neuronxcc-2.15.128.0+56dc5a86/0_REGISTRY/0.0.25.dev0/training/llama/meta-llama/Llama-3.2-1B/02fad0789e3ac4bfabe5.json

{"architectures": ["LlamaForCausalLM"], "attention_bias": false, "attention_dropout": 0.0, "bos_token_id": 128256, "eos_token_id": 128257, "head_dim": 64, "hidden_act": "silu", "hidden_size": 2048, "initializer_range": 0.02, "intermediate_size": 8192, "max_position_embeddings": 131072, "mlp_bias": false, "model_type": "llama", "neuron": {"compiler_version": "2.15.128.0+56dc5a86", "input_specs": {"chosen": ["<|im_start|>user\nAlex needs to catch a train. The train arrives randomly some time between 1:00 and 2:00, waits for 10 minutes, and then leaves. If Alex also arrives randomly between 1:00 and 2:00, what is the probability that the train will be there when Alex arrives?<|im_end|>\n<|im_start|>assistant\nI need to find the fraction of the time between 1:00 and 2:00 that Alex and the train are both at the station.\nI can think of this as a geometric problem, where the x-axis is the time Alex arrives and the y-axis is the time the train arrives.\nThe region of interest is the square with vertices (1:00, 1:00), (2:00, 1:00), (2:00, 2:00), and (1:00, 2:00).\nThe train is there when Alex arrives if and only if the point (x,y) is within 10 minutes of the line y = x.\nThis means that the point (x,y) must satisfy |x - y| <= 10/60, where x and y are measured in hours.\nGraphically, this is the region between the two parallel lines y = x + 10/60 and y = x - 10/60.\nThe area of this region is the fraction of the square that is shaded.\nI can calculate this area by subtracting the areas of the two right triangles that are not shaded from the area of the whole square.\nThe area of the whole square is 1 hour * 1 hour = 1 square hour.\nThe area of each right triangle is 1/2 * base * height.\nThe base of each triangle is 50/60 hours, since they are cut off by the lines y = x + 10/60 and y = x - 10/60.\nThe height of each triangle is also 50/60 hours, since they are symmetric about the line y = x.\nSo the area of each triangle is 1/2 * 50/60 * 50/60 = 25/72 square hours.\nTherefore, the area of the shaded region is 1 - 2 * 25/72 = 22/72 square hours.\nThis means that the probability that Alex and the train are both at the station is 22/72, which can be simplified to 11/36.\n# Answer\n\n11/36<|im_end|>\n"], "chosen_attention_mask": [1, 512], "chosen_input_ids": [1, 512], "chosen_labels": [1, 512], "prompt": ["Alex needs to catch a train. The train arrives randomly some time between 1:00 and 2:00, waits for 10 minutes, and then leaves. If Alex also arrives randomly between 1:00 and 2:00, what is the probability that the train will be there when Alex arrives?"], "prompt_attention_mask": [1, 512], "prompt_input_ids": [1, 512], "question": ["Alex needs to catch a train. The train arrives randomly some time between 1:00 and 2:00, waits for 10 minutes, and then leaves. If Alex also arrives randomly between 1:00 and 2:00, what is the probability that the train will be there when Alex arrives?"], "rejected": ["<|im_start|>user\nAlex needs to catch a train. The train arrives randomly some time between 1:00 and 2:00, waits for 10 minutes, and then leaves. If Alex also arrives randomly between 1:00 and 2:00, what is the probability that the train will be there when Alex arrives?<|im_end|>\n<|im_start|>assistant\nWe put the time the train arrives on the $y$-axis and the time  Alex arrives on the $x$-axis, and shade in the region where Alex arrives while the train is there.\n\n[asy]\nfill((0,0)--(60,60)--(60,50)--(10,0)--cycle, gray(.7));\ndraw((0,0)--(60,0), Arrow);\ndraw((0,0)--(0,60), Arrow);\nlabel(\"1:00\", (0,0), SW);\nlabel(\"2:00\", (60,0), S);\nlabel(\"2:00\", (0,60), W);\n[/asy]\n\nThe probability that Alex arrives while the train is at the station is the ratio of the shaded area to the whole square. If we divide the axes into 60 units, the shaded region can be split up into a triangle of area 50 square units and a parallelogram of area 500 square units, and the whole square has an area of 3600 square units. The ratio is $550/3600=\\boxed{\\frac{11}{72}}$.<|im_end|>\n"], "rejected_attention_mask": [1, 512], "rejected_input_ids": [1, 512], "rejected_labels": [1, 512], "source": ["prm_dpo_pairs"]}, "model_class": "PeftModelForCausalLM", "num_neuron_cores_per_node": 2, "pipeline_parallel_size": 1, "precision": "bfloat16", "tensor_parallel_size": 1, "training": true}, "num_attention_heads": 32, "num_hidden_layers": 16, "num_key_value_heads": 8, "pad_token_id": 128257, "pretraining_tp": 1, "rms_norm_eps": 1e-05, "rope_scaling": {"factor": 32.0, "high_freq_factor": 4.0, "low_freq_factor": 1.0, "original_max_position_embeddings": 8192, "rope_type": "llama3"}, "rope_theta": 500000.0, "tie_word_embeddings": true, "torch_dtype": "bfloat16", "use_cache": true, "vocab_size": 128258}