Upload LlamaForCausalLM
Browse files- README.md +34 -74
- config.json +2 -2
- generation_config.json +1 -1
- model-00001-of-00003.safetensors +1 -1
- model-00002-of-00003.safetensors +1 -1
- model-00003-of-00003.safetensors +1 -1
README.md
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---
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base_model: deepseek-ai/deepseek-math-7b-base
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tags:
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- alignment-handbook
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- generated_from_trainer
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widget:
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5- Finally, since we need the polynomial to have two distinct integer
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roots, we need to ensure that \\( r_1 \\) and \\( r_2 \\) are distinct.
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Let's start by finding all pairs \\((r_1, r_2)\\) such that \\( r_1
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\\cdot r_2 = 36 \\). We'll then determine the values of \\( k \\) and
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ensure the roots are distinct.
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```python import itertools
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# Find all pairs (r1, r2) such that r1 * r2 = 36 product_36 = 36
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factor_pairs = []
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for i in range(1, product_36 + 1):
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if product_36 % i == 0:
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pair = (i, product_36 // i)
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if pair[0] != pair[1]: # Ensure distinct pairs
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factor_pairs.append(pair)
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# Calculate k for each pair and ensure distinct integer roots
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valid_k_values = set()
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for r1, r2 in factor_pairs:
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if r1 != r2:
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k = -(r1 + r2)
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valid_k_values.add(k)
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print((len(valid_k_values), sorted(valid_k_values)))
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```
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```output
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(4, [-37, -20, -15,-13])
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```
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The distinct integer values of \\( k \\) that make the
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polynomial \\( x^2 + kx + 36 \\) have two distinct integer roots are
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\\(-37, -20, -15, \\text{and} -13\\).
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Therefore, the number of such values of \\( k \\) is:
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[ \\boxed{4} \\]
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pipeline_tag: text-generation
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model-index:
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- name: NuminaMath-7B-TIR
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results: []
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license: apache-2.0
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---
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<!-- This model card has been generated automatically according to the information the Trainer had access to. You
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---
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base_model: deepseek-ai/deepseek-math-7b-base
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license: apache-2.0
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pipeline_tag: text-generation
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tags:
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- alignment-handbook
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- generated_from_trainer
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widget:
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- example_title: Math problem
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messages:
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- role: user
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content: For how many values of the constant $k$ will the polynomial $x^{2}+kx+36$
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have two distinct integer roots?
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output:
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text: "### Solution: \n1- For the polynomial \\\\( x^2 + kx + 36 \\\\) to have\
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\ two distinct integer roots, let's denote these roots by \\\\( r_1 \\\\) and\
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\ \\\\( r_2 \\\\).\n\n\n2- According to Vieta's formulas, the sum of the roots\
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\ \\\\( r_1 + r_2 \\\\) is equal to \\\\(-k\\\\), and the product of the roots\
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\ \\\\( r_1 \\\\cdot r_2 \\\\) is equal to 36.\n\n\n3- To find the distinct\
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\ integer pairs \\\\((r_1, r_2)\\\\) whose product is 36, we need to determine\
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\ all pairs of integers \\\\((r_1, r_2)\\\\) such that \\\\( r_1 \\\\cdot r_2\
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\ = 36 \\\\) and \\\\( r_1 \\\\neq r_2 \\\\).\n\n\n4- From the equation \\\\\
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( r_1 + r_2 = -k \\\\), for each valid pair \\\\((r_1, r_2)\\\\), we can compute\
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\ the corresponding value of \\\\( k \\\\).\n\n\n5- Finally, since we need the\
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\ polynomial to have two distinct integer roots, we need to ensure that \\\\\
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( r_1 \\\\) and \\\\( r_2 \\\\) are distinct.\nLet's start by finding all pairs\
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\ \\\\((r_1, r_2)\\\\) such that \\\\( r_1 \\\\cdot r_2 = 36 \\\\). We'll then\
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\ determine the values of \\\\( k \\\\) and ensure the roots are distinct.\n\
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```python import itertools\n# Find all pairs (r1, r2) such that r1 * r2 = 36\
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\ product_36 = 36 factor_pairs = []\nfor i in range(1, product_36 + 1):\n if\
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\ product_36 % i == 0:\n pair = (i, product_36 // i)\n if pair[0] != pair[1]:\
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\ # Ensure distinct pairs\n factor_pairs.append(pair)\n \n # Calculate\
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\ k for each pair and ensure distinct integer roots\n valid_k_values = set()\n\
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\ for r1, r2 in factor_pairs:\n if r1 != r2:\n k = -(r1 + r2)\n\
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\ valid_k_values.add(k)\n \n print((len(valid_k_values), sorted(valid_k_values)))\n\
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\ ```\n \n ```output\n (4, [-37, -20, -15,-13])\n ```\n The distinct integer\
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\ values of \\\\( k \\\\) that make the\npolynomial \\\\( x^2 + kx + 36 \\\\\
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) have two distinct integer roots are \\\\(-37, -20, -15, \\\\text{and} -13\\\
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\\).\nTherefore, the number of such values of \\\\( k \\\\) is:\n[ \\\\boxed{4}\
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\ \\\\]"
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model-index:
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- name: NuminaMath-7B-TIR
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results: []
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---
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<!-- This model card has been generated automatically according to the information the Trainer had access to. You
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config.json
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{
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"_name_or_path": "AI-MO/
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"architectures": [
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"LlamaForCausalLM"
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],
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"rope_theta": 10000.0,
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"tie_word_embeddings": false,
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"torch_dtype": "bfloat16",
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"transformers_version": "4.
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"use_cache": true,
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"vocab_size": 102400
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}
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{
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"_name_or_path": "AI-MO/NuminaMath-7B-TIR-decontaminated",
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"architectures": [
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"LlamaForCausalLM"
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],
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"rope_theta": 10000.0,
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"tie_word_embeddings": false,
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"torch_dtype": "bfloat16",
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"transformers_version": "4.42.3",
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"use_cache": true,
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"vocab_size": 102400
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}
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generation_config.json
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"_from_model_config": true,
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"bos_token_id": 100000,
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"eos_token_id": 100001,
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"transformers_version": "4.
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}
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"_from_model_config": true,
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"bos_token_id": 100000,
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"eos_token_id": 100001,
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"transformers_version": "4.42.3"
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}
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