{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/tinygsm-achieving-80-on-gsm8k-with-small","title":"TinyGSM: achieving >80% on GSM8k with small language models","arxiv_id":"2312.09241","date":"2023-12-14","proceeding":null,"authors":["Bingbin Liu","Sebastien Bubeck","Ronen Eldan","Janardhan Kulkarni","Yuanzhi Li","Anh Nguyen","Rachel Ward","Yi Zhang"],"abstract":"Small-scale models offer various computational advantages, and yet to which extent size is critical for problem-solving abilities remains an open question. Specifically for solving grade school math, the smallest model size so far required to break the 80\\% barrier on the GSM8K benchmark remains to be 34B. Our work studies how high-quality datasets may be the key for small language models to acquire mathematical reasoning. We introduce \\texttt{TinyGSM}, a synthetic dataset of 12.3M grade school math problems paired with Python solutions, generated fully by GPT-3.5. After finetuning on \\texttt{TinyGSM}, we find that a duo of a 1.3B generation model and a 1.3B verifier model can achieve 81.5\\% accuracy, outperforming existing models that are orders of magnitude larger. This also rivals the performance of the GPT-3.5 ``teacher'' model (77.4\\%), from which our model's training data is generated. Our approach is simple and has two key components: 1) the high-quality dataset \\texttt{TinyGSM}, 2) the use of a verifier, which selects the final outputs from multiple candidate generations.","url_abs":"https://arxiv.org/abs/2312.09241v1","url_pdf":"https://arxiv.org/pdf/2312.09241v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[],"tasks":[{"task_slug":"arithmetic-reasoning","task_name":"Arithmetic Reasoning"},{"task_slug":"gsm8k","task_name":"GSM8K"},{"task_slug":"math","task_name":"Math"},{"task_slug":"mathematical-reasoning","task_name":"Mathematical Reasoning"}],"methods":[{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"attention-dropout","method_name":"Attention Dropout"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"cosine-annealing","method_name":"Cosine Annealing"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"gpt-3","method_name":"GPT-3"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"linear-warmup-with-cosine-annealing","method_name":"Linear Warmup With Cosine Annealing"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"weight-decay","method_name":"Weight Decay"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/arithmetic-reasoning-on-gsm8k","task":"Arithmetic Reasoning","dataset":"GSM8K","model":"Phi-GSM+V 1.3B+1.3B (verify48@1)","rank_in_archive_order":65,"of":164,"metrics":{"Accuracy":"81.5","Parameters (Billion)":"2.6"},"uses_additional_data":false},{"leaderboard":"/sota/arithmetic-reasoning-on-gsm8k","task":"Arithmetic Reasoning","dataset":"GSM8K","model":"Phi-GSM 2.7B (fine-tuned)","rank_in_archive_order":89,"of":164,"metrics":{"Accuracy":"74.3","Parameters (Billion)":"2.7"},"uses_additional_data":false}],"syntology":{"syntology_url":"https://syntology.ai/paper/2312.09241","atlas_url":"https://app.syntology.ai/?focus=2312.09241","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}