[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-85685-en":3,"doc-seo-85685-105":29,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},85685,137441390410,"Hazel","https://ap-avatar.wpscdn.com/avatar/2000252f4ab5702993?_k=1776741390130283984",8,"Research & Report","Manifold Constrained Tabular Deep Neural Networks","Tabular classification is frequently driven by discrete, condition-triggered rules, while tabular deep neural networks often rely on Euclidean representations that assume smooth global variation and semantic locality. This geometric mismatch can hinder efficient modeling of rule-partitioned structures. HDE-Net addresses this by constraining a hierarchical decision model in hyperbolic space: heterogeneous features are mapped to latent decision nodes in the Poincaré ball, numerical features use soft decision routing, and an entropy-aware capacity allocator adapts latent node counts. On the TALENT-tiny-core benchmark, HDE-Net attains the best average rank with strong efficiency.","Manifold Constrained Tabular Deep Neural Networks  \nTian Li  \nNewcastle University Newcastle upon Tyne, UK [t.li56@newcastle.ac.uk](t.li56@newcastle.ac.uk)  \nVarun Ojha  \nNewcastle University Newcastle upon Tyne, UK [varun.ojha@newcastle.ac.uk](varun.ojha@newcastle.ac.uk)  \nLucy Robinson  \nNewcastle University Newcastle upon Tyne, UK [Lucy.Robinson2@newcastle.ac.uk](Lucy.Robinson2@newcastle.ac.uk)  \nHuizhi Liang∗ Newcastle University Newcastle upon Tyne, UK [Huizhi.Liang@newcastle.ac.uk](Huizhi.Liang@newcastle.ac.uk)  \narXiv :2607 .09710v1 [ cs .LG] 23 Jun 2026  \nAbstract  \nTabular classification is often governed by local, condition-triggered rules rather than smooth global patterns. However, tabular deep neural networks (DNNs) are typically built upon Euclidean representations that favor smooth variations and semantic locality. This potential geometric mismatch can make it challenging for tabular DNNs to efficiently represent the discrete, rule-partitioned structures often underlying tabular classification. To address this issue, we propose HDE-Net, a manifold-constrained DNN that enables hierarchical decision modeling in hyperbolic space. We first abstract heterogeneous features into unified Latent Decision Nodes (LDNs) and embed them in the Poincaré ball, forming a continuous representation that resembles tree-structured reasoning. For numerical features, we introduce a Soft Decision Routing mechanism that approximates range-based local rules in a differentiable manner, bringing their LDN semantics closer to those of categorical features. An entropy-aware capacity allocation algorithm further adapts the number of LDNs per numerical feature to balance expressiveness and complexity. On the TALENT-tiny-core classification benchmark (30 datasets), HDE-Net achieves the best average rank, outperforming both industrial GBDTs and recent tabular DNNs while maintaining high efficiency.  \nCCS Concepts  \n• Computing methodologies → Modeling methodologies.  \nKeywords  \nTabular Representation Learning, Geometric Deep Learning, Deep Tabular Learning  \n1 Introduction  \nDespite the success of Deep Neural Networks (DNNs) in perceptual domains, tabular data remains central to many high-stakes realworld applications, such as financial risk assessment and healthcare diagnostics [1–4] . Unlike perceptual data (e.g., images and text), which often exhibit homogeneous semantic units and spatial or sequential invariances, tabular data is typically heterogeneous and may be governed by discrete, condition-triggered rules. Recent large-scale tabular benchmarks [4] show that Gradient-Boosted Decision Trees (GBDTs), such as XGBoost [5] and CatBoost [6], remain strong baselines across diverse feature compositions, while tabular DNNs often display dataset-specific performance variations.  \n∗ Corresponding Author  \nOne possible explanation is that GBDTs align well with ruleoriented structures commonly observed in tabular tasks. They perform task-driven space partitioning, recursively decomposing the feature space into a hierarchy of symbolic decision rules (e.g., 􀁸 > 19 or 􀁸 = male) . In contrast, many tabular DNNs operate under Euclidean assumptions of smoothness and continuous manifolds. From this perspective, a form of geometric mismatch may arise: the flat geometry of Euclidean space can be less suitable for representing the exponential branching patterns induced by hierarchical decision rules. As a result, neural models may rely on deeper or more complex architectures to approximate relatively simple rule-based relationships [1, 7–9] .  \nTable 1: Performance breakdown on the TALENT-tiny core classification benchmark by feature composition. Overall (All datasets), Num-Only (Datasets contain only numerical features), Num-Heavy (Numerical dominant datasets), and Cat-Heavy (Categorical dominant datasets). Values represent Average Rank (lower is better). Parentheses indicate rank shifts relative to the Overall performance (Green/-: Improved Rank; Red/+: Wo","cbCaitASLAU7kNuK","https://ap.wps.com/l/cbCaitASLAU7kNuK","pdf",2898272,1,10,"English","en",105,"# Abstract\n# Introduction","[{\"question\":\"Why can Euclidean-based tabular DNNs struggle with rule-driven tabular classification?\",\"answer\":\"Tabular tasks often follow discrete, condition-triggered rules, while Euclidean representations favor smooth global patterns. This can make it difficult to represent hierarchical, branching decision structures efficiently.\"},{\"question\":\"What is the core idea behind HDE-Net?\",\"answer\":\"HDE-Net builds a manifold-constrained, hierarchical decision model in hyperbolic space. It embeds latent decision nodes in the Poincaré ball to produce a representation resembling tree-structured reasoning.\"},{\"question\":\"How does HDE-Net handle numerical features compared with categorical features?\",\"answer\":\"For numerical features, it introduces Soft Decision Routing to approximate range-based local rules in a differentiable way, improving alignment of numerical semantics with categorical latent decision node semantics.\"}]",1784205590,25,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":27},"manifold-constrained-tabular-deep-neural-networks","",{"@graph":35,"@context":85},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/manifold-constrained-tabular-deep-neural-networks/85685/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why can Euclidean-based tabular DNNs struggle with rule-driven tabular classification?","Question",{"text":75,"@type":76},"Tabular tasks often follow discrete, condition-triggered rules, while Euclidean representations favor smooth global patterns. This can make it difficult to represent hierarchical, branching decision structures efficiently.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the core idea behind HDE-Net?",{"text":80,"@type":76},"HDE-Net builds a manifold-constrained, hierarchical decision model in hyperbolic space. It embeds latent decision nodes in the Poincaré ball to produce a representation resembling tree-structured reasoning.",{"name":82,"@type":73,"acceptedAnswer":83},"How does HDE-Net handle numerical features compared with categorical features?",{"text":84,"@type":76},"For numerical features, it introduces Soft Decision Routing to approximate range-based local rules in a differentiable way, improving alignment of numerical semantics with categorical latent decision node semantics.","https://schema.org",{"og:url":51,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,134],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":45,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":45,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":21,"doc_module":4,"doc_module_name":45,"category_name":132,"show_sort_weight":21,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":45,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]