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ac2. Checkpoint saved
after training step 17 (0-indexed). Strict upstream eval parity:
1100s hard kill, verbatim prompts/entrypoints, group 64x8, T=1.0, kl 0.1.1{
2 "step": 17,
3 "progress/batch": 17,
4 "optim/lr": 4e-05,
5 "progress/done_frac": 0.36,
6 "puct/buffer_size": 277,
7 "puct/sampled_size": 8,
8 "puct/T": 8704,
9 "puct/scale_last": 0.19098317596260406,
10 "puct/buffer_value/mean": 0.9247212628763299,
11 "puct/buffer_value/std": 0.05035750154069582,
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14 "puct/buffer_timestep/mean": 7.794223826714801,
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17 "puct/buffer_timestep/max": 16.0,
18 "puct/buffer_construction_len/mean": 3577.7870036101085,
19 "puct/buffer_construction_len/std": 2390.045913213367,
20 "puct/buffer_construction_len/min": 1024.0,
21 "puct/buffer_construction_len/max": 32768.0,
22 "puct/sampled_value/mean": 0.947178490589921,
23 "puct/sampled_value/std": 0.00022550363446937195,
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26 "puct/sampled_timestep/mean": 16.0,
27 "puct/sampled_timestep/std": 0.0,
28 "puct/sampled_timestep/min": 16.0,
29 "puct/sampled_timestep/max": 16.0,
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": 5721.727853536606,
35 "env/all/ac_tokens_per_turn": 8580.013671875,
36 "env/all/ob_tokens_per_turn": 3683.75,
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": 4392967,
41 "env/all/total_ob_tokens": 1886080,
42 "env/all/time/sampling_mean": 322.494564817287,
43 "env/all/time/sampling_max": 421.2100670337677,
44 "env/all/time/env_step_mean": 2676.460171020124,
45 "env/all/time/env_step_max": 5313.328110694885,
46 "env/all/reward/mean": 0.2832135951613881,
47 "env/all/reward/max": 0.9474669279340687,
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": 0.2832135951613881,
53 "env/all/correctness": 0.337890625,
54 "env/all/correctness/min": 0.0,
55 "env/all/correctness/max": 1.0,
56 "env/all/raw_score": 0.8381812758533567,
57 "env/all/raw_score/min": 0.026758781901906874,
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59 "env/all/initial_raw_score": 0.947178490589921,
60 "env/all/initial_raw_score/min": 0.9468955460447651,
61 "env/all/initial_raw_score/max": 0.9474390362025952,
62 "env/all/msg": "Success; raw_score=0.9468231135643477",
63 "env/all/parsed_code": "```python\nimport numpy as np\nfrom typing import Tuple, List\nimport random\nimport time\n\n# Helper functions for L2_sq, L1, L-infinity and their gradients\ndef _simpson_l2sq(conv: np.ndarray) -> Tuple[float, np.ndarray]:\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 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 if conv.size == 0:\n return 0.0, np.zeros_like(conv)\n m = float(np.max(conv))\n if m <= 0.0:\n return m, np.zeros_like(conv)\n mask = conv == m\n count = int(mask.sum())\n if count == 0:\n return m, np.zeros_like(conv)\n grad = mask.astype(conv.dtype) / count\n return m, grad\n\ndef _objective_and_grad_conv(conv: np.ndarray) -> Tuple[float, np.ndarray]:\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 h_rev = h[::-1]\n g_h = np.convolve(g_conv, h_rev, mode=\"valid\")\n return 2.0 * g_h\n\n# Upsampling function and refinement function\ndef _upsample_1d(h: np.ndarray) -> np.ndarray:\n n = h.shape[0]\n x_old = np.linspace(-0.5, 0.5, n)\n x_new = np.linspace(-0.5, 0.5, 2 * n)\n return np.interp(x_new, x_old, h)\n\ndef _single_candidate_finetune(h0: np.ndarray, lr=5e-3, steps=60000) -> Tuple[np.ndarray, float]:\n h = h0.astype(np.float32).copy()\n opt = _Adam(h.shape, lr=lr, dtype=h.dtype)\n last_c = 0.0\n for _ in range(steps):\n h_clip = np.clip(h, 0.0, None)\n conv = np.convolve(h_clip, h_clip, mode=\"full\")\n c_val, g_conv = _objective_and_grad_conv(conv)\n g_h = _grad_h_from_conv_grad(h_clip, g_conv)\n h = np.clip(opt.step(h, g_h.astype(h.dtype)), 0.0, None)\n last_c = c_val\n return h, float(last_c)\n\nclass _Adam:\n def __init__(self, shape, lr=3e-2, beta1=0.9, beta2=0.999, eps=1e-8, dtype=np.float32):\n self.m = np.zeros(shape, dtype=dtype)\n self.v = np.zeros(shape, dtype=dtype)\n self.t = 0\n self.lr = lr\n self.b1 = beta1\n self.b2 = beta2\n self.eps = eps\n\n def step(self, params, grad):\n self.t += 1\n self.m = self.b1 * self.m + (1 - self.b1) * grad\n self.v = self.b2 * self.v + (1 - self.b2) * (grad * grad)\n m_hat = self.m / (1 - self.b1 ** self.t)\n v_hat = self.v / (1 - self.b2 ** self.t)\n return params + self.lr * m_hat / (np.sqrt(v_hat) + self.eps)\n\ndef construct_function():\n \"\"\"\n Optimizes a sequence of non-negative heights using a multi-scale strategy with refined initial sequences\n and adaptive learning rate/noise parameters to maximize the evaluation score.