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ac2. Checkpoint saved
after training step 13 (0-indexed). Strict upstream eval parity:
1100s hard kill, verbatim prompts/entrypoints, group 64x8, T=1.0, kl 0.1.1{
2 "step": 13,
3 "progress/batch": 13,
4 "optim/lr": 4e-05,
5 "progress/done_frac": 0.28,
6 "puct/buffer_size": 216,
7 "puct/sampled_size": 8,
8 "puct/T": 6656,
9 "puct/scale_last": 0.43720195436973397,
10 "puct/buffer_value/mean": 0.9174719359136638,
11 "puct/buffer_value/std": 0.06166769625087179,
12 "puct/buffer_value/min": 0.5041471954736918,
13 "puct/buffer_value/max": 0.9413491498434258,
14 "puct/buffer_timestep/mean": 5.7407407407407405,
15 "puct/buffer_timestep/std": 3.9024455067027692,
16 "puct/buffer_timestep/min": -1.0,
17 "puct/buffer_timestep/max": 12.0,
18 "puct/buffer_construction_len/mean": 2760.4953703703704,
19 "puct/buffer_construction_len/std": 2894.1880809869135,
20 "puct/buffer_construction_len/min": 1024.0,
21 "puct/buffer_construction_len/max": 32768.0,
22 "puct/sampled_value/mean": 0.9398158400668137,
23 "puct/sampled_value/std": 0.0002717363704238413,
24 "puct/sampled_value/min": 0.939571785997762,
25 "puct/sampled_value/max": 0.9402823046213817,
26 "puct/sampled_timestep/mean": 12.0,
27 "puct/sampled_timestep/std": 0.0,
28 "puct/sampled_timestep/min": 12.0,
29 "puct/sampled_timestep/max": 12.0,
30 "puct/sampled_construction_len/mean": 2048.0,
31 "puct/sampled_construction_len/std": 0.0,
32 "puct/sampled_construction_len/min": 2048.0,
33 "puct/sampled_construction_len/max": 2048.0,
34 "time/sampling": 4373.747488737106,
35 "env/all/ac_tokens_per_turn": 8581.767578125,
36 "env/all/ob_tokens_per_turn": 4288.75,
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": 4393865,
41 "env/all/total_ob_tokens": 2195840,
42 "env/all/time/sampling_mean": 335.48248348385096,
43 "env/all/time/sampling_max": 439.2223379611969,
44 "env/all/time/env_step_mean": 1661.8326786267571,
45 "env/all/time/env_step_max": 3928.8106858730316,
46 "env/all/reward/mean": 0.44001521675238997,
47 "env/all/reward/max": 0.940670288035645,
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": 0.44001521675238997,
53 "env/all/correctness": 0.490234375,
54 "env/all/correctness/min": 0.0,
55 "env/all/correctness/max": 1.0,
56 "env/all/raw_score": 0.8975609202279827,
57 "env/all/raw_score/min": 0.544812101374306,
58 "env/all/raw_score/max": 0.940670288035645,
59 "env/all/initial_raw_score": 0.9398158400668135,
60 "env/all/initial_raw_score/min": 0.939571785997762,
61 "env/all/initial_raw_score/max": 0.9402823046213817,
62 "env/all/msg": "Success; raw_score=0.904293558714165",
63 "env/all/parsed_code": "```python\nimport numpy as np\nfrom typing import Tuple\nimport time\nimport random\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\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\n lhs = y[:-1]\n rhs = y[1:]\n l2_sq = (dx / 3.0) * np.sum(lhs * lhs + lhs * rhs + rhs * rhs)\n\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) if m > 0 else np.zeros_like(conv)\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\n if l1 <= 0.0 or linf <= 0.0:\n return 0.0, np.zeros_like(conv)\n\n denom = l1 * linf\n c_value = l2_sq / denom\n\n num_grad = g_l2 * denom - l2_sq * (g_l1 * linf + l1 * g_linf)\n g_conv = num_grad / (denom * denom)\n\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=\"valid\")\n return 2.0 * g_h\n\nclass _Adam:\n \"\"\"Lightweight Adam optimizer for numpy arrays (per-candidate).