W0909 00:25:54.152000 1345976 torch/distributed/run.py:766] W0909 00:25:54.152000 1345976 torch/distributed/run.py:766] ***************************************** W0909 00:25:54.152000 1345976 torch/distributed/run.py:766] Setting OMP_NUM_THREADS environment variable for each process to be 1 in default, to avoid your system being overloaded, please further tune the variable for optimal performance in your application as needed. W0909 00:25:54.152000 1345976 torch/distributed/run.py:766] ***************************************** [2025-09-09 00:29:23,076] [INFO] [real_accelerator.py:254:get_accelerator] Setting ds_accelerator to cuda (auto detect) [2025-09-09 00:29:23,081] [INFO] [real_accelerator.py:254:get_accelerator] Setting ds_accelerator to cuda (auto detect) [2025-09-09 00:29:23,143] [INFO] [real_accelerator.py:254:get_accelerator] Setting ds_accelerator to cuda (auto detect) [2025-09-09 00:29:23,223] [INFO] [real_accelerator.py:254:get_accelerator] Setting ds_accelerator to cuda (auto detect) [2025-09-09 00:29:23,632] [INFO] [real_accelerator.py:254:get_accelerator] Setting ds_accelerator to cuda (auto detect) [2025-09-09 00:29:23,634] [INFO] [real_accelerator.py:254:get_accelerator] Setting ds_accelerator to cuda (auto detect) [2025-09-09 00:29:23,636] [INFO] [real_accelerator.py:254:get_accelerator] Setting ds_accelerator to cuda (auto detect) [2025-09-09 00:29:23,856] [INFO] [real_accelerator.py:254:get_accelerator] Setting ds_accelerator to cuda (auto detect) Warning: The cache directory for DeepSpeed Triton autotune, /home/zxd283/.triton/autotune, appears to be on an NFS system. While this is generally acceptable, if you experience slowdowns or hanging when DeepSpeed exits, it is recommended to set the TRITON_CACHE_DIR environment variable to a non-NFS path. Warning: The cache directory for DeepSpeed Triton autotune, /home/zxd283/.triton/autotune, appears to be on an NFS system. While this is generally acceptable, if you experience slowdowns or hanging when DeepSpeed exits, it is recommended to set the TRITON_CACHE_DIR environment variable to a non-NFS path. Warning: The cache directory for DeepSpeed Triton autotune, /home/zxd283/.triton/autotune, appears to be on an NFS system. While this is generally acceptable, if you experience slowdowns or hanging when DeepSpeed exits, it is recommended to set the TRITON_CACHE_DIR environment variable to a non-NFS path. Warning: The cache directory for DeepSpeed Triton autotune, /home/zxd283/.triton/autotune, appears to be on an NFS system. While this is generally acceptable, if you experience slowdowns or hanging when DeepSpeed exits, it is recommended to set the TRITON_CACHE_DIR environment variable to a non-NFS path. Warning: The cache directory for DeepSpeed Triton autotune, /home/zxd283/.triton/autotune, appears to be on an NFS system. While this is generally acceptable, if you experience slowdowns or hanging when DeepSpeed exits, it is recommended to set the TRITON_CACHE_DIR environment variable to a non-NFS path. Warning: The cache directory for DeepSpeed Triton autotune, /home/zxd283/.triton/autotune, appears to be on an NFS system. While this is generally acceptable, if you experience slowdowns or hanging when DeepSpeed exits, it is recommended to set the TRITON_CACHE_DIR environment variable to a non-NFS path. Warning: The cache directory for DeepSpeed Triton autotune, /home/zxd283/.triton/autotune, appears to be on an NFS system. While this is generally acceptable, if you experience slowdowns or hanging when DeepSpeed exits, it is recommended to set the TRITON_CACHE_DIR environment variable to a non-NFS path. Warning: The cache directory for DeepSpeed Triton autotune, /home/zxd283/.triton/autotune, appears to be on an NFS system. While this is generally acceptable, if you experience slowdowns or hanging when DeepSpeed exits, it is recommended to set the TRITON_CACHE_DIR environment variable to a non-NFS path. [2025-09-09 00:30:37,186] [INFO] [comm.py:669:init_distributed] cdb=None [2025-09-09 00:30:37,197] [INFO] [comm.py:669:init_distributed] cdb=None [2025-09-09 00:30:37,197] [INFO] [comm.py:700:init_distributed] Initializing TorchBackend in DeepSpeed with backend nccl Using the `WANDB_DISABLED` environment variable is deprecated and will be removed in v5. Use the --report_to flag to control the integrations used for logging result (for instance --report_to none). [2025-09-09 00:30:37,435] [INFO] [comm.py:669:init_distributed] cdb=None [2025-09-09 00:30:37,509] [INFO] [comm.py:669:init_distributed] cdb=None [INFO|2025-09-09 00:30:37] llamafactory.hparams.parser:410 >> Process rank: 0, world size: 8, device: cuda:0, distributed training: True, compute dtype: torch.bfloat16 [2025-09-09 00:30:37,744] [INFO] [comm.py:669:init_distributed] cdb=None Using the `WANDB_DISABLED` environment variable is deprecated and will be removed in v5. Use the --report_to flag to control the integrations used for logging result (for instance --report_to none). [2025-09-09 00:30:37,851] [INFO] [comm.py:669:init_distributed] cdb=None [2025-09-09 00:30:37,852] [INFO] [comm.py:669:init_distributed] cdb=None [2025-09-09 00:30:37,853] [INFO] [comm.py:669:init_distributed] cdb=None [INFO|2025-09-09 00:30:37] llamafactory.hparams.parser:410 >> Process rank: 3, world size: 8, device: cuda:3, distributed training: True, compute dtype: torch.bfloat16 [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,141 >> loading file vocab.json [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,141 >> loading file merges.txt [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,141 >> loading file tokenizer.json [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,141 >> loading file added_tokens.json [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,141 >> loading file special_tokens_map.json [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,141 >> loading file tokenizer_config.json [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,142 >> loading file chat_template.jinja Using the `WANDB_DISABLED` environment variable is deprecated and will be removed in v5. Use the --report_to flag to control the integrations used for logging result (for instance --report_to none). Using the `WANDB_DISABLED` environment variable is deprecated and will be removed in v5. Use the --report_to flag to control the integrations used for logging result (for instance --report_to none). [INFO|tokenization_utils_base.py:2299] 2025-09-09 00:30:38,364 >> Special tokens have been added in the vocabulary, make sure the associated word embeddings are fine-tuned or trained. [INFO|configuration_utils.py:696] 2025-09-09 00:30:38,369 >> loading configuration file /scratch/pioneer/jobs/job.2746985.pioneer/qwen-7b/config.json [INFO|configuration_utils.py:770] 2025-09-09 00:30:38,410 >> Model config Qwen2Config { "architectures": [ "Qwen2ForCausalLM" ], "attention_dropout": 0.0, "bos_token_id": 151643, "eos_token_id": 151645, "hidden_act": "silu", "hidden_size": 3584, "initializer_range": 0.02, "intermediate_size": 18944, "max_position_embeddings": 32768, "max_window_layers": 28, "model_type": "qwen2", "num_attention_heads": 28, "num_hidden_layers": 28, "num_key_value_heads": 4, "rms_norm_eps": 1e-06, "rope_scaling": null, "rope_theta": 1000000.0, "sliding_window": 131072, "tie_word_embeddings": false, "torch_dtype": "bfloat16", "transformers_version": "4.52.4", "use_cache": true, "use_sliding_window": false, "vocab_size": 152064 } [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,412 >> loading file vocab.json [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,412 >> loading file merges.txt [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,412 >> loading file tokenizer.json [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,412 >> loading file added_tokens.json [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,412 >> loading file special_tokens_map.json [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,412 >> loading file tokenizer_config.json [INFO|tokenization_utils_base.py:2021] 2025-09-09 00:30:38,412 >> loading file chat_template.jinja [INFO|2025-09-09 00:30:38] llamafactory.hparams.parser:410 >> Process rank: 1, world size: 8, device: cuda:1, distributed training: True, compute dtype: torch.bfloat16 [INFO|2025-09-09 00:30:38] llamafactory.hparams.parser:410 >> Process rank: 4, world size: 8, device: cuda:4, distributed training: True, compute dtype: torch.bfloat16 Using the `WANDB_DISABLED` environment variable is deprecated and will be removed in v5. Use the --report_to flag to control the integrations used for logging result (for instance --report_to none). Using the `WANDB_DISABLED` environment variable is deprecated and will be removed in v5. Use the --report_to flag to control the integrations used for logging result (for instance --report_to none). Using the `WANDB_DISABLED` environment variable is deprecated and