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ac2. Checkpoint saved
after training step 3 (0-indexed). Strict upstream eval parity:
1100s hard kill, verbatim prompts/entrypoints, group 64x8, T=1.0, kl 0.1.1{
2 "step": 3,
3 "progress/batch": 3,
4 "optim/lr": 4e-05,
5 "progress/done_frac": 0.08,
6 "puct/buffer_size": 56,
7 "puct/sampled_size": 8,
8 "puct/T": 1536,
9 "puct/scale_last": 0.4311711689780785,
10 "puct/buffer_value/mean": 0.8786828308754202,
11 "puct/buffer_value/std": 0.10282027935069332,
12 "puct/buffer_value/min": 0.5041471954736918,
13 "puct/buffer_value/max": 0.9353183644517703,
14 "puct/buffer_timestep/mean": 0.7142857142857143,
15 "puct/buffer_timestep/std": 1.0301575072754257,
16 "puct/buffer_timestep/min": -1.0,
17 "puct/buffer_timestep/max": 2.0,
18 "puct/buffer_construction_len/mean": 2620.1964285714284,
19 "puct/buffer_construction_len/std": 1496.2118287247354,
20 "puct/buffer_construction_len/min": 1024.0,
21 "puct/buffer_construction_len/max": 7414.0,
22 "puct/sampled_value/mean": 0.9280942179538929,
23 "puct/sampled_value/std": 0.004049658211058752,
24 "puct/sampled_value/min": 0.9250532055312745,
25 "puct/sampled_value/max": 0.9353183644517703,
26 "puct/sampled_timestep/mean": 2.0,
27 "puct/sampled_timestep/std": 0.0,
28 "puct/sampled_timestep/min": 2.0,
29 "puct/sampled_timestep/max": 2.0,
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": 5528.579762935638,
35 "env/all/ac_tokens_per_turn": 8168.765625,
36 "env/all/ob_tokens_per_turn": 4448.875,
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": 4182408,
41 "env/all/total_ob_tokens": 2277824,
42 "env/all/time/sampling_mean": 317.33958581928164,
43 "env/all/time/sampling_max": 419.49098467826843,
44 "env/all/time/env_step_mean": 2369.4111329298466,
45 "env/all/time/env_step_max": 5103.121490955353,
46 "env/all/reward/mean": 0.15013181923791874,
47 "env/all/reward/max": 0.9372054014294389,
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": 0.15013181923791874,
53 "env/all/correctness": 0.169921875,
54 "env/all/correctness/min": 0.0,
55 "env/all/correctness/max": 1.0,
56 "env/all/raw_score": 0.8835343844806254,
57 "env/all/raw_score/min": 0.19935812667126523,
58 "env/all/raw_score/max": 0.9372054014294389,
59 "env/all/initial_raw_score": 0.9280942179538929,
60 "env/all/initial_raw_score/min": 0.9250532055312745,
61 "env/all/initial_raw_score/max": 0.9353183644517703,
62 "env/all/msg": "Evaluation timed out after 1100 seconds.",
63 "env/all/parsed_code": "```python\nimport numpy as np\nfrom typing import Tuple\nimport random\n\ndef _simpson_l2sq(conv: np.ndarray) -> Tuple[float, np.ndarray]:\n \"\"\"\n Compute ||f*f||_2^2 via Simpson-like piecewise-linear rule with endpoint zeros,\n and return its gradient w.r.t conv (same length as conv).\n \"\"\"\n m = conv.size\n if m == 0:\n return 0.0, np.zeros_like(conv)\n\n dx = 1.0 / (m + 1)\n\n y = np.empty(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\n return float(l2_sq), grad_conv\n\n\ndef _l1(conv: np.ndarray) -> Tuple[float, np.ndarray]:\n \"\"\"||f*f||_1 = dx * sum(conv); gradient is dx * ones.\"\"\"\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\n\ndef _linf(conv: np.ndarray) -> Tuple[float, np.ndarray]:\n \"\"\"||f*f||_inf = max(conv); subgradient: uniform over argmax set.\"\"\"\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) / count\n return m, grad\n\n\ndef _objective_and_grad_conv(conv: np.ndarray) -> Tuple[float, np.ndarray]:\n \"\"\"\n Compute C = l2_sq / (l1 * linf) and gradient dC/d(conv) using quotient rule.\n \"\"\"\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\n\ndef _grad_h_from_conv_grad(h: np.ndarray, g_conv: np.ndarray) -> np.ndarray:\n \"\"\"\n Given dC/d(conv) and conv = h * h (full convolution),\n dC/dh = 2 * (g_conv convolved with reverse(h)) in valid mode (length N).\n \"\"\"\n h_rev = h[::-1]\n g_h = np.convolve(g_conv, h_rev, mode=\"valid\")\n return 2.0 * g_h\n\n\nclass _Adam:\n \"\"\"Lightweight Adam optimizer for numpy arrays (per-candidate).\"\"\"\n\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\n\ndef _batch_objective(h_batch: np.ndarray) -> Tuple[np.ndarray, list[np.ndarray]]:\n \"\"\"Vectorized objective/conv-grad evaluation over a batch.\"\"\"\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\n\ndef _phase_update(h_batch, opt_list, lr, add_noise=False, t=0, eta=1e-2, gamma=0.6):\n \"\"\"One optimization step for the whole 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\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 = []\n for i in range(keep_n):\n new_opts.append(opt_list[idx[i]])\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\n\ndef _upsample_1d(h: np.ndarray) -> np.ndarray:\n \"\"\"Linear 2x upsampling on the search grid.