\"\"\"\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 _batch_objective(h_batch: np.ndarray) -> Tuple[np.ndarray, list[np.ndarray]]:\n \"\"\"Vectorized evaluation of objective and gradient.\"\"\"\n bsz = h_batch.shape[0]\n c_vals = np.zeros(bsz, dtype=np.float32)\n conv_grads = [None] * bsz\n for b in range(bsz):\n h = np.clip(h_batch[b], 0.0, None)\n conv = np.convolve(h, h, mode=\"full\")\n c_val, g_conv = _objective_and_grad_conv(conv)\n c_vals[b] = c_val\n conv_grads[b] = g_conv\n return c_vals, conv_grads\n\ndef _phase_update(h_batch, opt_list, lr, add_noise=False, t=0, eta=1e-1, gamma=0.3):\n \"\"\"Update all candidates in the batch.\"\"\"\n bsz = h_batch.shape[0]\n c_vals, conv_grads = _batch_objective(h_batch)\n grads = np.zeros_like(h_batch, dtype=h_batch.dtype)\n for b in range(bsz):\n clipped = np.clip(h_batch[b], 0.0, None)\n grads[b] = _grad_h_from_conv_grad(clipped, conv_grads[b])\n\n if add_noise:\n sigma = eta / ((t + 1) ** gamma)\n grads = grads + sigma * np.random.normal(size=grads.shape).astype(grads.dtype)\n\n for b in range(bsz):\n opt = opt_list[b]\n opt.lr = lr\n h_new = opt.step(h_batch[b], grads[b].astype(h_batch.dtype))\n h_batch[b] = np.clip(h_new, 0.0, None)\n\n return h_batch, c_vals\n\ndef _elitist_respawn(h_batch, c_vals, keep_frac, init_sampler, opt_list):\n \"\"\"Keep top fraction and respawn the rest.\"\"\"\n bsz = h_batch.shape[0]\n keep_n = max(1, int(bsz * keep_frac))\n idx = np.argsort(c_vals)[-keep_n:]\n survivors = h_batch[idx].copy()\n\n fresh = init_sampler(bsz - keep_n)\n new_batch = np.concatenate([survivors, fresh], axis=0)\n\n new_opts = [opt_list[i] for i in idx]\n for _ in range(bsz - keep_n):\n new_opts.append(_Adam(shape=h_batch.shape[1:], lr=opt_list[0].lr, dtype=h_batch.dtype))\n\n return new_batch, new_opts\n\ndef _upsample_1d(h: np.ndarray) -> np.ndarray:\n \"\"\"Upsample by linear interpolation.\"\"\"\n return np.interp(np.linspace(0, 1, 2 * h.size), np.linspace(0, 1, h.size), h)\n\ndef _single_candidate_finetune(h0: np.ndarray, lr=3e-3, steps=150_000) -> Tuple[np.ndarray, float]:\n \"\"\"Refine a single candidate using Adam with projection.\"\"\"\n h = h0.astype(np.float32).copy()\n opt = _Adam(h.shape, lr=lr, dtype=h.dtype)\n best_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 best_c = max(best_c, c_val)\n return h, float(best_c)\n\ndef construct_function():\n \"\"\"\n Construct optimized step function sequence to improve C2 lower bound.