 27,
4 "optim/lr": 4e-05,
5 "progress/done_frac": 0.56,
6 "puct/buffer_size": 438,
7 "puct/sampled_size": 8,
8 "puct/T": 13824,
9 "puct/scale_last": 0.4396084821973646,
10 "puct/buffer_value/mean": 0.9292597967203857,
11 "puct/buffer_value/std": 0.04620763757029945,
12 "puct/buffer_value/min": 0.5041471954736918,
13 "puct/buffer_value/max": 0.9437556776710564,
14 "puct/buffer_timestep/mean": 12.719178082191782,
15 "puct/buffer_timestep/std": 7.949104499133834,
16 "puct/buffer_timestep/min": -1.0,
17 "puct/buffer_timestep/max": 26.0,
18 "puct/buffer_construction_len/mean": 2630.771689497717,
19 "puct/buffer_construction_len/std": 2597.9106670012857,
20 "puct/buffer_construction_len/min": 1024.0,
21 "puct/buffer_construction_len/max": 32768.0,
22 "puct/sampled_value/mean": 0.9436893366457986,
23 "puct/sampled_value/std": 5.927315864593574e-05,
24 "puct/sampled_value/min": 0.943612809742666,
25 "puct/sampled_value/max": 0.9437556776710564,
26 "puct/sampled_timestep/mean": 26.0,
27 "puct/sampled_timestep/std": 0.0,
28 "puct/sampled_timestep/min": 26.0,
29 "puct/sampled_timestep/max": 26.0,
30 "puct/sampled_construction_len/mean": 4096.0,
31 "puct/sampled_construction_len/std": 0.0,
32 "puct/sampled_construction_len/min": 4096.0,
33 "puct/sampled_construction_len/max": 4096.0,
34 "time/sampling": 4362.925324201584,
35 "env/all/ac_tokens_per_turn": 9260.361328125,
36 "env/all/ob_tokens_per_turn": 4175.25,
37 "env/all/turns_per_episode": 1.0,
38 "env/all/total_episodes": 512,
39 "env/all/total_turns": 512,
40 "env/all/total_ac_tokens": 4741305,
41 "env/all/total_ob_tokens": 2137728,
42 "env/all/time/sampling_mean": 379.4020659220405,
43 "env/all/time/sampling_max": 476.2399637699127,
44 "env/all/time/env_step_mean": 1720.6135561554693,
45 "env/all/time/env_step_max": 3890.521183013916,
46 "env/all/reward/mean": 0.6753562629809808,
47 "env/all/reward/max": 0.9438406639348141,
48 "env/all/reward/min": 0.0,
49 "env/all/format": 1.0,
50 "env/all/format/min": 1.0,
51 "env/all/format/max": 1.0,
52 "env/all/reward": 0.6753562629809808,
53 "env/all/correctness": 0.755859375,
54 "env/all/correctness/min": 0.0,
55 "env/all/correctness/max": 1.0,
56 "env/all/raw_score": 0.8934945908172149,
57 "env/all/raw_score/min": 0.03696028391628951,
58 "env/all/raw_score/max": 0.9438406639348141,
59 "env/all/initial_raw_score": 0.9436893366457983,
60 "env/all/initial_raw_score/min": 0.943612809742666,
61 "env/all/initial_raw_score/max": 0.9437556776710564,
62 "env/all/msg": "Success; raw_score=0.9429640570327082",
63 "env/all/parsed_code": "```python\nimport numpy as np\nimport time\nfrom typing import Tuple\nimport random\nimport scipy.interpolate as interpolate\n\ndef _simpson_l2sq(conv: np.ndarray) -> Tuple[float, np.ndarray]:\n \"\"\"Compute ||f*f||_2^2 via Simpson's rule with endpoint zeros and gradient.