\n \"\"\"\n np.random.seed(42)\n \n # Load previous best sequence\n height_sequence_1 = globals().get(\"height_sequence_1\", None)\n target_length = 4096\n initial_n = 64 # Starting sequence length\n h = np.zeros(target_length, dtype=np.float32)\n \n if height_sequence_1 is not None:\n # Use the previous best and upscale\n initial_h = np.array(height_sequence_1, dtype=np.float32)\n initial_n = min(len(initial_h), target_length)\n x_old = np.linspace(-0.5, 0.5, len(initial_h))\n x_new = np.linspace(-0.5, 0.5, initial_n)\n h = np.interp(x_new, x_old, initial_h)\n else:\n # Generate symmetric initial sequence with Gaussian shape\n half_length = initial_n // 2\n mu = 0.0\n sigma = 0.1 # Gaussian standard deviation\n x = np.linspace(-0.5, 0.5, initial_n)\n symmetrical_seq = 1000.0 * np.exp(- (x - mu)**2 / (2 * sigma**2))\n x_old = np.linspace(-0.5, 0.5, initial_n)\n x_new = np.linspace(-0.5, 0.5, initial_n)\n h = np.interp(x_new, x_old, symmetrical_seq)\n h = np.pad(h, (0, target_length - initial_n), 'constant', constant_values=0)\n \n # Parameters\n learning_rate = 2.0\n noise_scale_initial = 20.0 # Increased noise for better exploration\n noise_decay = 0.995 # Slower decay for more exploration\n learning_rate_decay = 0.99\n upscale_steps = 100_000 # More steps for better optimization\n refine_steps = 100_000 # Fewer steps to save time\n \n start_time = time.time()\n \n # Multi-scale optimization with structured initial steps\n current_length = initial_n\n scale_factor = 2\n \n for _ in range(10): # Upscale 10 times for better exploration\n if current_length < target_length:\n # Upsample\n h = _upsample_1d(h)\n current_length *= 2\n n = len(h)\n # Remove symmetry enforcement\n # if n % 2 == 0:\n # h[n//2:] = h[:n//2][::-1]\n # else:\n # h[n//2+1:] = h[:n//2][::-1]\n \n # Initial optimization with noise\n h_opt = np.copy(h)\n for step in range(upscale_steps): # Fixed number of steps per upscale\n clipped_h = np.clip(h_opt, 0.0, None)\n conv = np.convolve(clipped_h, clipped_h, mode='full')\n obj_val, grad_conv = _objective_and_grad_conv(conv)\n grad_h = _grad_h_from_conv_grad(clipped_h, grad_conv)\n \n noise_scale = noise_scale_initial * (noise_decay ** step)\n learning_rate_current = learning_rate * (learning_rate_decay ** step)\n \n noise = noise_scale * np.random.normal(size=h_opt.shape)\n h_opt = np.clip(h_opt + learning_rate_current * grad_h + noise, 0.0, 1000.0)\n \n h_sum = np.sum(h_opt)\n if h_sum < 0.01:\n h_opt = np.clip(h_opt + (0.01 - h_sum) / h_opt.shape[0], 0.0, 1000.0)\n \n remaining_time = 1000 - (time.time() - start_time)\n if remaining_time < 5:\n print(f\"Time remaining: {remaining_time} seconds. Performing final refinement.\")\n break\n h = h_opt\n \n # Final refinement with smaller learning rate\n h_refined, _ = _single_candidate_finetune(h, lr=5e-3, steps=refine_steps)\n \n h_final = np.clip(h_refined, 0.0, 1000.0)\n heights = h_final.tolist()\n r_value = evaluate_sequence(heights)\n print(f\"Final C2 lower bound: {r_value}\")\n return heights\n```",
64 "env/all/time/policy": 322.494564817287,
65 "env/all/time/policy/min": 127.46445822715759,
66 "env/all/time/policy/max": 421.2100670337677,
67 "env/all/time/env_step": 2676.460171020124,
68 "env/all/time/env_step/min": 0.00532841682434082,
69 "env/all/time/env_step/max": 5313.328110694885,
70 "env/all/time/reward_compute": 2.5564804673194885e-07,
71 "env/all/time/reward_compute/min": 1.9371509552001953e-07,
72 "env/all/time/reward_compute/max": 3.129243850708008e-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": 0.028596628457307816,
77 "advantage/min": -1.0,
78 "advantage/max": 5.532862186431885,
79 "time/assemble_training_data": 10.30665111541748,
80 "time/kl_vs_base": 95.33949851989746,
81 "kl_policy_base": 0.0006840918795205653,
82 "time/train": 595.3462994098663,
83 "time/save_checkpoint": 17.528019428253174,
84 "time/total": 6444.043220996857
85}[2026-07-09T06:42:12+00:00] job=1812634 node=node-30 ngpu=3 ntrain=1 replicas=2 flash_attn=no
[2026-07-09T07:26:33+00:00] job=1812736 node=node-12 ngpu=3 ntrain=1 replicas=2 flash_attn=yes
[2026-07-09T09:27:32+00:00] job=1813133 node=node-14 ngpu=3 ntrain=1 replicas=2 flash_attn=yes
[2026-07-09T16:26:04+00:00] job=1813134 node=node-4 ngpu=6 ntrain=2 replicas=4 flash_attn=yes