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{"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\nOutline the steps to graph a quadratic equation on a coordinate plane..\n Take a deep breath, think step by step, and give an accurate response<|im_end|>\n<|im_start|>assistant\nGraphing a quadratic equation on a coordinate plane can be done by following these steps:\n\n1. Identify the key components of the quadratic equation:\n - The vertex (h, k): This is the highest or lowest point of the curve.\n - The axis of symmetry: This is the vertical line that passes through the vertex.\n - The x-intercepts: These are the points where the quadratic curve intersects the x-axis.\n - The y-intercept: This is the point where the quadratic curve intersects the y-axis.\n\n2. Determine the vertex of the quadratic equation:\n - Use the formula: h = -b / (2a), where \"a\" and \"b\" are the coefficients of the quadratic equation in the standard form, ax^2 + bx + c.\n - Substitute the value of h into the equation to find the value of k.\n\n3. Calculate the axis of symmetry:\n - The axis of symmetry is a vertical line passing through the vertex.\n - The equation of the axis of symmetry is given by x = h.\n\n4. Find the x-intercepts:\n - Set the quadratic equation equal to zero and solve for x.\n - The solutions of the quadratic equation give the x-coordinates of the intercepts.\n\n5. Determine the y-intercept:\n - Substitute x = 0 into the quadratic equation and solve for y.\n\n6. Plot the points:\n - Plot the vertex (h, k).\n - Plot the two x-intercepts, if any.\n - Plot the y-intercept.\n\n7. Draw the curve:\n - Connect the plotted points using a smooth curve.\n - If you know additional points on the curve, plot them and include them in the drawing.\n\n8. Label the graph:\n - Label the vertex, x-intercepts, and y-intercept.\n - Add the equation of the quadratic function, if desired.\n\nRemember, graphing a quadratic equation accurately requires patience and attention to detail.<|im_end|>\n"], "chosen_attention_mask": [1, 512], "chosen_input_ids": [1, 512], "chosen_labels": [1, 512], "prompt": ["Outline the steps to graph a quadratic equation on a coordinate plane..\n Take a deep breath, think step by step, and give an accurate response"], "prompt_attention_mask": [1, 512], "prompt_input_ids": [1, 512], "question": ["Outline the steps to graph a quadratic equation on a coordinate plane..\n Take a deep breath, think step by step, and give an accurate response"], "rejected": ["<|im_start|>user\nOutline the steps to graph a quadratic equation on a coordinate plane..\n Take a deep breath, think step by step, and give an accurate response<|im_end|>\n<|im_start|>assistant\nCertainly! Here are the steps to graph a quadratic equation on a coordinate plane:\n\n1. Understand the form of the quadratic equation: Quadratic equations are typically written in the form y = ax\u00b2 + bx + c, where a, b, and c are constants.\n\n2. Identify the key characteristics: The quadratic equation contains important information that helps us graph it. The value of \"a\" determines whether the parabola opens upwards (a > 0) or downwards (a < 0). The vertex is given by the point (-b/(2a), f(-b/(2a))), where f(x) is the quadratic equation.\n\n3. Find the axis of symmetry: The axis of symmetry is a vertical line that passes through the vertex of the parabola. It is given by the equation x = -b/(2a).\n\n4. Determine the vertex: Plug the x-coordinate from step 3 back into the quadratic equation to find the y-coordinate of the vertex.\n\n5. Plot the vertex: Mark the vertex on the coordinate plane with a point (x, y).\n\n6. Find additional points: Choose two or more x-values on each side of the vertex and plug them into the quadratic equation to determine the corresponding y-values. This will give you additional points to plot on the graph.\n\n7. Plot the additional points: Mark the points obtained from step 6 on the coordinate plane.\n\n8. Draw the parabola: Once all the points are plotted, use a smooth curve to connect the points. The shape of the parabolic curve should follow the pattern determined by the value of \"a\".\n\n9. Label the graph: Label the axis of symmetry and any key points, such as the vertex or any x or y-intercepts.\n\nRemember, practice makes perfect! Graphing quadratic equations will become easier with more exposure and experience.<|im_end|>\n"], "rejected_attention_mask": [1, 512], "rejected_input_ids": [1, 512], "rejected_labels": [1, 512], "source": ["distilabel-math-preference-dpo"]}, "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}