{"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/on-the-prime-number-divisibility-by-deep","title":"Classification of integers based on residue classes via modern deep learning algorithms","arxiv_id":"2304.01333","date":"2023-04-03","proceeding":null,"authors":["Da Wu","Jingye Yang","Mian Umair Ahsan","Kai Wang"],"abstract":"Judging whether an integer can be divided by prime numbers such as 2 or 3 may appear trivial to human beings, but can be less straightforward for computers. Here, we tested multiple deep learning architectures and feature engineering approaches on classifying integers based on their residues when divided by small prime numbers. We found that the ability of classification critically depends on the feature space. We also evaluated Automated Machine Learning (AutoML) platforms from Amazon, Google and Microsoft, and found that they failed on this task without appropriately engineered features. Furthermore, we introduced a method that utilizes linear regression on Fourier series basis vectors, and demonstrated its effectiveness. Finally, we evaluated Large Language Models (LLMs) such as GPT-4, GPT-J, LLaMA and Falcon, and demonstrated their failures. In conclusion, feature engineering remains an important task to improve performance and increase interpretability of machine-learning models, even in the era of AutoML and LLMs.","url_abs":"https://arxiv.org/abs/2304.01333v3","url_pdf":"https://arxiv.org/pdf/2304.01333v3.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":[{"paper_slug":"on-the-prime-number-divisibility-by-deep","repo_url":"https://github.com/wglab/integer_divsibility","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"automl","task_name":"AutoML"},{"task_slug":"feature-engineering","task_name":"Feature Engineering"}],"methods":[{"method_slug":"absolute-position-encodings","method_name":"Absolute Position Encodings"},{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"gpt-4","method_name":"GPT-4"},{"method_slug":"label-smoothing","method_name":"Label Smoothing"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"linear-regression","method_name":"Linear Regression"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"position-wise-feed-forward-layer","method_name":"Position-Wise Feed-Forward Layer"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"transformer","method_name":"Transformer"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}