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In this paper, we demonstrate that positional encoding can be used not only as a high-dimensional embedding but also decomposed as a series of meaningful points. We propose the Positional Encoding Projected Sampling, where we treat the projection of the original coordinate at each frequency as a point of interest. We describe the motion of each point with respect to the frequencies and show that it follows a unique pattern. Finally, we use the unique motion of each point as a basis decomposition for doing learned positional encoding using grids. We prove, using three competitive applications \u2013 image representation, texture compression, and signed distance function\u2013 that the proposed approach outperforms the current state of the art methods, and often requires 25% less parameters for equivalent reconstruction error or rendering.<\/jats:p>","DOI":"10.1145\/3806062","type":"journal-article","created":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T12:35:16Z","timestamp":1777638916000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["PEPS: Positional Encoding Projected Sampling"],"prefix":"10.1145","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6473-583X","authenticated-orcid":false,"given":"Guillaume","family":"Perez","sequence":"first","affiliation":[{"name":"AMD","place":["Murcia, Spain"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-8823-3248","authenticated-orcid":false,"given":"Janarbek","family":"Matai","sequence":"additional","affiliation":[{"name":"AMD","place":["San Diego, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5158-8455","authenticated-orcid":false,"given":"Takahiro","family":"Harada","sequence":"additional","affiliation":[{"name":"AMD","place":["Santa Clara, USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2026,5,1]]},"reference":[{"key":"e_1_3_2_2_1","article-title":"HIP: C++ Heterogeneous-Compute Interface for Portability","year":"2016","unstructured":"AMD. 2016. 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