will be removed in v5. Use the --report_to flag to control the integrations used for logging result (for instance --report_to none). Using the `WANDB_DISABLED` environment variable is deprecated and will be removed in v5. Use the --report_to flag to control the integrations used for logging result (for instance --report_to none). [INFO|tokenization_utils_base.py:2299] 2025-09-09 00:30:38,630 >> Special tokens have been added in the vocabulary, make sure the associated word embeddings are fine-tuned or trained. [INFO|2025-09-09 00:30:38] llamafactory.hparams.parser:410 >> Process rank: 5, world size: 8, device: cuda:5, distributed training: True, compute dtype: torch.bfloat16 [INFO|2025-09-09 00:30:38] llamafactory.data.loader:143 >> Loading dataset /scratch/pioneer/jobs/job.2746985.pioneer/openthought114k_math_rightplan_train/openthought114k_math_plan_10000.jsonl... [INFO|2025-09-09 00:30:38] llamafactory.hparams.parser:410 >> Process rank: 2, world size: 8, device: cuda:2, distributed training: True, compute dtype: torch.bfloat16 [INFO|2025-09-09 00:30:38] llamafactory.hparams.parser:410 >> Process rank: 7, world size: 8, device: cuda:7, distributed training: True, compute dtype: torch.bfloat16 [INFO|2025-09-09 00:30:38] llamafactory.hparams.parser:410 >> Process rank: 6, world size: 8, device: cuda:6, distributed training: True, compute dtype: torch.bfloat16 /home/zxd283/entropy/arpo/lib/python3.12/site-packages/torch/distributed/distributed_c10d.py:4631: UserWarning: No device id is provided via `init_process_group` or `barrier `. Using the current device set by the user. warnings.warn( # warn only once [rank3]:[W909 00:30:38.157193674 ProcessGroupNCCL.cpp:4718] [PG ID 0 PG GUID 0 Rank 3] using GPU 3 as device used by this process is currently unknown. This can potentially cause a hang if this rank to GPU mapping is incorrect. You can pecify device_id in init_process_group() to force use of a particular device. [INFO|2025-09-09 00:30:38] llamafactory.data.loader:143 >> Sampled 10000 examples from dataset /scratch/pioneer/jobs/job.2746985.pioneer/openthought114k_math_rightplan_train/openthought114k_math_plan_10000.jsonl. Converting format of dataset (num_proc=16): 0%| | 0/10000 [00:00system Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop well-considered thinking process. Please structure your response into three main sections: Planning, Thought and Solution. In the Planning section, a high-level execution plan is provided for the problem. It consists of plain-language bullet points that describe the overall strategy, decomposition steps, conditional reasoning, and validation checks. No formulas, variables, or calculations are included, using the specified format: {plan with steps separated with ' '} Only one block should appear, and it must come before any other section. In the Thought section, detail your reasoning process using the specified format: {thought with steps separated with ' '} Each step should include detailed considerations such as analisying questions, summarizing relevant findings, brainstorming new ideas, verifying the accuracy of the current steps, refining any errors, and revisiting previous steps, avoid excessive repetition or speculative loops; stop when the reasoning is sufficient to support a reliable conclusion. In the Solution section, based on various attempts, explorations, and reflections from the Thought section, systematically present the final solution that you deem correct. The solution should remain a logical, accurate, concise expression style and detail necessary step needed to reach the conclusion, formatted as follows: {final formatted, precise, and clear solution} Now, try to solve the following question through the above guidelines:<|im_end|> <|im_start|>user Return your final response within \boxed{}. When measuring a part, random errors occur that follow a normal distribution with a parameter $\sigma=10$ mm. Find the probability that the measurement is made with an error not exceeding $15$ mm.<|im_end|> <|im_start|>assistant - Define the problem as finding the probability that a normal random variable with mean zero and standard deviation ten lies within ±15. - Convert the error bounds to standard z-scores using the formula (value minus mean) divided by standard deviation. - Use symmetry of the normal distribution to compute the area between the two z-scores as twice the cumulative probability up to the positive z-score minus one. - If the cumulative probability for the positive z-score is available, apply the formula directly; otherwise, use a standard normal table or computational tool. - Validate the result by cross-checking with known empirical rules or alternative methods such as the error function. - Ensure the final probability is expressed as a decimal rounded to four places. Okay, so I need to find the probability that a measurement error doesn't exceed 15 mm. The errors follow a normal distribution with a standard deviation σ = 10 mm. Hmm, normal distribution problems usually involve z-scores and the standard normal table. Let me recall how to approach this. First, the normal distribution is symmetric around the mean. Since we're dealing with errors, I assume the mean error μ is 0 mm because random errors are equally likely to be positive or negative. So the distribution is N(0, 10²). The question asks for the probability that the error is between -15 mm and 15 mm. In other words, P(-15 ≤ X ≤ 15). To find this probability, I need to convert the values to z-scores. The z-score formula is z = (X - μ)/σ. Here, μ is 0, so z = X/σ. Calculating the z-scores for 15 and -15: For X = 15: z = 15/10 = 1.5 For X = -15: z = -15/10 = -1.5 So now, the problem becomes finding P(-1.5 ≤ Z ≤ 1.5) where Z is the standard normal variable (mean 0, standard deviation 1). I remember that the standard normal distribution table gives the cumulative probability from negative infinity up to a z-score. So to find the area between -1.5 and 1.5, I can find the cumulative probability up to 1.5 and subtract the cumulative probability up to -1.5. Alternatively, since the normal distribution is symmetric, P(Z ≤ -1.5) is equal to 1 - P(Z ≤ 1.5). Therefore, P(-1.5 ≤ Z ≤ 1.5) = P(Z ≤ 1.5) - P(Z ≤ -1.5) = P(Z ≤ 1.5) - [1 - P(Z ≤ 1.5)] = 2*P(Z ≤ 1.5) - 1. Let me confirm that. If the total area under the curve is 1, then the area from -infinity to 1.5 is P(Z ≤ 1.5), and the area from -infinity to -1.5 is P(Z ≤ -1.5). The area between -1.5 and 1.5 is the difference between these two. Since the distribution is symmetric, the area below -1.5 is the same as the area above 1.5. So yes, the area between -1.5 and 1.5 is 1 - 2*P(Z ≤ -1.5) or 2*P(Z ≤ 1.5) - 1. Either way, I need to look up the z-score of 1.5 in the standard normal table. Looking at the standard normal table, for z = 1.5, the cumulative probability is 0.9332. Let me verify that. The row for 1.5 and column 0.00 gives 0.9332. Yes, that seems right. So P(Z ≤ 1.5) = 0.9332. Then, P(-1.5 ≤ Z ≤ 1.5) = 2*0.9332 - 1 = 1.8664 - 1 = 0.8664. So approximately 86.64% probability. Wait, but let me double-check. If I use the empirical rule, for normal distributions, about 68% of data is within 1σ, 95% within 2σ, and 99.7% within 3σ. Here, 15 mm is 1.5σ from the mean. The empirical rule doesn't cover 1.5σ exactly, but maybe we can estimate. Since 1σ is 68%, 2σ is 95%, so 1.5σ should be between 68% and 95%. Our calculated value is ~86.6%, which is reasonable. That seems plausible. Alternatively, if I use a calculator or more precise z-table, maybe the value is slightly different? Let me check a more detailed table. For z = 1.5, some tables break it down into more decimal places. For example, z = 1.50 is 0.93319, which rounds to 0.9332. So the value is accurate. Therefore, the probability is 0.8664, or 86.64%. But wait, the problem states "an error not exceeding 15 mm". Does that mean |X| ≤ 15 mm, which is what I calculated, or is it X ≤ 15 mm? Hmm. The wording says "error not exceeding 15 mm". Since errors can be positive or negative, but the magnitude is what's being considered. So, yes, it's the absolute error, so |X| ≤ 15 mm. Therefore, my calculation is correct. So converting to z-scores, getting 1.5 and -1.5, calculating the area between them, which is 0.8664. Alternatively, using a calculator function, if I compute the probability between -15 and 15 with μ=0 and σ=10, using the normal CDF: In some notation, P(-15 < X < 15) = Φ((15 - 0)/10) - Φ((-15 - 0)/10) = Φ(1.5) - Φ(-1.5). Which again is 0.9332 - 0.0668 = 0.8664. Yes, that's consistent. So the answer is approximately 0.8664, or 86.64%. Alternatively, is there a more precise value? Let me check the exact value from the standard normal distribution. The cumulative distribution function for Z=1.5 is 0.933192799. So 2*0.933192799 -1 = 0.866385598, which is approximately 0.8664, or 86.64%. Therefore, the probability is approximately 