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Conventional surface extraction methods for implicit representations, such as the widely used Marching Cubes algorithm, rely on spatial decomposition and sampling, leading to inaccuracies due to fixed and limited resolution. We introduce a novel approach for analytically extracting surfaces from neural implicit functions. Our method operates natively in parallel and can navigate large neural architectures. By leveraging the fact that each neuron partitions the domain, we develop a depth-first traversal strategy to efficiently track the encoded surface. The resulting meshes faithfully capture the full geometric information from the network without ad-hoc spatial discretization, achieving unprecedented accuracy across diverse shapes and network architectures while maintaining competitive speed.<\/jats:p>","DOI":"10.1145\/3763328","type":"journal-article","created":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T17:15:39Z","timestamp":1764868539000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Marching Neurons: Accurate Surface Extraction for Neural Implicit Shapes"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0482-902X","authenticated-orcid":false,"given":"Christian","family":"Stippel","sequence":"first","affiliation":[{"name":"TU Wien, Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-9122-4408","authenticated-orcid":false,"given":"Felix","family":"Mujkanovic","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Informatics, Saarbr\u00fccken, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-7784-7957","authenticated-orcid":false,"given":"Thomas","family":"Leimk\u00fchler","sequence":"additional","affiliation":[{"name":"Max Planck Institute for Informatics, Saarbr\u00fccken, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3586-4741","authenticated-orcid":false,"given":"Pedro","family":"Hermosilla","sequence":"additional","affiliation":[{"name":"TU Wien, Vienna, Austria"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2025,12,4]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"Tomas Akenine-Moller Eric Haines and Naty Hoffman. 2019. 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