{"id":6,"date":"2026-05-08T00:29:04","date_gmt":"2026-05-08T00:29:04","guid":{"rendered":"https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/?page_id=6"},"modified":"2026-05-08T00:54:42","modified_gmt":"2026-05-08T00:54:42","slug":"related-works","status":"publish","type":"page","link":"https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/related-works\/","title":{"rendered":"Related Works: Foundations of 3D Grounding"},"content":{"rendered":"\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"572\" src=\"https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/Screenshot-2026-05-07-at-8.54.31-PM-1024x572.png\" alt=\"\" class=\"wp-image-36\" srcset=\"https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/Screenshot-2026-05-07-at-8.54.31-PM-1024x572.png 1024w, https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/Screenshot-2026-05-07-at-8.54.31-PM-300x168.png 300w, https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/Screenshot-2026-05-07-at-8.54.31-PM-768x429.png 768w, https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/Screenshot-2026-05-07-at-8.54.31-PM.png 1460w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><strong>Rotary Positional Embeddings (RoPE)<\/strong> This project builds on <strong>RoPE<\/strong>, originally a 1D technique for language models to encode relative position through complex rotations. We utilize <strong>3D axial RoPE<\/strong>, which divides feature vectors into chunks (x, y, and z) to capture spatial relationships in three-dimensional space. However, standard RoPE assumes all modalities share a single, perfectly aligned coordinate frame\u2014an assumption we relax through our learnable calibration layer.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"615\" src=\"https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/image-1-1024x615.png\" alt=\"\" class=\"wp-image-35\" title=\"Screenshot 2026-02-26 at 9.03.01\u202fPM.png\" srcset=\"https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/image-1-1024x615.png 1024w, https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/image-1-300x180.png 300w, https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/image-1-768x461.png 768w, https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/image-1-1536x922.png 1536w, https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/wp-content\/uploads\/sites\/150\/2026\/05\/image-1.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p><strong>3D Flow and Diffusion Actors<\/strong> Our architectural backbones are the state-of-the-art <strong>3D Diffuser Actor (3DDA)<\/strong> and <strong>3D FlowMatch Actor (3DFA)<\/strong>. These models outperform 2D baselines by generating end-effector keyposes directly within 3D scene representations. We extend these specialized policies to handle uncalibrated real-world data.<\/p>\n\n\n\n<p><strong>Foundation VLA Models<\/strong> We leverage large-scale pre-trained backbones, specifically <strong>NVIDIA GR00T N1.5<\/strong> and <em>\u03c0<\/em> 0.5\u200b. By integrating our calibration mechanism into these multi-billion parameter models, we aim to combine their vast semantic knowledge with 3D operational precision.<\/p>\n\n\n\n<p><strong>Geometry-Aware Embeddings<\/strong> We draw inspiration from recent research in learnable positional encodings, such as <strong>ComRoPE<\/strong> and <strong>LieRE<\/strong>, which explore the use of <strong>Lie algebra<\/strong> to parameterize rotations in a way that respects geometric constraints.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rotary Positional Embeddings (RoPE) This project builds on RoPE, originally a 1D technique for language models to encode relative position through complex rotations. We utilize 3D axial RoPE, which divides feature vectors into chunks (x, y, and z) to capture spatial relationships in three-dimensional space. However, standard RoPE assumes all modalities share a single, perfectly [&hellip;]<\/p>\n","protected":false},"author":283,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-6","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Related Works: Foundations of 3D Grounding - Learning 3D-VLAs with Noisy Miscalibrated Data<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mscvprojects.ri.cmu.edu\/2026teamf8\/related-works\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Related Works: Foundations of 3D Grounding - Learning 3D-VLAs with Noisy Miscalibrated Data\" \/>\n<meta property=\"og:description\" content=\"Rotary Positional Embeddings (RoPE) This project builds on RoPE, originally a 1D technique for language models to encode relative position through complex rotations. 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