86.64%. Wait, sometimes answers are expressed in terms of fractions or using exact values. But since the question is about probability, we can present it as 0.8664, or convert it to a percentage, 86.64%. Alternatively, using the error function (erf), since the normal distribution CDF can be expressed in terms of erf. The formula is P(-a ≤ X ≤ a) = erf(a / (σ√2)). Let's verify that. Given X ~ N(μ, σ²), then P(μ - a ≤ X ≤ μ + a) = erf(a / (σ√2)). Here, μ=0, so P(-a ≤ X ≤ a) = erf(a/(σ√2)). In our case, a =15, σ=10. So erf(15/(10*√2)) = erf(15/(14.1421)) ≈ erf(1.06066). Let me compute erf(1.06066). Looking up erf(1.06) and erf(1.07) from a table or using a calculator: erf(1.06) ≈ 0.8621 erf(1.07) ≈ 0.8643 But 1.06066 is approximately 1.0607, which is between 1.06 and 1.07. Let's interpolate. The difference between 1.06 and 1.07 is 0.01 in the argument. The value at 1.06 is 0.8621, at 1.07 is 0.8643, difference of 0.0022 over 0.01. Our value is 1.06066, which is 1.06 + 0.00066. So the fraction is 0.00066/0.01 = 0.066. So we add 0.066 * 0.0022 ≈ 0.000145. Therefore, erf(1.06066) ≈ 0.8621 + 0.000145 ≈ 0.862245. But wait, this gives P(-15 ≤ X ≤15) = erf(1.06066) ≈ 0.862245, which is approximately 0.8622, but this contradicts the previous value of 0.8664. Wait, why is there a discrepancy? Wait, perhaps I made a mistake in the formula. Let me check the relation between the error function and the normal distribution. The error function is defined as erf(x) = (2/√π) ∫₀ˣ e^(-t²) dt. The relationship between the standard normal distribution and erf is: For X ~ N(0,1), P(-a ≤ X ≤ a) = erf(a / √2). But in our case, X ~ N(0,10²), so to standardize it, we have Z = X/10 ~ N(0,1). Therefore, P(-15 ≤ X ≤15) = P(-1.5 ≤ Z ≤1.5) = erf(1.5 / √2). Wait, let me confirm. For a standard normal variable Z, P(-z ≤ Z ≤ z) = erf(z / √2). So in this case, z=1.5, so erf(1.5 / √2). Let's compute that. 1.5 / √2 ≈ 1.5 / 1.4142 ≈ 1.06066. Therefore, erf(1.06066) ≈ ? Using a calculator or a more precise erf table: The value of erf(1.06066) can be computed more accurately. Let me use an approximation formula or an online calculator. Alternatively, use the Taylor series expansion. But maybe this is complicating. Alternatively, since we know that P(-1.5 ≤ Z ≤1.5) = 2Φ(1.5) -1, and Φ(1.5) is 0.933192799, so 0.933192799*2 -1 = 0.866385598, which is approximately 0.8664. But according to the erf method, it should be the same. Wait, erf(1.5 / sqrt(2)) = erf(1.06066) ≈ 0.8622. But this contradicts the value of 0.8664. There must be a mistake here. Wait, no. Let me check again. The relation is P(-a ≤ X ≤ a) for X ~ N(0, σ²) is equal to erf(a / (σ sqrt(2))). In this case, σ=10, a=15. So: erf(15 / (10 * sqrt(2))) = erf(15/(14.1421)) = erf(1.06066) ≈ 0.8622. But according to the standard normal table, it's approximately 0.8664. Which is correct? Wait, I must be mixing formulas. Let me clarify. For a general normal distribution N(μ, σ²), the probability P(μ - a ≤ X ≤ μ + a) can be expressed using the error function as: P = erf(a / (σ sqrt(2))) But in our case, X ~ N(0,10²), so μ=0, σ=10, a=15. So P(-15 ≤ X ≤15) = erf(15 / (10 * sqrt(2))) = erf(1.5 / sqrt(2)) ≈ erf(1.06066). But according to standard normal CDF, this probability is 2Φ(1.5) -1 ≈ 2*0.9332 -1 ≈ 0.8664. But according to the error function, it's erf(1.06066) ≈ 0.8622. These are two different results. Why is there a discrepancy? Wait, no, actually, the correct relation is: For X ~ N(0, σ²), P(|X| ≤ a) = erf(a / (σ sqrt(2))). But also, in terms of the standard normal variable Z = X/σ ~ N(0,1), P(|Z| ≤ z) = 2Φ(z) -1, where z = a/σ. Therefore, combining these two expressions: erf(z / sqrt(2)) = 2Φ(z) -1. Therefore, Φ(z) = [1 + erf(z / sqrt(2))]/2. So, if we take z =1.5, then Φ(1.5) = [1 + erf(1.5 / sqrt(2))]/2. Let's compute erf(1.5 / sqrt(2)) ≈ erf(1.06066) ≈ 0.8622. Then Φ(1.5) ≈ (1 + 0.8622)/2 ≈ 0.9311, but we know Φ(1.5) is 0.9332. So there is a discrepancy here. This suggests that the approximation of erf(1.06066) as 0.8622 is not accurate enough. Therefore, probably the error function value needs to be calculated more precisely. Let's use a better approximation for erf(1.06066). Alternatively, use the fact that Φ(1.5) = 0.933192799, so 2Φ(1.5) -1 = 0.866385598. Therefore, this should equal erf(1.5 / sqrt(2)) = erf(1.06066). Therefore, erf(1.06066) ≈ 0.866385598 ≈ 0.8664. Therefore, my previous value of 0.8622 must be incorrect. Probably, the table I was referring to was not precise enough or I made a miscalculation. Therefore, the correct value is indeed approximately 0.8664. Thus, the probability is 0.8664, or 86.64%. Therefore, the answer is approximately 0.8664, which can be written as 86.64% or as a fraction if needed. But the question doesn't specify the form, so either is acceptable. However, typically, probabilities are given as decimals rounded to four decimal places or percentages with two decimal places. Alternatively, using a calculator for the error function, if possible. For example, using a calculator, erf(1.06066) can be computed more accurately. Let me try with an approximate formula. The error function can be approximated using the following series expansion: erf(x) = (2/√π) ∑_{n=0}^∞ (-1)^n x^{2n+1}/(n! (2n+1)) But calculating this manually would be tedious. Alternatively, use a polynomial approximation. For x ≥ 0, the Handbook of Mathematical Functions by Abramowitz and Stegun provides an approximation for erf(x) with a maximum error of 1.5×10−7: erf(x) ≈ 1 - (a₁t + a₂t² + a₃t³ + a₄t⁴ + a₅t⁵)e^{-x²} where t = 1/(1 + px), p = 0.3275911, and the coefficients are: a₁ = 0.254829592, a₂ = -0.284496736, a₃ = 1.421413741, a₄ = -1.453152027, a₅ = 1.061405429. Let's apply this to x =1.06066. First, compute t = 1/(1 + p x). p=0.3275911, x=1.06066. p x = 0.3275911 *1.06066 ≈ 0.3275911*1.06 ≈ 0.34725 (more precisely: 1.06066 *0.3275911 ≈ 1.06*0.32759 ≈ 0.34725, then 0.00066*0.3275911≈0.000216, so total ≈0.34725 +0.000216≈0.347466). So t ≈1/(1 +0.347466)=1/1.347466≈0.7416. Then compute the polynomial: a₁t + a₂t² + a₃t³ + a₄t⁴ + a₅t⁵. Compute each term: a₁ t = 0.254829592 *0.7416 ≈0.25483*0.74 ≈0.1886 (more precisely: 0.25483*0.7416≈0.25483*0.7=0.17838, 0.25483*0.0416≈0.0106, total≈0.17838+0.0106≈0.18898) a₂ t² = -0.284496736*(0.7416)^2 ≈-0.2845*(0.5499)≈-0.2845*0.5≈-0.14225, -0.2845*0.0499≈-0.0142, total≈-0.14225-0.0142≈-0.15645 a₃ t³ =1.421413741*(0.7416)^3≈1.4214*(0.7416*0.7416*0.7416). Compute 0.7416³: 0.7416*0.7416≈0.5499, then 0.5499*0.7416≈0.4076. So 1.4214*0.4076≈0.5795 a₄ t⁴= -1.453152027*(0.7416)^4≈-1.4532*(0.7416⁴). 0.7416⁴≈0.4076*0.7416≈0.3023. So -1.4532*0.3023≈-0.4393 a₅ t⁵=1.061405429*(0.7416)^5≈1.0614*(0.7416^5). 0.7416^5≈0.3023*0.7416≈0.2243. So 1.0614*0.2243≈0.2380 Now sum all terms: 0.18898 -0.15645 +0.5795 -0.4393 +0.2380 ≈ First, 0.18898 -0.15645 ≈0.03253 0.03253 +0.5795 ≈0.61203 0.61203 -0.4393 ≈0.17273 0.17273 +0.2380 ≈0.41073 Multiply by e^{-x²} where x=1.06066. Compute x²≈1.1249. e^{-1.1249} ≈0.3246. Therefore, the terms sum to 0.41073 *0.3246≈0.1333. Then erf(x) ≈1 -0.1333≈0.8667. Therefore, erf(1.06066)≈0.8667, which matches our previous result of approximately 0.8664. The slight difference is due to approximation errors in the calculation. Therefore, the exact value is approximately 0.8664, confirming our initial result. Thus, the probability that the measurement error does not exceed 15 mm is approximately 0.8664, or 86.64%. I think that's thorough. I considered different methods to confirm the result: using z-scores and standard normal tables, relating to the error function, and even performing an approximation of the error function to verify. All methods lead to the same conclusion, so I'm confident the answer is correct. The probability that the measurement error does not exceed 15 mm is calculated by converting the error limits to z-scores and finding the corresponding area under the standard normal distribution. 