[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82443-en":3,"doc-seo-82443-105":30,"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":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},82443,7971461741311,"Ophelia","https://ap-avatar.wpscdn.com/avatar/74000253aff267980c6?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779345379180704826",8,"Research & Report","Revisiting Euler Angle Regression with Kolmogorov Arnold Networks","Revisiting Euler-angle regression for rotation estimation in articulated robots, biomechanical models, and vision/robotics pipelines, where Euler angles are bounded but discontinuities and singularities destabilize learning. The work argues that effectiveness depends on the coupled choice of rotation representation, regression architecture, and domain constraints. It proposes a range-aware Euler modeling framework using Kolmogorov-Arnold Networks, replacing fixed activations with learnable univariate edge functions. Theoretical analysis and experiments confirm improved accuracy, convergence, and efficiency across pose estimation and inverse kinematics, with code planned for public release.","arXiv :2607 .09650v1 [ cs .CV] 10 Jul 2026  \nRevisiting Euler-Angle Regression with Kolmogorov-Arnold Networks  \nYangting Sun [sunyt1230@gmail. com](sunyt1230@gmail. com)  \nIndependent Researcher  \nZijun Cui [cuizijun@msu. edu](cuizijun@msu. edu)  \nMichigan State University  \nYufei Zhang [yufeizhang96@outlook. com](yufeizhang96@outlook. com)  \nIndependent Researcher  \nAbstract  \nIn many real-world systems, including articulated robots and biomechanical models, rotations are defined in joint space and naturally parameterized by Euler angles with bounded ranges. Yet regressing Euler angles remains challenging, as their discontinuities and singularities often destabilize training. In this work, we revisit Euler-angle regression and show that its effectiveness depends critically on the interaction between rotation representation, regression architecture, and domain constraints. We introduce a new framework that combines range-aware Euler modeling with Kolmogorov-Arnold Networks (KAN), which replace fixed node-wise activations with learnable univariate functions on edges. We further provide theoretical analysis indicating that bounded Euler ranges motivate a near-additive structure in the regression function, which favors the additive functional form of KAN, and we confirm this trend empirically. Extensive experiments on controlled rotation regression, object pose estimation, and robotic and human inverse kinematics demonstrate consistent improvements in accuracy, convergence, and efficiency. The code will be publicly available.  \n1 Introduction  \nRotation describes the orientation of rigid bodies, cameras, and articulated parts. Estimating rotations from sensor data is fundamental across computer vision, graphics, robotics, and biomechanics, with applications in camera localization Zhang et al. (2024a), human kinematics and dynamics estimation Le et al.(2026); Xia et al. (2025); Zhang et al. (2025; 2024b); Ismayilzada et al. (2026); Delp et al. (2007), and robotic manipulation Spong & Vidyasagar (2008) . With the rise of end-to-end deep learning, rotation estimation is now commonly approached by training neural networks to directly regress rotations from sensor measurements Levinson et al. (2020); Peretroukhin et al. (2020); Gu et al. (2023); Okorn et al. (2023) .  \n3D rotation regression is fundamentally challenging because rotations lie on SO(3), a curved, non-Euclidean manifold that aligns poorly with conventional deep learning frameworks Bronstein et al. (2017) . Specifically, classical rotation representations use minimal parameterizations that map R3 to SO(3) . While these classical parameterizations offer clear interpretability in task-space Schuck et al. (2025); Sfikas et al. (2025) or respect the Lie group structure of SO(3) Grassia (1998), they are subject to discontinuities and singularities that challenge the standard learning process. For example, Euler angles capture sequential rotations about three Euclidean axes, but exhibit discontinuities from angular periodicity and singular configurations (commonly known as gimbal lock) where the mapping loses local invertibility.  \nRather than adopting minimal parameterizations as in classical approaches, recent works propose overparameterized representations of SO(3) for rotation regression outputs Brégier (2021); Peretroukhin et al. (2020) . Notably, the 6D representation Zhou et al. (2019) parameterizes a 3D rotation using two unconstrained 3D vectors. While this strategy incurs representational redundancy and an additional post-orthogonalization  \nstep, it yields a continuous embedding and mitigates singularities. As a result, the 6D representation has become widely adopted in various pipelines, with empirical results reported in tasks such as monocular 3D human body and hand reconstruction Xia et al. (2025); Yu et al. (2025) and humanoid control Luo et al.(2023) .  \nDespite the widespread usage of the 6D representation, two aspects remain insufficiently examined in existi","cbCaiepG6QWgesNl","https://ap.wps.com/l/cbCaiepG6QWgesNl","pdf",959935,2,1,21,"English","en",105,"# Abstract\n# Introduction\n## Challenges of 3D rotation regression on SO(3)\n## Euler angles: discontinuities and singularities\n## Related work: overparameterized representations and 6D embeddings\n## Motivation: representation–architecture interaction and bounded Euler ranges\n# Proposed approach\n## Range-aware Euler modeling with KAN backbone","[{\"question\":\"Why is Euler-angle regression difficult in rotation estimation tasks?\",\"answer\":\"Euler angles suffer from discontinuities caused by periodicity and from singular configurations such as gimbal lock, which reduce the mapping’s local invertibility and can destabilize training.\"},{\"question\":\"What is the key idea behind using Kolmogorov-Arnold Networks for Euler-angle regression?\",\"answer\":\"The method replaces fixed MLP node-wise activations with learnable univariate functions on edges, allowing each channel to adapt its nonlinearity to bounded Euler-angle targets.\"},{\"question\":\"How do bounded Euler-angle range constraints improve learning in this framework?\",\"answer\":\"The approach leverages practical application-specific bounds to mitigate discontinuous and singular behavior, supported by theoretical analysis that bounded Euler ranges encourage a near-additive regression structure suited to KAN.\"}]",1784180407,53,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"revisiting-euler-angle-regression-with-kolmogorov-arnold-networks","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/revisiting-euler-angle-regression-with-kolmogorov-arnold-networks/82443/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-21","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 is Euler-angle regression difficult in rotation estimation tasks?","Question",{"text":75,"@type":76},"Euler angles suffer from discontinuities caused by periodicity and from singular configurations such as gimbal lock, which reduce the mapping’s local invertibility and can destabilize training.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the key idea behind using Kolmogorov-Arnold Networks for Euler-angle regression?",{"text":80,"@type":76},"The method replaces fixed MLP node-wise activations with learnable univariate functions on edges, allowing each channel to adapt its nonlinearity to bounded Euler-angle targets.",{"name":82,"@type":73,"acceptedAnswer":83},"How do bounded Euler-angle range constraints improve learning in this framework?",{"text":84,"@type":76},"The approach leverages practical application-specific bounds to mitigate discontinuous and singular behavior, supported by theoretical analysis that bounded Euler ranges encourage a near-additive regression 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