\n Key improvements include:\n - Increased diversity through larger batch size and novel patterns\n - Enhanced exploration with adaptive noise and learning rates\n - Improved elitism and refinement phases\n - More aggressive gradient-based optimization\n \"\"\"\n # Optimized hyperparameters for enhanced exploration\n n_start = 256 # Smaller initial resolution for faster exploration\n bsz = 512 # Larger batch size for more diversity\n total_iter = 150_000 # More efficient exploration within time limit\n explore_steps = 75_000 # Split exploration for better convergence\n drop_every = 500 # More frequent elitism\n keep_frac = 0.8 # Better diversity preservation\n\n # Initialize with previous best if available\n if 'height_sequence_1' in globals():\n prev = np.array(height_sequence_1, dtype=np.float32)\n else:\n prev = np.ones(n_start, dtype=np.float32)\n\n # Resample to initial length\n prev = np.clip(prev, 0.0, 1000.0)\n if prev.shape[0] != n_start:\n x_old = np.linspace(-0.5, 0.5, prev.shape[0])\n x_new = np.linspace(-0.5, 0.5, n_start)\n prev = np.interp(x_new, x_old, prev).astype(np.float32)\n\n # Diverse initialization with structured patterns\n def init_sampler(m):\n out = np.random.uniform(0.0, 1000.0, size=(m, n_start)).astype(np.float32)\n out[0] = prev # Include previous best\n\n for i in range(1, m):\n # Randomly select from 10 patterns\n pattern_idx = np.random.randint(0, 10)\n if pattern_idx == 0:\n # Gaussian-like distribution\n mean = np.random.uniform(0.2, 0.8)\n std = np.random.uniform(0.1, 0.3)\n out[i] = np.random.normal(loc=mean, scale=std, size=n_start).astype(np.float32)\n elif pattern_idx == 1:\n # Exponential distribution\n scale = np.random.uniform(0.1, 0.5)\n out[i] = np.random.exponential(scale=scale, size=n_start).astype(np.float32)\n elif pattern_idx == 2:\n # Sine wave with randomized frequency and phase\n freq = np.random.uniform(0.1, 0.5)\n phase = np.random.uniform(0, 2 * np.pi)\n t = np.linspace(-0.5, 0.5, n_start)\n out[i] = 0.5 * (1 + np.sin(2 * np.pi * freq * t + phase)).astype(np.float32)\n elif pattern_idx == 3:\n # Multi-peak pattern\n num_peaks = np.random.randint(5, 10)\n out[i] = np.zeros(n_start)\n for _ in range(num_peaks):\n pos = np.random.randint(0, n_start - 1)\n height = np.random.uniform(50.0, 100.0)\n out[i][pos] = height\n elif pattern_idx == 4:\n # Random sparse spikes\n out[i] = np.random.uniform(0.0, 0.1, size=n_start).astype(np.float32)\n spike_pos = np.random.choice(n_start, 5, replace=False)\n out[i][spike_pos] += np.random.uniform(0.5, 1.5, size=5).astype(np.float32)\n elif pattern_idx == 5:\n # Decaying exponential pattern\n t = np.linspace(0, 1, n_start)\n out[i] = np.exp(-t * np.random.uniform(1.0, 5.0)).astype(np.float32)\n elif pattern_idx == 6:\n # Comb pattern with periodic peaks\n period = np.random.randint(20, 50)\n peak_height = np.random.uniform(50.0, 100.0)\n out[i] = np.zeros(n_start)\n for k in range(n_start // period):\n pos = k * period + np.random.randint(0, period)\n out[i][pos] = peak_height\n elif pattern_idx == 7:\n # Alternating high and low values\n out[i] = np.random.uniform(0.0, 1000.0, size=n_start).astype(np.float32)\n for j in range(n_start):\n if j % 2 == 0:\n out[i][j] = np.random.uniform(0.0, 800.0)\n else:\n out[i][j] = np.random.uniform(0.0, 200.0)\n elif pattern_idx == 8:\n # Sum of multiple sine waves\n freqs = np.random.uniform(0.1, 0.5, size=3)\n phases = np.random.uniform(0, 2 * np.pi, size=3)\n amps = np.random.uniform(0.3, 0.7, size=3)\n t = np.linspace(-0.5, 0.5, n_start)\n out[i] = 0.5 * (1 + np.sin(2 * np.pi * freqs[0] * t + phases[0])) * amps[0] + \\\n 0.5 * (1 + np.sin(2 * np.pi * freqs[1] * t + phases[1])) * amps[1] + \\\n 0.5 * (1 + np.sin(2 * np.pi * freqs[2] * t + phases[2])) * amps[2]\n out[i] = np.clip(out[i], 0.0, 1000.0)\n elif pattern_idx == 9:\n # Random walk pattern\n out[i] = np.zeros(n_start)\n prev_val = 0.0\n for j in range(n_start):\n step = np.random.normal(loc=0.0, scale=5.0)\n prev_val += step\n out[i][j] = np.clip(prev_val, 0.0, 1000.0)\n # Ensure non-negative and within bounds\n out[i] = np.clip(out[i], 0.0, 1000.0)\n return out\n\n h_batch = init_sampler(bsz)\n opt_list = [_Adam(shape=(n_start,), lr=0.02, dtype=np.float32) for _ in range(bsz)]\n best_h = h_batch.copy()\n best_c = np.full(bsz, -np.inf, dtype=np.float32)\n\n start_time = time.time()\n\n for t in range(total_iter):\n if t < explore_steps:\n # Explosive phase with adaptive noise and learning rate\n h_batch, c_vals = _phase_update(\n h_batch, opt_list, lr=0.04, add_noise=True, t=t, eta=1e-1, gamma=0.3\n )\n else:\n # Exploitation phase with refined parameters\n h_batch, c_vals = _phase_update(\n h_batch, opt_list, lr=5e-5, add_noise=True, t=t, eta=5e-2, gamma=0.5\n )\n\n # Update best candidates\n improved_idx = c_vals > best_c\n best_c = np.where(improved_idx, c_vals, best_c)\n best_h[improved_idx] = h_batch[improved_idx]\n\n # Periodic elitist respawn for diversity\n if (t + 1) % drop_every == 0:\n h_batch, opt_list = _elitist_respawn(\n h_batch, c_vals, keep_frac=keep_frac, init_sampler=init_sampler, opt_list=opt_list\n )\n\n # Periodic logging and early stopping\n if t % 500 == 0:\n elapsed = time.time() - start_time\n print(f\"Iteration {t} (elapsed: {elapsed:.1f}s) - Best score: {best_c[np.argmax(best_c)]:.6f}\")\n if elapsed > 950:\n print(\"Reached time limit, stopping early.\")\n break\n\n # Refinement process with multi-resolution\n idx = np.argmax(best_c)\n h_star = np.clip(best_h[idx].astype(np.float32), 0.0, None)\n h_up1 = _upsample_1d(h_star)\n h_up1, _ = _single_candidate_finetune(h_up1, lr=3e-3, steps=100_000)\n\n h_up2 = _upsample_1d(h_up1)\n h_up2, _ = _single_candidate_finetune(h_up2, lr=3e-3, steps=100_000)\n\n h_final = np.clip(h_up2, 0.0, 1000.0)\n heights = h_final.tolist()\n r_value = evaluate_sequence(heights)\n print(f\"Final C2 lower bound: {r_value:.6f}\")\n return heights\n```",
64 "env/all/time/policy": 335.48248348385096,
65 "env/all/time/policy/min": 154.72077918052673,
66 "env/all/time/policy/max": 439.2223379611969,
67 "env/all/time/env_step": 1661.8326786267571,
68 "env/all/time/env_step/min": 0.006005525588989258,
69 "env/all/time/env_step/max": 3928.8106858730316,
70 "env/all/time/reward_compute": 2.6496127247810364e-07,
71 "env/all/time/reward_compute/min": 2.0116567611694336e-07,
72 "env/all/time/reward_compute/max": 3.986060619354248e-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": 0.025641728192567825,
77 "advantage/min": -1.0,
78 "advantage/max": 11.765484809875488,
79 "time/assemble_training_data": 8.669291257858276,
80 "time/kl_vs_base": 99.56005096435547,
81 "kl_policy_base": 0.000664810708258301,
82 "time/train": 626.874852180481,
83 "time/save_checkpoint": 17.97040104866028,
84 "time/total": 5129.900453090668
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