1. **Given**: - Normal distribution parameters: Mean (μ) = 0 mm, Standard Deviation (σ) = 10 mm. - Error limit: ±15 mm. 2. **Convert to Z-scores**: \[ Z = \frac{X - \mu}{\sigma} \implies Z = \frac{15}{10} = 1.5 \quad \text{and} \quad Z = \frac{-15}{10} = -1.5 \] 3. **Find the Probability**: The area between \( Z = -1.5 \) and \( Z = 1.5 \) in the standard normal distribution is: \[ P(-1.5 \leq Z \leq 1.5) = 2 \cdot \Phi(1.5) - 1 \] Using standard normal tables or a calculator: \[ \Phi(1.5) \approx 0.9332 \implies 2 \cdot 0.9332 - 1 = 0.8664 \] **Final Answer**: The probability is \(\boxed{0.8664}\). <|im_end|> label_ids: [-100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, -100, 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13, 20, 1124, 8, 323, 17767, 1863, 284, 220, 16, 13, 20, 1124, 8, 304, 279, 5297, 4622, 7982, 374, 25, 2303, 256, 1124, 9640, 256, 393, 4080, 16, 13, 20, 1124, 273, 80, 1863, 1124, 273, 80, 220, 16, 13, 20, 8, 284, 220, 17, 1124, 50853, 1124, 45167, 7, 16, 13, 20, 8, 481, 220, 16, 198, 256, 1124, 60, 2303, 256, 12091, 5297, 4622, 12632, 476, 264, 29952, 25, 2303, 256, 1124, 9640, 256, 1124, 45167, 7, 16, 13, 20, 8, 1124, 48053, 220, 15, 13, 24, 18, 18, 17, 1124, 6383, 550, 220, 17, 1124, 50853, 220, 15, 13, 24, 18, 18, 17, 481, 220, 16, 284, 220, 15, 13, 23, 21, 21, 19, 198, 256, 1124, 2533, 334, 19357, 21806, 95518, 2303, 785, 18927, 374, 1124, 11520, 79075, 90, 15, 13, 23, 21, 21, 19, 11035, 3593, 151645, 198] labels: - Define the problem as finding the probability that a normal random variable with mean zero and standard deviation ten lies within ±15. - Convert the error bounds to standard z-scores using the formula (value minus mean) divided by standard deviation. - Use symmetry of the normal distribution to compute the area between the two z-scores as twice the cumulative probability up to the positive z-score minus one. - If the cumulative probability for the positive z-score is available, apply the formula directly; otherwise, use a standard normal table or computational tool. - Validate the result by cross-checking with known empirical rules or alternative methods such as the error function. - Ensure the final probability is expressed as a decimal rounded to four places. Okay, so I need to find the probability that a measurement error doesn't exceed 15 mm. The errors follow a normal distribution with a standard deviation σ = 10 mm. Hmm, normal distribution problems usually involve z-scores and the standard normal table. Let me recall how to approach this. First, the normal distribution is symmetric around the mean. Since we're dealing with errors, I assume the mean error μ is 0 mm because random errors are equally likely to be positive or negative. So the distribution is N(0, 10²). The question asks for the probability that the error is between -15 mm and 15 mm. In other words, P(-15 ≤ X ≤ 15). To find this probability, I need to convert the values to z-scores. The z-score formula is z = (X - μ)/σ. Here, μ is 0, so z = X/σ. Calculating the z-scores for 15 and -15: For X = 15: z = 15/10 = 1.5 For X = -15: z = -15/10 = -1.5 So now, the problem becomes finding P(-1.5 ≤ Z ≤ 1.5) where Z is the standard normal variable (mean 0, standard deviation 1). I remember that the standard normal distribution table gives the cumulative probability from negative infinity up to a z-score. So to find the area between -1.5 and 1.5, I can find the cumulative probability up to 1.5 and subtract the cumulative probability up to -1.5. Alternatively, since the normal distribution is symmetric, P(Z ≤ -1.5) is equal to 1 - P(Z ≤ 1.5). Therefore, P(-1.5 ≤ Z ≤ 1.5) = P(Z ≤ 1.5) - P(Z ≤ -1.5) = P(Z ≤ 1.5) - [1 - P(Z ≤ 1.5)] = 2*P(Z ≤ 1.5) - 1. Let me confirm that. If the total area under the curve is 1, then the area from -infinity to 1.5 is P(Z ≤ 1.5), and the area from -infinity to -1.5 is P(Z ≤ -1.5). The area between -1.5 and 1.5 is the difference between these two. Since the distribution is symmetric, the area below -1.5 is the same as the area above 1.5. So yes, the area between -1.5 and 1.5 is 1 - 2*P(Z ≤ -1.5) or 2*P(Z ≤ 1.5) - 1. Either way, I need to look up the z-score of 1.5 in the standard normal table. Looking at the standard normal table, for z = 1.5, the cumulative probability is 0.9332. Let me verify that. The row for 1.5 and column 0.00 gives 0.9332. Yes, that seems right. So P(Z ≤ 1.5) = 0.9332. Then, P(-1.5 ≤ Z ≤ 1.5) = 2*0.9332 - 1 = 1.8664 - 1 = 0.8664. So approximately 86.64% probability. Wait, but let me double-check. If I use the empirical rule, for normal distributions, about 68% of data is within 1σ, 95% within 2σ, and 99.7% within 3σ. Here, 15 mm is 1.5σ from the mean. The empirical rule doesn't cover 1.5σ exactly, but maybe we can estimate. Since 1σ is 68%, 2σ is 95%, so 1.5σ should be between 68% and 95%. Our calculated value is ~86.6%, which is reasonable. That seems plausible. Alternatively, if I use a calculator or more precise z-table, maybe the value is slightly different? Let me check a more detailed table. For z = 1.5, some tables break it down into more decimal places. For example, z = 1.50 is 0.93319, which rounds to 0.9332. So the value is accurate. Therefore, the probability is 0.8664, or 86.64%. But wait, the problem states "an error not exceeding 15 mm". Does that mean |X| ≤ 15 mm, which is what I calculated, or is it X ≤ 15 mm? Hmm. The wording says "error not exceeding 15 mm". Since errors can be positive or negative, but the magnitude is what's being considered. So, yes, it's the absolute error, so |X| ≤ 15 mm. Therefore, my calculation is correct. So converting to z-scores, getting 1.5 and -1.5, calculating the area between them, which is 0.8664. Alternatively, using a calculator function, if I compute the probability between -15 and 15 with μ=0 and σ=10, using the normal CDF: In some notation, P(-15 < X < 15) = Φ((15 - 0)/10) - Φ((-15 - 0)/10) = Φ(1.5) - Φ(-1.5). Which again is 0.9332 - 0.0668 = 0.8664. Yes, that's consistent. So the answer is approximately 0.8664, or 86.64%. Alternatively, is there a more precise value? Let me check the exact value from the standard normal distribution. The cumulative distribution function for Z=1.5 is 0.933192799. So 2*0.933192799 -1 = 0.866385598, which is approximately 0.8664, or 86.64%. Therefore, the probability is approximately 86.64%. Wait, sometimes answers are expressed in terms of fractions or using exact values. But since the question is about probability, we can present it as 0.8664, or convert it to a percentage, 86.64%. Alternatively, using the error function (erf), since the normal distribution CDF can be expressed in terms of erf. The formula is P(-a ≤ X ≤ a) = erf(a / (σ√2)). Let's verify that. Given X ~ N(μ, σ²), then P(μ - a ≤ X ≤ μ + a) = erf(a / (σ√2)). Here, μ=0, so P(-a ≤ X ≤ a) = erf(a/(σ√2)). In our case, a =15, σ=10. So erf(15/(10*√2)) = erf(15/(14.1421)) ≈ erf(1.06066). Let me compute erf(1.06066). Looking up erf(1.06) and erf(1.07) from a table or using a calculator: erf(1.06) ≈ 0.8621 erf(1.07) ≈ 0.8643 But 1.06066 is approximately 1.0607, which is between 1.06 and 1.07. Let's interpolate. The difference between 1.06 and 1.07 is 0.01 in the argument. The value at 1.06 is 0.8621, at 1.07 is 0.8643, difference of 0.0022 over 0.01. Our value is 1.06066, which is 1.06 + 0.00066. So the fraction is 0.00066/0.01 = 0.066. So we add 0.066 * 0.0022 ≈ 0.000145. Therefore, erf(1.06066) ≈ 0.8621 + 0.000145 ≈ 0.862245. But wait, this gives P(-15 ≤ X ≤15) = erf(1.06066) ≈ 0.862245, which is approximately 0.8622, but this contradicts the previous value of 0.8664. Wait, why is there a discrepancy? Wait, perhaps I made a mistake in the formula. Let me check the relation between the error function and the normal distribution. The error function is defined as erf(x) = (2/√π) ∫₀ˣ e^(-t²) dt. The relationship between the standard normal distribution and erf is: For X ~ N(0,1), P(-a ≤ X ≤ a) = erf(a / √2). But in our case, X ~ N(0,10²), so to standardize it, we have Z = X/10 ~ N(0,1). Therefore, P(-15 ≤ X ≤15) = P(-1.5 ≤ Z ≤1.5) = erf(1.5 / √2). Wait, let me confirm. For a standard normal variable Z, P(-z ≤ Z ≤ z) = erf(z / √2). So in this case, z=1.5, so erf(1.5 / √2). Let's compute that. 1.5 / √2 ≈ 1.5 / 1.4142 ≈ 1.06066. Therefore, erf(1.06066) ≈ ? Using a calculator or a more precise erf table: The value of erf(1.06066) can be computed more accurately. Let me use an approximation formula or an online calculator. Alternatively, use the Taylor series expansion. But maybe this is complicating. Alternatively, since we know that P(-1.5 ≤ Z ≤1.5) = 2Φ(1.5) -1, and Φ(1.5) is 0.933192799, so 0.933192799*2 -1 = 0.866385598, which is approximately 0.8664. But according to the erf method, it should be the same. Wait, erf(1.5 / sqrt(2)) = erf(1.06066) ≈ 0.8622. But this contradicts the value of 0.8664. There must be a mistake here. Wait, no. Let me check again. The relation is P(-a ≤ X ≤ a) for X ~ N(0, σ²) is equal to erf(a / (σ sqrt(2))). In this case, σ=10, a=15. So: erf(15 / (10 * sqrt(2))) = erf(15/(14.1421)) = erf(1.06066) ≈ 0.8622. But according to the standard normal table, it's approximately 0.8664. Which is correct? Wait, I must be mixing formulas. Let me clarify. For a general normal distribution N(μ, σ²), the probability P(μ - a ≤ X ≤ μ + a) can be expressed using the error function as: P = erf(a / (σ sqrt(2))) But in our case, X ~ N(0,10²), so μ=0, σ=10, a=15. So P(-15 ≤ X ≤15) = erf(15 / (10 * sqrt(2))) = erf(1.5 / sqrt(2)) ≈ erf(1.06066). But according to standard normal CDF, this probability is 2Φ(1.5) -1 ≈ 2*0.9332 -1 ≈ 0.8664. But according to the error function, it's erf(1.06066) ≈ 0.8622. These are two different results. Why is there a discrepancy? Wait, no, actually, the correct relation is: For X ~ N(0, σ²), P(|X| ≤ a) = erf(a / (σ sqrt(2))). But also, in terms of the standard normal variable Z = X/σ ~ N(0,1), P(|Z| ≤ z) = 2Φ(z) -1, where