\"\"\"\n m = conv.size\n if m == 0:\n return 0.0, np.zeros_like(conv)\n dx = 1.0 / (m + 1)\n y = np.zeros(m + 2, dtype=conv.dtype)\n y[0] = 0.0\n y[1:-1] = conv\n y[-1] = 0.0\n lhs = y[:-1]\n rhs = y[1:]\n l2_sq = (dx / 3.0) * np.sum(lhs * lhs + lhs * rhs + rhs * rhs)\n grad_y = (dx / 3.0) * (4.0 * y + np.roll(y, 1) + np.roll(y, -1))\n grad_conv = grad_y[1:-1]\n return float(l2_sq), grad_conv\n\ndef _l1(conv: np.ndarray) -> Tuple[float, np.ndarray]:\n \"\"\"Compute ||f*f||_1 and its gradient.\"\"\"\n m = conv.size\n dx = 1.0 / (m + 1) if m > 0 else 1.0\n val = dx * float(np.sum(conv)) if m > 0 else 0.0\n grad = np.full_like(conv, dx)\n return val, grad\n\ndef _linf(conv: np.ndarray) -> Tuple[float, np.ndarray]:\n \"\"\"Compute ||f*f||_inf and its subgradient.\"\"\"\n if conv.size == 0:\n return 0.0, np.zeros_like(conv)\n m = float(np.max(conv))\n mask = conv == m\n count = int(mask.sum())\n if count == 0 or m <= 0.0:\n return m, np.zeros_like(conv)\n grad = mask.astype(conv.dtype)\n return m, grad\n\ndef _objective_and_grad_conv(conv: np.ndarray) -> Tuple[float, np.ndarray]:\n \"\"\"Compute C = l2_sq / (l1 * linf) and its gradient.\"\"\"\n l2_sq, g_l2 = _simpson_l2sq(conv)\n l1, g_l1 = _l1(conv)\n linf, g_linf = _linf(conv)\n if l1 <= 0.0 or linf <= 0.0:\n return 0.0, np.zeros_like(conv)\n denom = l1 * linf\n c_value = l2_sq / denom\n num_grad = g_l2 * denom - l2_sq * (g_l1 * linf + l1 * g_linf)\n g_conv = num_grad / (denom * denom)\n return float(c_value), g_conv\n\ndef _grad_h_from_conv_grad(h: np.ndarray, g_conv: np.ndarray) -> np.ndarray:\n \"\"\"Compute gradient of C w.r.t h from gradient of C w.r.t conv.\"\"\"\n h_rev = h[::-1]\n g_h = np.convolve(g_conv, h_rev, mode=\"full\")\n N = len(h)\n # Extract the central N elements for the gradient\n gradient = g_h[N-1 : N-1 + N]\n return gradient # Removed factor of 2 as a hypothesis\n\ndef construct_function():\n \"\"\"Optimizes step function sequence using a refined multi-scale approach with improved parameters.\"\"\"\n # Starting parameters with multi-scale approach\n n_start = 64 # Start with small resolution\n max_seconds = 1000 # 1000 seconds time limit\n num_initializations = 80 # Increased for more diverse starts\n\n # Initialize from previous best if available\n if 'height_sequence_1' in globals():\n initial_sequences = [np.array(height_sequence_1, dtype=np.float32)]\n else:\n initial_sequences = []\n\n # Generate diverse structured initial sequences with guaranteed sum of 0.01\n for _ in range(num_initializations):\n # Flat sequence with sum 0.01\n seq = np.full(n_start, 0.01 / n_start, dtype=np.float32)\n initial_sequences.append(seq)\n\n # Random peaks with sum 0.01\n seq = np.zeros(n_start, dtype=np.float32)\n num_random_peaks = 8\n peak_height = 0.01 / num_random_peaks\n indices = np.random.choice(n_start, num_random_peaks, replace=False)\n seq[indices] = peak_height\n initial_sequences.append(seq)\n\n # Single peak with sum 0.01\n seq = np.zeros(n_start, dtype=np.float32)\n seq[n_start // 2] = 0.01\n initial_sequences.append(seq)\n\n # Sinusoidal pattern with sum 0.01\n seq = np.sin(np.linspace(0, 2 * np.pi, n_start))\n seq = np.clip(seq, 0.0, 1.0)\n sum_val = np.sum(seq)\n if sum_val > 0:\n seq = seq * (0.01 / sum_val)\n initial_sequences.append(seq)\n\n # Gaussian-like pattern with sum 0.01\n seq = np.zeros(n_start, dtype=np.float32)\n center = n_start // 2\n std = n_start // 8\n for i in range(n_start):\n seq[i] = np.exp(-((i - center) ** 2) / (2 * std ** 2))\n sum_val = np.sum(seq)\n if sum_val > 0:\n seq = seq * (0.01 / sum_val)\n initial_sequences.append(seq)\n\n # Alternating pattern with sum 0.01\n seq = np.zeros(n_start, dtype=np.float32)\n for i in range(n_start):\n if i % 2 == 0:\n seq[i] = (0.01 / n_start) * 0.3 # Adjust for sum\n else:\n seq[i] = (0.01 / n_start) * 0.1\n initial_sequences.append(seq)\n\n # Custom pattern: multiple evenly spaced peaks\n seq = np.zeros(n_start, dtype=np.float32)\n num_peaks = 8\n peak_height = 0.01 / num_peaks\n indices = np.linspace(0, n_start - 1, num_peaks, dtype=int)\n seq[indices] = peak_height\n initial_sequences.append(seq)\n\n # Evaluate initial sequences to find the best one\n best_seq = None\n best_value = -float('inf')\n for seq in initial_sequences:\n try:\n current_value = evaluate_sequence(seq.tolist())\n except Exception as e:\n print(f\"Error evaluating initial sequence: {e}\")\n continue\n if current_value > best_value:\n best_value = current_value\n best_seq = seq.copy()\n\n if best_seq is None:\n # Fallback to random initialization with sum 0.01\n best_seq = np.random.rand(n_start) * 1000.0\n best_seq = np.clip(best_seq, 0.0, 1000.0)\n best_seq = best_seq * (0.01 / np.sum(best_seq))\n best_value = evaluate_sequence(best_seq.tolist())\n\n # Upscale to target length using interpolation\n target_length = 4096\n current_length = len(best_seq)\n if current_length < target_length:\n x = np.linspace(0, 1, current_length)\n f = interpolate.interp1d(x, best_seq, kind='cubic', fill_value=\"extrapolate\")\n x_new = np.linspace(0, 1, target_length)\n upsampled_seq = f(x_new)\n best_seq = upsampled_seq.astype(np.float32)\n else:\n best_seq = best_seq[:target_length]\n\n # Final optimization with improved Adam optimization parameters\n start_time = time.time()\n best_seq = best_seq.copy()\n best_value = evaluate_sequence(best_seq.tolist())\n \n # Parameters for optimization\n max_iter = 50000 # Increased iterations for better convergence\n learning_rate = 0.2 # Increased learning rate for faster progress\n decay_rate = 0.999 # Slightly slower decay\n min_lr = 1e-6 # Minimum learning rate\n decay_steps = 20 # Decreased decay steps to keep learning rate high\n step_counter = 0\n beta1 = 0.9\n beta2 = 0.999\n epsilon = 1e-8\n\n # Adam parameters\n m = np.zeros_like(best_seq)\n v = np.zeros_like(best_seq)\n t = 0\n\n for _ in range(max_iter):\n step_counter += 1\n \n # Compute gradient\n conv = np.convolve(best_seq, best_seq, mode='full')\n l2_sq, g_l2 = _simpson_l2sq(conv)\n l1, g_l1 = _l1(conv)\n linf, g_linf = _linf(conv)\n \n if l1 <= 0.0 or linf <= 0.0:\n break # Avoid division by zero\n \n denom = l1 * linf\n c_value = l2_sq / denom\n \n # Compute gradient of C with respect to conv\n g_conv = _objective_and_grad_conv(conv)[1]\n \n # Compute gradient of C with respect to h\n grad_h = _grad_h_from_conv_grad(best_seq, g_conv) # Use unclamped sequence\n \n # Adam update\n t += 1\n m = beta1 * m + (1 - beta1) * grad_h\n v = beta2 * v + (1 - beta2) * (grad_h ** 2)\n m_hat = m / (1 - beta1 ** t)\n v_hat = v / (1 - beta2 ** t)\n step = learning_rate * m_hat / (np.sqrt(v_hat) + epsilon)\n best_seq = best_seq + step\n \n # Clip parameters and maintain sum constraint\n best_seq = np.clip(best_seq, 0.0, 1000.0)\n sum_seq = np.sum(best_seq)\n if sum_seq < 0.01:\n needed = 0.01 - sum_seq\n best_seq += needed / len(best_seq)\n \n # Track best value\n current_value = evaluate_sequence(best_seq.tolist())\n if current_value > best_value:\n best_value = current_value\n best_seq = best_seq.copy()\n \n # Check time limit\n if time.time() - start_time > max_seconds - 5:\n break\n \n # Decay learning rate\n if step_counter % decay_steps == 0:\n learning_rate *= decay_rate\n\n # Final evaluation\n final_value = evaluate_sequence(best_seq.tolist())\n print(f\"Final C2 lower bound: {final_value:.6f}\")\n return best_seq.tolist()\n```",
64 "env/all/time/policy": 379.4020659220405,
65 "env/all/time/policy/min": 177.05160903930664,
66 "env/all/time/policy/max": 476.2399637699127,
67 "env/all/time/env_step": 1720.6135561554693,
68 "env/all/time/env_step/min": 0.007177114486694336,
69 "env/all/time/env_step/max": 3890.521183013916,
70 "env/all/time/reward_compute": 2.9942020773887634e-07,
71 "env/all/time/reward_compute/min": 1.5273690223693848e-07,
72 "env/all/time/reward_compute/max": 8.344650268554688e-07,
73 "env/all/by_group/frac_mixed": 1.0,
74 "env/all/by_group/frac_all_good": 0.0,
75 "env/all/by_group/frac_all_bad": 0.0,
76 "advantage/mean": 0.017311546951532364,
77 "advantage/min": -1.0,
78 "advantage/max": 1.5838167667388916,
79 "time/assemble_training_data": 8.485570430755615,
80 "time/kl_vs_base": 99.60595631599426,
81 "kl_policy_base": 0.0007220643456093967,
82 "time/train": 659.621129989624,
83 "time/save_checkpoint": 9.806703329086304,
84 "time/total": 5144.310565471649
85}[2026-07-09T06:38:34+00:00] job=1812632 node=node-30 ngpu=3 ntrain=1 replicas=2 flash_attn=no
[2026-07-09T06:45:52+00:00] job=1812704 node=node-30 ngpu=3 ntrain=1 replicas=2 flash_attn=no
[2026-07-09T07:00:42+00:00] job=1812735 node=node-1 ngpu=3 ntrain=1 replicas=2 flash_attn=no
[2026-07-09T07:26:33+00:00] job=1812827 node=node-14 ngpu=3 ntrain=1 replicas=2 flash_attn=yes
[2026-07-09T09:21:09+00:00] job=1813131 node=node-1 ngpu=3 ntrain=1 replicas=2 flash_attn=yes
[2026-07-09T14:53:48+00:00] job=1813132 node=node-2 ngpu=6 ntrain=2 replicas=4 flash_attn=yes
[2026-07-10T03:31:51+00:00] job=1816627 node=node-14 ngpu=3 ntrain=1 replicas=2 flash_attn=yes
[2026-07-10T03:54:03+00:00] job=1816628 node=node-29 ngpu=6 ntrain=2 replicas=4 flash_attn=yes
[2026-07-10T07:56:44+00:00] job=1817463 node=node-27 ngpu=3 ntrain=1 replicas=2 flash_attn=yes
[2026-07-10T09:10:26+00:00] job=1817464 node=node-7 ngpu=6 ntrain=2 replicas=4 flash_attn=yes