neuronxcc-2.15.128.0+56dc5a86/0_REGISTRY/0.0.25.dev0/training/llama/meta-llama/Llama-3.2-1B-Instruct/00a47eab71eb9eb6c543.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\nThe Lucas numbers $L_n$ are given by the recursion $L_0 = 2, L_1 = 1$, and $L_n = L_{n-1} + L_{n-2}$. Find the units digit of $L_{L_{10}}$.<|im_end|>\n<|im_start|>assistant\nI need to find the units digit of $L_{L_{10}}$, which is a Lucas number whose index is another Lucas number.\nTo do that, I need to know the value of $L_{10}$, which I can find by using the recursion.\nI start from the given values of $L_0$ and $L_1$, and work my way up: $L_2 = L_1 + L_0 = 1 + 2 = 3, L_3 = L_2 + L_1 = 3 + 1 = 4, L_4 = L_3 + L_2 = 4 + 3 = 7, L_5 = L_4 + L_3 = 7 + 4 = 11, L_6 = L_5 + L_4 = 11 + 7 = 18, L_7 = L_6 + L_5 = 18 + 11 = 29, L_8 = L_7 + L_6 = 29 + 18 = 47, L_9 = L_8 + L_7 = 47 + 29 = 76, L_{10} = L_9 + L_8 = 76 + 47 = 123$.\nSo $L_{10} = 123$, and I need to find the units digit of $L_{123}$.\nI notice that the units digit of the Lucas numbers repeat in a cycle of 12: 2, 1, 3, 4, 7, 1, 8, 9, 7, 6, 3, 9, and then back to 2.\nSo to find the units digit of $L_{123}$, I just need to find the remainder when I divide 123 by 12, which is 3.\nThat means the units digit of $L_{123}$ is the same as the units digit of $L_3$, which is 4.\n# Answer\n\n4<|im_end|>\n"], "chosen_attention_mask": [1, 512], "chosen_input_ids": [1, 512], "chosen_labels": [1, 512], "prompt": ["The Lucas numbers $L_n$ are given by the recursion $L_0 = 2, L_1 = 1$, and $L_n = L_{n-1} + L_{n-2}$. Find the units digit of $L_{L_{10}}$."], "prompt_attention_mask": [1, 512], "prompt_input_ids": [1, 512], "question": ["The Lucas numbers $L_n$ are given by the recursion $L_0 = 2, L_1 = 1$, and $L_n = L_{n-1} + L_{n-2}$. Find the units digit of $L_{L_{10}}$."], "rejected": ["<|im_start|>user\nThe Lucas numbers $L_n$ are given by the recursion $L_0 = 2, L_1 = 1$, and $L_n = L_{n-1} + L_{n-2}$. Find the units digit of $L_{L_{10}}$.<|im_end|>\n<|im_start|>assistant\nFirst, we need to find $L_{10}$. We find that \\begin{align*}L_2 &= L_1 + L_0 = 3,\\\\ L_3 &= L_2 + L_1 = 4,\\\\ L_4 &= 7,\\\\ L_5 &= 11,\\\\ L_6 &= 18,\\\\ L_7 &= 29,\\\\ L_8 &= 47,\\\\ L_9 &= 76,\\\\ L_{10} &= 123\\end{align*}Thus, $L_{L_{10}} = L_{123}$. To find its units digit, we continue listing more values in the sequence until we reach a pattern: the units digit of $L_{11}$ is that of $123 + 76$, and so is $9$; that of $L_{12}$ is $2$; and that of $L_{13}$ is $1$. Hence, the units digit repeats starting from here, with a period of $12$. As $123 = 12 \\times 10 + 3$, then the units digit of $L_{123}$ is the same as that of $L_3$, or $\\boxed{4}$.<|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}