z = a/σ. Therefore, combining these two expressions: erf(z / sqrt(2)) = 2Φ(z) -1. Therefore, Φ(z) = [1 + erf(z / sqrt(2))]/2. So, if we take z =1.5, then Φ(1.5) = [1 + erf(1.5 / sqrt(2))]/2. Let's compute erf(1.5 / sqrt(2)) ≈ erf(1.06066) ≈ 0.8622. Then Φ(1.5) ≈ (1 + 0.8622)/2 ≈ 0.9311, but we know Φ(1.5) is 0.9332. So there is a discrepancy here. This suggests that the approximation of erf(1.06066) as 0.8622 is not accurate enough. Therefore, probably the error function value needs to be calculated more precisely. Let's use a better approximation for erf(1.06066). Alternatively, use the fact that Φ(1.5) = 0.933192799, so 2Φ(1.5) -1 = 0.866385598. Therefore, this should equal erf(1.5 / sqrt(2)) = erf(1.06066). Therefore, erf(1.06066) ≈ 0.866385598 ≈ 0.8664. Therefore, my previous value of 0.8622 must be incorrect. Probably, the table I was referring to was not precise enough or I made a miscalculation. Therefore, the correct value is indeed approximately 0.8664. Thus, the probability is 0.8664, or 86.64%. Therefore, the answer is approximately 0.8664, which can be written as 86.64% or as a fraction if needed. But the question doesn't specify the form, so either is acceptable. However, typically, probabilities are given as decimals rounded to four decimal places or percentages with two decimal places. Alternatively, using a calculator for the error function, if possible. For example, using a calculator, erf(1.06066) can be computed more accurately. Let me try with an approximate formula. The error function can be approximated using the following series expansion: erf(x) = (2/√π) ∑_{n=0}^∞ (-1)^n x^{2n+1}/(n! (2n+1)) But calculating this manually would be tedious. Alternatively, use a polynomial approximation. For x ≥ 0, the Handbook of Mathematical Functions by Abramowitz and Stegun provides an approximation for erf(x) with a maximum error of 1.5×10−7: erf(x) ≈ 1 - (a₁t + a₂t² + a₃t³ + a₄t⁴ + a₅t⁵)e^{-x²} where t = 1/(1 + px), p = 0.3275911, and the coefficients are: a₁ = 0.254829592, a₂ = -0.284496736, a₃ = 1.421413741, a₄ = -1.453152027, a₅ = 1.061405429. Let's apply this to x =1.06066. First, compute t = 1/(1 + p x). p=0.3275911, x=1.06066. p x = 0.3275911 *1.06066 ≈ 0.3275911*1.06 ≈ 0.34725 (more precisely: 1.06066 *0.3275911 ≈ 1.06*0.32759 ≈ 0.34725, then 0.00066*0.3275911≈0.000216, so total ≈0.34725 +0.000216≈0.347466). So t ≈1/(1 +0.347466)=1/1.347466≈0.7416. Then compute the polynomial: a₁t + a₂t² + a₃t³ + a₄t⁴ + a₅t⁵. Compute each term: a₁ t = 0.254829592 *0.7416 ≈0.25483*0.74 ≈0.1886 (more precisely: 0.25483*0.7416≈0.25483*0.7=0.17838, 0.25483*0.0416≈0.0106, total≈0.17838+0.0106≈0.18898) a₂ t² = -0.284496736*(0.7416)^2 ≈-0.2845*(0.5499)≈-0.2845*0.5≈-0.14225, -0.2845*0.0499≈-0.0142, total≈-0.14225-0.0142≈-0.15645 a₃ t³ =1.421413741*(0.7416)^3≈1.4214*(0.7416*0.7416*0.7416). Compute 0.7416³: 0.7416*0.7416≈0.5499, then 0.5499*0.7416≈0.4076. So 1.4214*0.4076≈0.5795 a₄ t⁴= -1.453152027*(0.7416)^4≈-1.4532*(0.7416⁴). 0.7416⁴≈0.4076*0.7416≈0.3023. So -1.4532*0.3023≈-0.4393 a₅ t⁵=1.061405429*(0.7416)^5≈1.0614*(0.7416^5). 0.7416^5≈0.3023*0.7416≈0.2243. So 1.0614*0.2243≈0.2380 Now sum all terms: 0.18898 -0.15645 +0.5795 -0.4393 +0.2380 ≈ First, 0.18898 -0.15645 ≈0.03253 0.03253 +0.5795 ≈0.61203 0.61203 -0.4393 ≈0.17273 0.17273 +0.2380 ≈0.41073 Multiply by e^{-x²} where x=1.06066. Compute x²≈1.1249. e^{-1.1249} ≈0.3246. Therefore, the terms sum to 0.41073 *0.3246≈0.1333. Then erf(x) ≈1 -0.1333≈0.8667. Therefore, erf(1.06066)≈0.8667, which matches our previous result of approximately 0.8664. The slight difference is due to approximation errors in the calculation. Therefore, the exact value is approximately 0.8664, confirming our initial result. Thus, the probability that the measurement error does not exceed 15 mm is approximately 0.8664, or 86.64%. I think that's thorough. I considered different methods to confirm the result: using z-scores and standard normal tables, relating to the error function, and even performing an approximation of the error function to verify. All methods lead to the same conclusion, so I'm confident the answer is correct. The probability that the measurement error does not exceed 15 mm is calculated by converting the error limits to z-scores and finding the corresponding area under the standard normal distribution. 1. **Given**: - Normal distribution parameters: Mean (μ) = 0 mm, Standard Deviation (σ) = 10 mm. - Error limit: ±15 mm. 2. **Convert to Z-scores**: \[ Z = \frac{X - \mu}{\sigma} \implies Z = \frac{15}{10} = 1.5 \quad \text{and} \quad Z = \frac{-15}{10} = -1.5 \] 3. **Find the Probability**: The area between \( Z = -1.5 \) and \( Z = 1.5 \) in the standard normal distribution is: \[ P(-1.5 \leq Z \leq 1.5) = 2 \cdot \Phi(1.5) - 1 \] Using standard normal tables or a calculator: \[ \Phi(1.5) \approx 0.9332 \implies 2 \cdot 0.9332 - 1 = 0.8664 \] **Final Answer**: The probability is \(\boxed{0.8664}\). <|im_end|> [INFO|configuration_utils.py:696] 2025-09-09 00:30:56,066 >> loading configuration file /scratch/pioneer/jobs/job.2746985.pioneer/qwen-7b/config.json [INFO|configuration_utils.py:770] 2025-09-09 00:30:56,066 >> Model config Qwen2Config { "architectures": [ "Qwen2ForCausalLM" ], "attention_dropout": 0.0, "bos_token_id": 151643, "eos_token_id": 151645, "hidden_act": "silu", "hidden_size": 3584, "initializer_range": 0.02, "intermediate_size": 18944, "max_position_embeddings": 32768, "max_window_layers": 28, "model_type": "qwen2", "num_attention_heads": 28, "num_hidden_layers": 28, "num_key_value_heads": 4, "rms_norm_eps": 1e-06, "rope_scaling": null, "rope_theta": 1000000.0, "sliding_window": 131072, "tie_word_embeddings": false, "torch_dtype": "bfloat16", "transformers_version": "4.52.4", "use_cache": true, "use_sliding_window": false, "vocab_size": 152064 } [INFO|2025-09-09 00:30:56] llamafactory.model.model_utils.kv_cache:143 >> KV cache is disabled during training. [INFO|modeling_utils.py:1148] 2025-09-09 00:31:21,245 >> loading weights file /scratch/pioneer/jobs/job.2746985.pioneer/qwen-7b/model.safetensors.index.json [INFO|modeling_utils.py:2241] 2025-09-09 00:31:21,246 >> Instantiating Qwen2ForCausalLM model under default dtype torch.bfloat16. [INFO|configuration_utils.py:1135] 2025-09-09 00:31:21,248 >> Generate config GenerationConfig { "bos_token_id": 151643, "eos_token_id": 151645, "use_cache": false } Loading checkpoint shards: 0%| | 0/4 [00:00> All model checkpoint weights were used when initializing Qwen2ForCausalLM. [INFO|modeling_utils.py:5139] 2025-09-09 00:31:24,691 >> All the weights of Qwen2ForCausalLM were initialized from the model checkpoint at /scratch/pioneer/jobs/job.2746985.pioneer/qwen-7b. If your task is similar to the task the model of the checkpoint was trained on, you can already use Qwen2ForCausalLM for predictions without further training. [INFO|configuration_utils.py:1088] 2025-09-09 00:31:24,694 >> loading configuration file /scratch/pioneer/jobs/job.2746985.pioneer/qwen-7b/generation_config.json [INFO|configuration_utils.py:1135] 2025-09-09 00:31:24,695 >> Generate config GenerationConfig { "bos_token_id": 151643, "do_sample": true, "eos_token_id": [ 151645, 151643 ], "pad_token_id": 151643, "repetition_penalty": 1.05, "temperature": 0.7, "top_k": 20, "top_p": 0.8 } [INFO|2025-09-09 00:31:24] llamafactory.model.model_utils.checkpointing:143 >> Gradient checkpointing enabled. [INFO|2025-09-09 00:31:24] llamafactory.model.model_utils.attention:143 >> Using torch SDPA for faster training and inference. [INFO|2025-09-09 00:31:24] llamafactory.model.adapter:143 >> Upcasting trainable params to float32. [INFO|2025-09-09 00:31:24] llamafactory.model.adapter:143 >> Fine-tuning method: Full Loading checkpoint shards: 100%|██████████| 4/4 [00:03<00:00, 1.38it/s] Loading checkpoint shards: 100%|██████████| 4/4 [00:03<00:00, 1.30it/s] [INFO|2025-09-09 00:31:24] llamafactory.model.loader:143 >> trainable params: 7,615,616,512 || all params: 7,615,616,512 || trainable%: 100.0000 Loading checkpoint shards: 100%|██████████| 4/4 [00:03<00:00, 1.24it/s] Loading checkpoint shards: 100%|██████████| 4/4 [00:03<00:00, 1.16it/s] Loading checkpoint shards: 100%|██████████| 4/4 [00:03<00:00, 1.23it/s] Loading checkpoint shards: 100%|██████████| 4/4 [00:03<00:00, 1.16it/s] Loading checkpoint shards: 100%|██████████| 4/4 [00:04<00:00, 1.08it/s] Loading checkpoint shards: 100%|██████████| 4/4 [00:04<00:00, 1.00s/it] Loading checkpoint shards: 100%|██████████| 4/4 [00:03<00:00, 1.10it/s] Loading checkpoint shards: 100%|██████████| 4/4 [00:03<00:00, 1.08it/s] Loading checkpoint shards: 100%|██████████| 4/4 [00:04<00:00, 1.00s/it] Loading checkpoint shards: 100%|██████████| 4/4 [00:04<00:00, 1.05s/it] [INFO|trainer.py:756] 2025-09-09 00:31:27,707 >> Using auto half precision backend [WARNING|2025-09-09 00:31:27] llamafactory.train.callbacks:154 >> Previous trainer log in this folder will be deleted. [2025-09-09 