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We observe that implicit representations require progressively lower accuracy as query points move farther from the target surface, and that even within the same iso-surface, representation difficulty varies spatially with local geometric complexity. However, conventional neural implicit models evaluate all query points with the same network depth and computational cost, ignoring this spatial variation and thereby incurring substantial computational waste. Motivated by this observation, we propose an efficient neural implicit geometry representation framework with spatially adaptive network depth (SAND). SAND leverages a volumetric network-depth map together with a tailed multi-layer perceptron (T-MLP) to model implicit representation. The volumetric depth map records, for each spatial region, the network depth required to achieve sufficient accuracy, while the T-MLP is a modified MLP designed to learn implicit functions such as signed distance functions, where an output branch, referred to as a tail, is attached to each hidden layer. This design allows network evaluation to terminate adaptively without traversing the full network and directs computational resources to geometrically important and complex regions, improving efficiency while preserving high-fidelity representations. Extensive experimental results demonstrate that our approach can significantly improve the inference-time query speed of implicit neural representations.<\/jats:p>","DOI":"10.1145\/3811341","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["SAND: Spatially Adaptive Network Depth for Fast Sampling of Neural Implicit Surfaces"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-9598-5353","authenticated-orcid":false,"given":"Chuanxiang","family":"Yang","sequence":"first","affiliation":[{"name":"Shandong University, Jinan, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3431-2021","authenticated-orcid":false,"given":"Junhui","family":"Hou","sequence":"additional","affiliation":[{"name":"City University of Hong Kong, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2933-5667","authenticated-orcid":false,"given":"Yuan","family":"Liu","sequence":"additional","affiliation":[{"name":"Hong Kong University of Science and Technology, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8551-0787","authenticated-orcid":false,"given":"Siyu","family":"Ren","sequence":"additional","affiliation":[{"name":"City University of Hong Kong, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6045-4392","authenticated-orcid":false,"given":"Guangshun","family":"Wei","sequence":"additional","affiliation":[{"name":"Shandong University, Jinan, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2729-5860","authenticated-orcid":false,"given":"Taku","family":"Komura","sequence":"additional","affiliation":[{"name":"University of Hong Kong, Hong Kong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6950-3261","authenticated-orcid":false,"given":"Yuanfeng","family":"Zhou","sequence":"additional","affiliation":[{"name":"Shandong University, Jinan, Shandong, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2284-3952","authenticated-orcid":false,"given":"Wenping","family":"Wang","sequence":"additional","affiliation":[{"name":"Computer Science and Engineering, Texas A&amp;M University, College Station, Texas, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR42600.2020.00264"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR52688.2022.01872"},{"key":"e_1_2_1_3_1","volume-title":"Proceedings, Part XXIX 16","author":"Chabra Rohan","year":"2020","unstructured":"Rohan Chabra, Jan E Lenssen, Eddy Ilg, Tanner Schmidt, Julian Straub, Steven Lovegrove, and Richard Newcombe. 2020. 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