[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-290255-105":59,"doc-detail-290255-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","kryptonite-n-machine-learning-strikes-back-paper","Kryptonite-N: Machine Learning Strikes Back - Paper","","Quinn et al introduce the “Kryptonite-N” challenge datasets to undermine the universal function approximation claim that machine learning can approximate any continuous function. The present work directly refutes this argument by demonstrating successful universal function approximation using Kryptonite dataset construction. The study shows that logistic regression with sufficient polynomial expansion and L1 regularization can solve the task for any dimension N, supported by systematic experimental design, data exploration, and model comparisons.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/kryptonite-n-machine-learning-strikes-back-paper/290255/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/kryptonite-n-machine-learning-strikes-back-paper/290255.png","ImageObject",300,407,{"name":92,"@type":93},"Finn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-13","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the “Kryptonite-N” challenge dataset meant to test?","Question",{"text":112,"@type":113},"It is proposed as a challenge to the universal function approximation argument, claiming that machine learning can “approximate any continuous function” may not hold under their setup.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does this work refute the “Kryptonite-N” claim?",{"text":117,"@type":113},"It demonstrates that universal function approximations can be applied successfully, showing that Kryptonite datasets are constructed predictably and can be solved with logistic regression using sufficient polynomial expansion and L1 regularization for any dimension N.",{"name":119,"@type":110,"acceptedAnswer":120},"What key observations are found during data exploration?",{"text":121,"@type":113},"Each dimension shows an approximate mean of 0.5 and range near [0 − ϵ, 1 + ϵ], with multimodal distributions peaking at 0 and 1, and near-zero correlation across dimensions, implying labels depend on a non-linear feature combination.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},290255,1790868252,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":46,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":31},34359740700684,"https://ap-avatar.wpscdn.com/avatar/1f400023980c374ae676?_k=1777273430885731487","Kryptonite-N: Machine Learning Strikes Back  \nNathan Bailey* 1 Kira Kim* 1 Albus Li* 1 Will Sumerfield* 1  \narXiv :2412 .20588v2 [ cs .LG] 26 Jan 2025  \nAbstract  \nQuinn et al propose challenge datasets in their work called “Kryptonite-N”. These datasets aim to counter the universal function approximation argument of machine learning, breaking the notation that machine learning can “approximate any continuous function”(Quinn & Luther, 2024) .  \nOur work refutes this claim and shows that universal function approximations can be applied successfully; the Kryptonite datasets are constructed predictably, allowing logistic regression with sufficient polynomial expansion and L1 regularizationto solve for any dimension N.  \n1. Introduction  \nRecent advancements in machine learning, namely LLMs like GPT-4, have gained not only popularity from its success in solving various complex problems (Chowdhery et al., 2022) but also some scepticism in its capabilities, as suggested by the “Kryptonite-N” paper (Quinn & Luther, 2024) . Quinn and Luther state despite applying binary logistic regression with a GPT-driven basis expansion technique, they still fail to achieve high-quality performance on the datasets.  \nIn this paper we refute the claims of the “Kryptonite-N”paper by showing that several models yield good resultson the dataset, therefore proving the validity of Universal Function Approximation. At first a comprehensive data exploration is performed to inform the experimental design. Based on the experiments, we discuss insights gained from the results followed by an analysis on sustainability of model lifecycle. Furthermore, we demonstrate the flaws in their GPT approaches and explain observed poor performance. Finally, we outline the process where we determined the construction of the datasets.  \n*Equal contribution 1Department of Computing, Imperial College London, London, United Kingdom. Correspondence to: Albus Li \u003C[yizhuo.li24@imperial.ac.uk](yizhuo.li24@imperial.ac.uk)>.  \n2. Data Exploration  \nInitial data exploration using quantitative metrics and visual representation is crucial to gain insights for data manipulation and modelling steps. We exclusively examined the training portion of the datasets, to ensure that we didn’t bias our models.  \nAfter assessing metrics from each dimension, we discovered unusual results: each dimension in each K-N dataset hasan approximate mean of 0.5, standard deviation of 0.5, and range of [0 − ϵ,1 + ϵ] . This prompted us to evaluate the data distribution by plotting the Probability Mass Function of each dimension for the K-9 Dataset.  \nWe learned several very important things from this graph. Firstly, each dimension appears to come from a multimodal distribution with peaks at at 0 and 1 . Each peak within a dimension takes the same shape, with there being three different distributions seen across the dimensions, which we classify as ”Burst-like”,”Gaussian-like”, and ”Spread-like”. Secondly, we see that there appears to be no correlation between which peak a data-point is sampled from and the label. This made us curious about the correlation between the dimensions and the labels, which we hypothesized to below based on this graph.  \nA correlation matrix shows our hypothesis is correct-thereis close to zero correlation across dimensions. This implies the labels must be based on a non-linear combination of features. We visualised the data via a 2-Dimensional Principal Component Analysis to better understand the data’s relationship with the labels, but that resulted in a circle of data points with little clustering of labels, especially at higher dimensions.  \nHowever, if we only visualise as slices in 2D, we can extrapolate that the points fall in kk distinct clusters, evenly spacedover k-Dimensional space. This reminded us of the XOR problem, a dataset which Multi-Layer Perceptrons fail to solve without non-linearities. The XOR function has points at each corner, with a non-linear relationship to","cbCain2rQALqg1F4","https://ap.wps.com/l/cbCain2rQALqg1F4","pdf",1421909,"English","# Abstract\n# 1. Introduction\n# 2. Data Exploration\n## Data distribution and correlation analysis\n## PCA visualization and clustering interpretation\n# 3. Methodology\n## 3.1. Data Standardisation\n## 3.2. Neural Networks","[{\"question\":\"What is the “Kryptonite-N” challenge dataset meant to test?\",\"answer\":\"It is proposed as a challenge to the universal function approximation argument, claiming that machine learning can “approximate any continuous function” may not hold under their setup.\"},{\"question\":\"How does this work refute the “Kryptonite-N” claim?\",\"answer\":\"It demonstrates that universal function approximations can be applied successfully, showing that Kryptonite datasets are constructed predictably and can be solved with logistic regression using sufficient polynomial expansion and L1 regularization for any dimension N.\"},{\"question\":\"What key observations are found during data exploration?\",\"answer\":\"Each dimension shows an approximate mean of 0.5 and range near [0 − ϵ, 1 + ϵ], with multimodal distributions peaking at 0 and 1, and near-zero correlation across dimensions, implying labels depend on a non-linear feature combination.\"}]","Kryptonite-N: Machine Learning Strikes Back - Paper | PDF",1789641139]