00:31:28,417] [INFO] [logging.py:107:log_dist] [Rank 0] DeepSpeed info: version=0.16.9, git-hash=unknown, git-branch=unknown [2025-09-09 00:31:28,418] [INFO] [config.py:735:__init__] Config mesh_device None world_size = 8 [2025-09-09 00:31:29,582] [INFO] [logging.py:107:log_dist] [Rank 0] DeepSpeed Flops Profiler Enabled: False [2025-09-09 00:31:29,584] [INFO] [logging.py:107:log_dist] [Rank 0] Using client Optimizer as basic optimizer [2025-09-09 00:31:29,585] [INFO] [logging.py:107:log_dist] [Rank 0] Removing param_group that has no 'params' in the basic Optimizer [2025-09-09 00:31:29,594] [INFO] [logging.py:107:log_dist] [Rank 0] DeepSpeed Basic Optimizer = AdamW [2025-09-09 00:31:29,594] [INFO] [utils.py:59:is_zero_supported_optimizer] Checking ZeRO support for optimizer=AdamW type= [2025-09-09 00:31:29,594] [INFO] [logging.py:107:log_dist] [Rank 0] Creating torch.bfloat16 ZeRO stage 2 optimizer [2025-09-09 00:31:29,594] [INFO] [stage_1_and_2.py:150:__init__] Reduce bucket size 500000000 [2025-09-09 00:31:29,594] [INFO] [stage_1_and_2.py:151:__init__] Allgather bucket size 500000000 [2025-09-09 00:31:29,594] [INFO] [stage_1_and_2.py:152:__init__] CPU Offload: False [2025-09-09 00:31:29,594] [INFO] [stage_1_and_2.py:153:__init__] Round robin gradient partitioning: True [2025-09-09 00:31:43,914] [INFO] [utils.py:781:see_memory_usage] Before initializing optimizer states [2025-09-09 00:31:43,915] [INFO] [utils.py:782:see_memory_usage] MA 17.73 GB Max_MA 17.73 GB CA 17.73 GB Max_CA 18 GB [2025-09-09 00:31:43,915] [INFO] [utils.py:789:see_memory_usage] CPU Virtual Memory: used = 167.91 GB, percent = 8.3% [2025-09-09 00:31:44,149] [INFO] [utils.py:781:see_memory_usage] After initializing optimizer states [2025-09-09 00:31:44,150] [INFO] [utils.py:782:see_memory_usage] MA 17.73 GB Max_MA 21.28 GB CA 21.28 GB Max_CA 21 GB [2025-09-09 00:31:44,150] [INFO] [utils.py:789:see_memory_usage] CPU Virtual Memory: used = 168.74 GB, percent = 8.4% [2025-09-09 00:31:44,150] [INFO] [stage_1_and_2.py:557:__init__] optimizer state initialized [2025-09-09 00:31:44,370] [INFO] [utils.py:781:see_memory_usage] After initializing ZeRO optimizer [2025-09-09 00:31:44,370] [INFO] [utils.py:782:see_memory_usage] MA 17.73 GB Max_MA 17.73 GB CA 21.28 GB Max_CA 21 GB [2025-09-09 00:31:44,371] [INFO] [utils.py:789:see_memory_usage] CPU Virtual Memory: used = 171.24 GB, percent = 8.5% [2025-09-09 00:31:44,372] [INFO] [logging.py:107:log_dist] [Rank 0] DeepSpeed Final Optimizer = DeepSpeedZeroOptimizer [2025-09-09 00:31:44,372] [INFO] [logging.py:107:log_dist] [Rank 0] DeepSpeed using configured LR scheduler = None [2025-09-09 00:31:44,372] [INFO] [logging.py:107:log_dist] [Rank 0] DeepSpeed LR Scheduler = None [2025-09-09 00:31:44,372] [INFO] [logging.py:107:log_dist] [Rank 0] step=0, skipped=0, lr=[0.0, 0.0], mom=[(0.9, 0.999), (0.9, 0.999)] [2025-09-09 00:31:44,373] [INFO] [config.py:1003:print] DeepSpeedEngine configuration: [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] activation_checkpointing_config { "partition_activations": false, "contiguous_memory_optimization": false, "cpu_checkpointing": false, "number_checkpoints": null, "synchronize_checkpoint_boundary": false, "profile": false } [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] aio_config ................... {'block_size': 1048576, 'queue_depth': 8, 'intra_op_parallelism': 1, 'single_submit': False, 'overlap_events': True, 'use_gds': False} [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] amp_enabled .................. False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] amp_params ................... False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] autotuning_config ............ { "enabled": false, "start_step": null, "end_step": null, "metric_path": null, "arg_mappings": null, "metric": "throughput", "model_info": null, "results_dir": "autotuning_results", "exps_dir": "autotuning_exps", "overwrite": true, "fast": true, "start_profile_step": 3, "end_profile_step": 5, "tuner_type": "gridsearch", "tuner_early_stopping": 5, "tuner_num_trials": 50, "model_info_path": null, "mp_size": 1, "max_train_batch_size": null, "min_train_batch_size": 1, "max_train_micro_batch_size_per_gpu": 1.024000e+03, "min_train_micro_batch_size_per_gpu": 1, "num_tuning_micro_batch_sizes": 3 } [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] bfloat16_enabled ............. True [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] bfloat16_immediate_grad_update True [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] checkpoint_parallel_write_pipeline False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] checkpoint_tag_validation_enabled True [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] checkpoint_tag_validation_fail False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] comms_config ................. [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] communication_data_type ...... None [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] compile_config ............... deepcompile=False free_activation=False offload_activation=False offload_opt_states=False double_buffer=True symmetric_memory=False debug_log=False offload_parameters=False sync_before_reduce=False sync_after_reduce=False sync_before_allgather=False sync_after_allgather=False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] compression_config ........... {'weight_quantization': {'shared_parameters': {'enabled': False, 'quantizer_kernel': False, 'schedule_offset': 0, 'quantize_groups': 1, 'quantize_verbose': False, 'quantization_type': 'symmetric', 'quantize_weight_in_forward': False, 'rounding': 'nearest', 'fp16_mixed_quantize': False, 'quantize_change_ratio': 0.001}, 'different_groups': {}}, 'activation_quantization': {'shared_parameters': {'enabled': False, 'quantization_type': 'symmetric', 'range_calibration': 'dynamic', 'schedule_offset': 1000}, 'different_groups': {}}, 'sparse_pruning': {'shared_parameters': {'enabled': False, 'method': 'l1', 'schedule_offset': 1000}, 'different_groups': {}}, 'row_pruning': {'shared_parameters': {'enabled': False, 'method': 'l1', 'schedule_offset': 1000}, 'different_groups': {}}, 'head_pruning': {'shared_parameters': {'enabled': False, 'method': 'topk', 'schedule_offset': 1000}, 'different_groups': {}}, 'channel_pruning': {'shared_parameters': {'enabled': False, 'method': 'l1', 'schedule_offset': 1000}, 'different_groups': {}}, 'layer_reduction': {'enabled': False}} [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] curriculum_enabled_legacy .... False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] curriculum_params_legacy ..... False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] data_efficiency_config ....... {'enabled': False, 'seed': 1234, 'data_sampling': {'enabled': False, 'num_epochs': 1000, 'num_workers': 0, 'pin_memory': False, 'curriculum_learning': {'enabled': False}, 'dynamic_batching': {'enabled': False, 'lr_scaling_method': 'linear', 'min_batch_size': 1, 'max_batch_size': None, 'sequence_picking_order': 'dataloader', 'verbose': False}}, 'data_routing': {'enabled': False, 'random_ltd': {'enabled': False, 'layer_token_lr_schedule': {'enabled': False}}}} [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] data_efficiency_enabled ...... False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] dataloader_drop_last ......... False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] disable_allgather ............ False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] dump_state ................... False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] dynamic_loss_scale_args ...... None [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] eigenvalue_enabled ........... False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] eigenvalue_gas_boundary_resolution 1 [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] eigenvalue_layer_name ........ bert.encoder.layer [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] eigenvalue_layer_num ......... 0 [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] eigenvalue_max_iter .......... 100 [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] eigenvalue_stability ......... 1e-06 [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] eigenvalue_tol ............... 0.01 [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] eigenvalue_verbose ........... False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] elasticity_enabled ........... False [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] flops_profiler_config ........ { "enabled": false, "recompute_fwd_factor": 0.0, "profile_step": 1, "module_depth": -1, "top_modules": 1, "detailed": true, "output_file": null } [2025-09-09 00:31:44,374] [INFO] [config.py:1007:print] fp16_auto_cast ............... None [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] fp16_enabled ................. False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] fp16_master_weights_and_gradients False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] global_rank .................. 