\"\"\"\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\n\ndef _single_candidate_finetune(h0: np.ndarray, lr=3e-3, steps=100_000) -> Tuple[np.ndarray, float]:\n \"\"\"Pure exploitation (no noise) on a single vector with Adam + projection.\"\"\"\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\n\ndef construct_function():\n \"\"\"\n Enhanced multi-resolution gradient-based search with dynamic noise scaling, \n diversified initialization, and adaptive elitism to maximize\n R(f) = ||f*f||_2^2 / (||f*f||_1 * ||f*f||_inf).\n \"\"\"\n # Use height_sequence_1 as the starting point for better initialization\n height_sequence_1 = globals().get(\"height_sequence_1\", [])\n if isinstance(height_sequence_1, list) and len(height_sequence_1) > 0:\n n = len(height_sequence_1)\n h_prev_best = np.array(height_sequence_1, dtype=np.float32)\n else:\n # Use a more informed initialization with Gaussian distribution\n n = 512 # Increased to allow for more resolution\n h_prev_best = np.random.normal(0.0, 0.5, n).astype(np.float32)\n \n h_prev_best = np.clip(h_prev_best, 0.0, None)\n if h_prev_best.shape[0] != n:\n x_old = np.linspace(-0.5, 0.5, h_prev_best.shape[0])\n x_new = np.linspace(-0.5, 0.5, n)\n h_prev_best = np.interp(x_new, x_old, h_prev_best).astype(np.float32)\n\n bsz = 128 # Increased batch size for better diversity\n total_iter = 200_000 # Extended for more exploration\n explore_steps = 100_000 # Sufficient exploration steps\n drop_every = 5_000 # More frequent elitism\n keep_frac = 0.5 # Reduced to maintain diversity\n lr_explore = 1e-1 # Higher initial exploration rate\n lr_exploit = 1e-2 # Lower exploitation rate\n eta, gamma = 1e-1, 0.5 # Adjusted noise parameters\n dtype = np.float32\n\n h_batch = np.random.normal(0.0, 0.5, (bsz, n)).astype(dtype)\n # Start with height_sequence_1 as the best\n if isinstance(height_sequence_1, list) and len(height_sequence_1) > 0:\n h_batch[0] = h_prev_best\n opt_list = [_Adam(shape=(n,), lr=lr_explore, dtype=dtype) for _ in range(bsz)]\n best_h = h_batch.copy()\n best_c = np.full(bsz, -np.inf, dtype=dtype)\n\n for t in range(total_iter):\n if t < explore_steps:\n h_batch, c_vals = _phase_update(\n h_batch, opt_list, lr=lr_explore, add_noise=True, t=t, eta=eta, gamma=gamma\n )\n else:\n h_batch, c_vals = _phase_update(\n h_batch, opt_list, lr=lr_exploit, add_noise=False, t=t, eta=eta, gamma=gamma\n )\n\n improved = c_vals > best_c\n best_c = np.where(improved, c_vals, best_c)\n best_h[improved] = h_batch[improved]\n\n if (t + 1) % drop_every == 0:\n h_batch, opt_list = _elitist_respawn(\n h_batch, c_vals, keep_frac=keep_frac, \n init_sampler=lambda m: np.random.normal(0.0, 0.5, (m, n)).astype(dtype), \n opt_list=opt_list\n )\n\n idx = int(np.argmax(best_c))\n h_star = np.clip(best_h[idx].astype(np.float32), 0.0, None)\n\n h_up1 = _upsample_1d(h_star)\n h_up1, _ = _single_candidate_finetune(h_up1, lr=5e-3, steps=150_000)\n\n h_up2 = _upsample_1d(h_up1)\n h_up2, _ = _single_candidate_finetune(h_up2, lr=5e-3, steps=150_000)\n\n h_up3 = _upsample_1d(h_up2)\n h_up3, _ = _single_candidate_finetune(h_up3, lr=5e-3, steps=150_000)\n\n heights = np.clip(h_up3, 0.0, None)\n r_value = evaluate_sequence(heights.tolist())\n print(f\"Final solution with C2 lower bound of {r_value}\")\n return heights.tolist()\n```",
64 "env/all/time/policy": 317.33958581928164,
65 "env/all/time/policy/min": 147.96830010414124,
66 "env/all/time/policy/max": 419.49098467826843,
67 "env/all/time/env_step": 2369.4111329298466,
68 "env/all/time/env_step/min": 0.0058748722076416016,
69 "env/all/time/env_step/max": 5103.121490955353,
70 "env/all/time/reward_compute": 6.435438990592957e-07,
71 "env/all/time/reward_compute/min": 1.7881393432617188e-07,
72 "env/all/time/reward_compute/max": 3.2782554626464844e-06,
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": 0.040190424770116806,
77 "advantage/min": -0.8404295444488525,
78 "advantage/max": 10.445591926574707,
79 "time/assemble_training_data": 9.521045207977295,
80 "time/kl_vs_base": 91.01070308685303,
81 "kl_policy_base": 0.00044688174966722727,
82 "time/train": 611.9614567756653,
83 "time/save_checkpoint": 12.909881353378296,
84 "time/total": 6258.367972612381
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