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Model: AI-MO/NuminaMath-7B-TIR-GPTQ Source: Original Platform
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README.md
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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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- aimo
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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: >-
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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: >-
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### Solution: 1. For the polynomial \\( x^2 + kx + 36 \\) to have two
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distinct integer roots, let's denote these roots by \\( r_1 \\) and \\(
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r_2 \\).\n\n2. According to Vieta's formulas, the sum of the roots \\( r_1
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+ r_2 \\) is equal to \\(-k\\), and the product of the roots \\( r_1
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\\cdot r_2 \\) is equal to 36.\n\n3. To find the distinct integer pairs
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\\((r_1, r_2)\\) whose product is 36, we need to determine all pairs of
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integers \\((r_1, r_2)\\) such that \\( r_1 \\cdot r_2 = 36 \\) and \\(
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r_1 \\neq r_2 \\).\n\n4. From the equation \\( r_1 + r_2 = -k \\), for
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each valid pair \\((r_1, r_2)\\), we can compute the corresponding value
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of \\( k \\).\n\n5. Finally, since we need the polynomial to have two
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distinct integer roots, we need to ensure that \\( r_1 \\) and \\( r_2 \\)
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are distinct.\n\nLet's start by finding all pairs \\((r_1, r_2)\\) such
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that \\( r_1 \\cdot r_2 = 36 \\). We'll then determine the values of \\( k
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\\) and ensure the roots are distinct.\n```python\nimport itertools\n\n#
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Find all pairs (r1, r2) such that r1 * r2 = 36\nproduct_36 =
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36\nfactor_pairs = []\n\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] !=
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pair[1]: # Ensure distinct pairs\n factor_pairs.append(pair)\n\n#
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Calculate k for each pair and ensure distinct integer
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roots\nvalid_k_values = set()\nfor r1, r2 in factor_pairs:\n if r1 !=
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r2:\n k = -(r1 + r2)\n
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valid_k_values.add(k)\n\nprint((len(valid_k_values),
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sorted(valid_k_values)))\n```\n```output\n(4, [-37, -20, -15,
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-13])\n```\nThe 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\\).\n\nTherefore, the number of such
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values of \\( k \\) is:\n\n\\[\n\\boxed{4}\n\\]\n
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pipeline_tag: text-generation
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model-index:
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- name: NuminaMath-7B-TIR-GPTQ
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results: []
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license: apache-2.0
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language:
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- en
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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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should probably proofread and complete it, then remove this comment. -->
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<img src="https://huggingface.co/AI-MO/NuminaMath-7B-TIR/resolve/main/thumbnail.png" alt="Numina Logo" width="800" style="margin-left:'auto' margin-right:'auto' display:'block'"/>
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# Model Card for NuminaMath 7B TIR GPTQ
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NuminaMath is a series of language models that are trained to solve math problems using tool-integrated reasoning (TIR). NuminaMath 7B TIR won the first progress prize of the [AI Math Olympiad (AIMO)](https://aimoprize.com), with a score of 29/50 on the public and private tests sets.
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This model is an 8-bit version of [`AI-MO/NuminaMath-7B-TIR`](https://huggingface.co/AI-MO/NuminaMath-7B-TIR), which we quantized with [AutoGPTQ](https://github.com/AutoGPTQ/AutoGPTQ) to run fast inference in the Kaggle submissions. Please consult the original model card for more details.
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config.json
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config.json
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{
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"_name_or_path": "AI-MO/deepseek-math-7b-sft",
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"architectures": [
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"LlamaForCausalLM"
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],
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"attention_bias": false,
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"attention_dropout": 0.0,
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"bos_token_id": 100000,
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"eos_token_id": 100001,
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"hidden_act": "silu",
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"hidden_size": 4096,
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"initializer_range": 0.02,
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"intermediate_size": 11008,
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"max_position_embeddings": 4096,
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"mlp_bias": false,
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"model_type": "llama",
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"num_attention_heads": 32,
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"num_hidden_layers": 30,
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"num_key_value_heads": 32,
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"pretraining_tp": 1,
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"quantization_config": {
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"bits": 8,
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"checkpoint_format": "gptq",
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"damp_percent": 0.01,
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"desc_act": true,
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"group_size": 128,
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"model_file_base_name": null,
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"model_name_or_path": null,
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"quant_method": "gptq",
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"static_groups": false,
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"sym": true,
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"true_sequential": true
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},
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"rms_norm_eps": 1e-06,
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"rope_scaling": null,
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"rope_theta": 10000.0,
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"tie_word_embeddings": false,
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"torch_dtype": "float16",
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"transformers_version": "4.40.1",
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"use_cache": true,
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"vocab_size": 102400
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}
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configuration.json
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configuration.json
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{"framework": "pytorch", "task": "text-generation", "allow_remote": true}
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gptq_model-8bit-128g.safetensors
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gptq_model-8bit-128g.safetensors
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version https://git-lfs.github.com/spec/v1
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quantize_config.json
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{
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"bits": 8,
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"group_size": 128,
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"damp_percent": 0.01,
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"desc_act": true,
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"static_groups": false,
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"sym": true,
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"true_sequential": true,
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"model_name_or_path": null,
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"quant_method": "gptq",
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"checkpoint_format": "gptq"
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}
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special_tokens_map.json
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special_tokens_map.json
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{
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"bos_token": {
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"content": "<|begin▁of▁sentence|>",
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"lstrip": false,
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"content": "<|end▁of▁sentence|>",
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"single_word": false
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}
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}
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199915
tokenizer.json
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tokenizer_config.json
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{
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"add_bos_token": true,
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"add_eos_token": false,
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"added_tokens_decoder": {
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"100000": {
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"content": "<|begin▁of▁sentence|>",
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"lstrip": false,
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"normalized": true,
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"rstrip": false,
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"single_word": false,
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"special": true
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},
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"100001": {
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"content": "<|end▁of▁sentence|>",
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"lstrip": false,
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"normalized": true,
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"rstrip": false,
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"single_word": false,
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"special": true
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}
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},
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"bos_token": "<|begin▁of▁sentence|>",
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"chat_template": "{% for message in messages %}{% if (message['role'] == 'system')%}{{ '' }}{% elif (message['role'] == 'user')%}{{ '### Problem: ' + message['content'] + '\n' }}{% elif (message['role'] == 'assistant')%}{{ '### Solution: ' + message['content'] + '\n' }}{% endif %}{% if loop.last and message['role'] == 'user' and add_generation_prompt %}{{ '### Solution: ' }}{% endif %}{% endfor %}",
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"clean_up_tokenization_spaces": false,
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"eos_token": "<|end▁of▁sentence|>",
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"legacy": true,
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"model_max_length": 4096,
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"pad_token": "<|end▁of▁sentence|>",
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"sp_model_kwargs": {},
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"tokenizer_class": "LlamaTokenizer",
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"unk_token": null,
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"use_default_system_prompt": false
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}
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