0 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] grad_accum_dtype ............. None [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] gradient_accumulation_steps .. 2 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] gradient_clipping ............ 1.0 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] gradient_predivide_factor .... 1.0 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] graph_harvesting ............. False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] hybrid_engine ................ enabled=False max_out_tokens=512 inference_tp_size=1 release_inference_cache=False pin_parameters=True tp_gather_partition_size=8 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] initial_dynamic_scale ........ 1 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] load_universal_checkpoint .... False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] loss_scale ................... 1.0 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] memory_breakdown ............. False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] mics_hierarchial_params_gather False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] mics_shard_size .............. -1 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] monitor_config ............... tensorboard=TensorBoardConfig(enabled=False, output_path='', job_name='DeepSpeedJobName') comet=CometConfig(enabled=False, samples_log_interval=100, project=None, workspace=None, api_key=None, experiment_name=None, experiment_key=None, online=None, mode=None) wandb=WandbConfig(enabled=False, group=None, team=None, project='deepspeed') csv_monitor=CSVConfig(enabled=False, output_path='', job_name='DeepSpeedJobName') [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] nebula_config ................ { "enabled": false, "persistent_storage_path": null, "persistent_time_interval": 100, "num_of_version_in_retention": 2, "enable_nebula_load": true, "load_path": null } [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] optimizer_legacy_fusion ...... False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] optimizer_name ............... None [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] optimizer_params ............. None [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] pipeline ..................... {'stages': 'auto', 'partition': 'best', 'seed_layers': False, 'activation_checkpoint_interval': 0, 'pipe_partitioned': True, 'grad_partitioned': True} [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] pld_enabled .................. False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] pld_params ................... False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] prescale_gradients ........... False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] scheduler_name ............... None [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] scheduler_params ............. None [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] seq_parallel_communication_data_type torch.float32 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] sparse_attention ............. None [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] sparse_gradients_enabled ..... False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] steps_per_print .............. inf [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] tensor_parallel_config ....... dtype=torch.float16 autotp_size=0 tp_overlap_comm=False tensor_parallel=TPConfig(tp_size=1, tp_grain_size=1, mpu=None, tp_group=None) injection_policy_tuple=None keep_module_on_host=False replace_with_kernel_inject=False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] timers_config ................ enabled=True synchronized=True [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] train_batch_size ............. 32 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] train_micro_batch_size_per_gpu 2 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] use_data_before_expert_parallel_ False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] use_node_local_storage ....... False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] wall_clock_breakdown ......... False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] weight_quantization_config ... None [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] world_size ................... 8 [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] zero_allow_untested_optimizer True [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] zero_config .................. stage=2 contiguous_gradients=True reduce_scatter=True reduce_bucket_size=500000000 use_multi_rank_bucket_allreduce=True allgather_partitions=True allgather_bucket_size=500000000 overlap_comm=False load_from_fp32_weights=True elastic_checkpoint=False offload_param=None offload_optimizer=None sub_group_size=1000000000 cpu_offload_param=None cpu_offload_use_pin_memory=None cpu_offload=None prefetch_bucket_size=50000000 param_persistence_threshold=100000 model_persistence_threshold=9223372036854775807 max_live_parameters=1000000000 max_reuse_distance=1000000000 gather_16bit_weights_on_model_save=False module_granularity_threshold=0 use_all_reduce_for_fetch_params=False stage3_gather_fp16_weights_on_model_save=False ignore_unused_parameters=True legacy_stage1=False round_robin_gradients=True zero_hpz_partition_size=1 zero_quantized_weights=False zero_quantized_nontrainable_weights=False zero_quantized_gradients=False zeropp_loco_param=None mics_shard_size=-1 mics_hierarchical_params_gather=False memory_efficient_linear=True pipeline_loading_checkpoint=False override_module_apply=True log_trace_cache_warnings=False [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] zero_enabled ................. True [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] zero_force_ds_cpu_optimizer .. True [2025-09-09 00:31:44,375] [INFO] [config.py:1007:print] zero_optimization_stage ...... 2 [2025-09-09 00:31:44,375] [INFO] [config.py:993:print_user_config] json = { "train_batch_size": 32, "train_micro_batch_size_per_gpu": 2, "gradient_accumulation_steps": 2, "gradient_clipping": 1.0, "zero_allow_untested_optimizer": true, "fp16": { "enabled": false, "loss_scale": 0, "loss_scale_window": 1000, "initial_scale_power": 16, "hysteresis": 2, "min_loss_scale": 1 }, "bf16": { "enabled": true }, "zero_optimization": { "stage": 2, "allgather_partitions": true, "allgather_bucket_size": 5.000000e+08, "overlap_comm": false, "reduce_scatter": true, "reduce_bucket_size": 5.000000e+08, "contiguous_gradients": true, "round_robin_gradients": true }, "steps_per_print": inf } [INFO|deepspeed.py:487] 2025-09-09 00:31:44,407 >> Attempting to resume from /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-600 [2025-09-09 00:31:44,407] [INFO] [torch_checkpoint_engine.py:27:load] [Torch] Loading checkpoint from /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-600/global_step599/mp_rank_00_model_states.pt... [2025-09-09 00:32:21,074] [INFO] [torch_checkpoint_engine.py:29:load] [Torch] Loaded checkpoint from /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-600/global_step599/mp_rank_00_model_states.pt. [2025-09-09 00:32:21,121] [INFO] [torch_checkpoint_engine.py:27:load] [Torch] Loading checkpoint from /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-600/global_step599/mp_rank_00_model_states.pt... [2025-09-09 00:32:26,959] [INFO] [torch_checkpoint_engine.py:29:load] [Torch] Loaded checkpoint from /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-600/global_step599/mp_rank_00_model_states.pt. [2025-09-09 00:32:28,788] [INFO] [torch_checkpoint_engine.py:27:load] [Torch] Loading checkpoint from /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-600/global_step599/bf16_zero_pp_rank_0_mp_rank_00_optim_states.pt... [2025-09-09 00:33:38,321] [INFO] [torch_checkpoint_engine.py:29:load] [Torch] Loaded checkpoint from /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-600/global_step599/bf16_zero_pp_rank_0_mp_rank_00_optim_states.pt. [2025-09-09 00:33:38,322] [INFO] [engine.py:3241:_get_all_zero_checkpoint_state_dicts] successfully read 8 ZeRO state_dicts for rank 0 [2025-09-09 00:33:39,542] [INFO] [engine.py:3191:_load_zero_checkpoint] loading 8 zero partition checkpoints for rank 0 [INFO|trainer.py:2409] 2025-09-09 00:33:39,593 >> ***** Running training ***** [INFO|trainer.py:2410] 2025-09-09 00:33:39,593 >> Num examples = 10,000 [INFO|trainer.py:2411] 2025-09-09 00:33:39,593 >> Num Epochs = 3 [INFO|trainer.py:2412] 2025-09-09 00:33:39,593 >> Instantaneous batch size per device = 2 [INFO|trainer.py:2415] 2025-09-09 00:33:39,593 >> Total train batch size (w. parallel, distributed & accumulation) = 32 [INFO|trainer.py:2416] 2025-09-09 00:33:39,593 >> Gradient Accumulation steps = 2 [INFO|trainer.py:2417] 2025-09-09 00:33:39,593 >> Total optimization steps = 939 [INFO|trainer.py:2418] 2025-09-09 00:33:39,595 >> Number of trainable parameters = 7,615,616,512 [INFO|trainer.py:2440] 2025-09-09 00:33:39,597 >> Continuing training from checkpoint, will skip to saved global_step [INFO|trainer.py:2441] 2025-09-09 00:33:39,597 >> Continuing training from epoch 1 [INFO|trainer.py:2442] 2025-09-09 00:33:39,597 >> Continuing training from global step 600 [INFO|trainer.py:2444] 2025-09-09 00:33:39,597 >> Will skip the first 1 epochs then the first 574 batches in the first epoch. 0%| | 0/939 [00:00> Saving model checkpoint to /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800 [INFO|configuration_utils.py:424] 2025-09-09 01:43:39,942 >> Configuration saved in /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/config.json [INFO|configuration_utils.py:904] 2025-09-09 01:43:39,948 >> Configuration saved in /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/generation_config.json /home/zxd283/entropy/arpo/lib/python3.12/site-packages/torch/distributed/distributed_c10d.py:4631: UserWarning: No device id is provided via `init_process_group` or `barrier `. Using the current device set by the user. warnings.warn( # warn only once /home/zxd283/entropy/arpo/lib/python3.12/site-packages/torch/distributed/distributed_c10d.py:4631: UserWarning: No device id is provided via `init_process_group` or `barrier `. Using the current device set by the user. warnings.warn( # warn only once /home/zxd283/entropy/arpo/lib/python3.12/site-packages/torch/distributed/distributed_c10d.py:4631: UserWarning: No device id is provided via `init_process_group` or `barrier `. Using the current device set by the user. warnings.warn( # warn only once /home/zxd283/entropy/arpo/lib/python3.12/site-packages/torch/distributed/distributed_c10d.py:4631: UserWarning: No device id is provided via `init_process_group` or `barrier `. Using the current device set by the user. warnings.warn( # warn only once /home/zxd283/entropy/arpo/lib/python3.12/site-packages/torch/distributed/distributed_c10d.py:4631: UserWarning: No device id is provided via `init_process_group` or `barrier `. Using the current device set by the user. warnings.warn( # warn only once /home/zxd283/entropy/arpo/lib/python3.12/site-packages/torch/distributed/distributed_c10d.py:4631: UserWarning: No device id is provided via `init_process_group` or `barrier `. Using the current device set by the user. warnings.warn( # warn only once /home/zxd283/entropy/arpo/lib/python3.12/site-packages/torch/distributed/distributed_c10d.py:4631: UserWarning: No device id is provided via `init_process_group` or `barrier `. Using the current device set by the user. warnings.warn( # warn only once [INFO|modeling_utils.py:3733] 2025-09-09 01:44:05,693 >> The model is bigger than the maximum size per checkpoint (5GB) and is going to be split in 4 checkpoint shards. You can find where each parameters has been saved in the index located at /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/model.safetensors.index.json. [INFO|tokenization_utils_base.py:2356] 2025-09-09 01:44:05,700 >> chat template saved in /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/chat_template.jinja [INFO|tokenization_utils_base.py:2525] 2025-09-09 01:44:05,732 >> tokenizer config file saved in /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/tokenizer_config.json [INFO|tokenization_utils_base.py:2534] 2025-09-09 01:44:05,743 >> Special tokens file saved in /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/special_tokens_map.json /home/zxd283/entropy/arpo/lib/python3.12/site-packages/torch/distributed/distributed_c10d.py:4631: UserWarning: No device id is provided via `init_process_group` or `barrier `. Using the current device set by the user. warnings.warn( # warn only once [2025-09-09 01:44:06,109] [INFO] [logging.py:107:log_dist] [Rank 0] [Torch] Checkpoint global_step799 is about to be saved! [2025-09-09 01:44:06,119] [INFO] [logging.py:107:log_dist] [Rank 0] Saving model checkpoint: /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/global_step799/mp_rank_00_model_states.pt [2025-09-09 01:44:06,119] [INFO] [torch_checkpoint_engine.py:21:save] [Torch] Saving /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/global_step799/mp_rank_00_model_states.pt... [2025-09-09 01:44:36,451] [INFO] [torch_checkpoint_engine.py:23:save] [Torch] Saved /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/global_step799/mp_rank_00_model_states.pt. [2025-09-09 01:44:36,466] [INFO] [torch_checkpoint_engine.py:21:save] [Torch] Saving /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/global_step799/bf16_zero_pp_rank_0_mp_rank_00_optim_states.pt... [2025-09-09 01:46:26,011] [INFO] [torch_checkpoint_engine.py:23:save] [Torch] Saved /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/global_step799/bf16_zero_pp_rank_0_mp_rank_00_optim_states.pt. [2025-09-09 01:46:26,244] [INFO] [engine.py:3701:_save_zero_checkpoint] zero checkpoint saved /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoint-800/global_step799/bf16_zero_pp_rank_0_mp_rank_00_optim_states.pt [2025-09-09 01:46:26,244] [INFO] [torch_checkpoint_engine.py:33:commit] [Torch] Checkpoint global_step799 is ready now! 85%|████████▌ | 801/939 [1:13:06<2:43:43, 71.19s/it] 85%|████████▌ | 802/939 [1:13:26<2:07:31, 55.85s/it] 86%|████████▌ | 803/939 [1:13:47<1:42:52, 45.38s/it] 86%|████████▌ | 804/939 [1:14:10<1:26:39, 38.52s/it] 86%|████████▌ | 805/939 [1:14:29<1:13:31, 32.92s/it] 86%|████████▌ | 806/939 [1:14:48<1:03:20, 28.58s/it] 86%|████████▌ | 807/939 [1:15:10<58:48, 26.73s/it] 86%|████████▌ | 808/939 [1:15:33<55:33, 25.45s/it] 86%|████████▌ | 809/939 [1:15:55<53:06, 24.51s/it] 86%|████████▋ | 810/939 [1:16:15<49:27, 23.00s/it] {'loss': 0.3809, 'grad_norm': 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'grad_norm': 0.48320916295051575, 'learning_rate': 3.4552248167507576e-09, 'epoch': 2.98} 99%|█████████▉| 930/939 [1:58:12<03:15, 21.70s/it] 99%|█████████▉| 931/939 [1:58:35<02:55, 21.93s/it] 99%|█████████▉| 932/939 [1:58:57<02:34, 22.04s/it] 99%|█████████▉| 933/939 [1:59:13<02:01, 20.19s/it] 99%|█████████▉| 934/939 [1:59:35<01:44, 20.82s/it] 100%|█████████▉| 935/939 [1:59:56<01:23, 20.79s/it] 100%|█████████▉| 936/939 [2:00:17<01:02, 20.92s/it] 100%|█████████▉| 937/939 [2:00:35<00:40, 20.20s/it] 100%|█████████▉| 938/939 [2:00:47<00:17, 17.53s/it][INFO|trainer.py:2676] 2025-09-09 02:34:26,860 >> Training completed. Do not forget to share your model on huggingface.co/models =) {'train_runtime': 7247.2658, 'train_samples_per_second': 4.139, 'train_steps_per_second': 0.13, 'train_loss': 0.13962188102543227, 'epoch': 3.0} 100%|█████████▉| 938/939 [2:00:47<00:17, 17.53s/it] 100%|█████████▉| 938/939 [2:00:47<00:07, 7.73s/it] [INFO|trainer.py:3993] 2025-09-09 02:34:30,765 >> Saving model checkpoint to /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train [INFO|configuration_utils.py:424] 2025-09-09 02:34:30,796 >> Configuration saved in /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/config.json [INFO|configuration_utils.py:904] 2025-09-09 02:34:30,801 >> Configuration saved in /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/generation_config.json [INFO|modeling_utils.py:3733] 2025-09-09 02:34:54,911 >> The model is bigger than the maximum size per checkpoint (5GB) and is going to be split in 4 checkpoint shards. You can find where each parameters has been saved in the index located at /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/model.safetensors.index.json. [INFO|tokenization_utils_base.py:2356] 2025-09-09 02:34:54,927 >> chat template saved in /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/chat_template.jinja [INFO|tokenization_utils_base.py:2525] 2025-09-09 02:34:54,932 >> tokenizer config file saved in /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/tokenizer_config.json [INFO|tokenization_utils_base.py:2534] 2025-09-09 02:34:54,937 >> Special tokens file saved in /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/special_tokens_map.json ***** train metrics ***** epoch = 3.0 total_flos = 11520729288GF train_loss = 0.1396 train_runtime = 2:00:47.26 train_samples_per_second = 4.139 train_steps_per_second = 0.13 Figure saved at: /scratch/pioneer/jobs/job.2746985.pioneer/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/checkpoints/qwen2.5_7b_math_sft_full_3_10k_plan_fom_train/training_loss.png [WARNING|2025-09-09 02:34:55] llamafactory.extras.ploting:148 >> No metric eval_loss to plot. [WARNING|2025-09-09 02:34:55] llamafactory.extras.ploting:148 >> No metric eval_accuracy to plot. [INFO|modelcard.py:450] 2025-09-09 02:34:55,637 >> Dropping the following result as it does not have all the necessary fields: {'task': {'name': 'Causal Language Modeling', 'type': 'text-generation'}}