{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-structured-dictionary-perspective-on","title":"A Structured Dictionary Perspective on Implicit Neural Representations","arxiv_id":"2112.01917","date":"2021-12-03","proceeding":"CVPR 2022 1","authors":["Gizem Yüce","Guillermo Ortiz-Jiménez","Beril Besbinar","Pascal Frossard"],"abstract":"Implicit neural representations (INRs) have recently emerged as a promising alternative to classical discretized representations of signals. Nevertheless, despite their practical success, we still do not understand how INRs represent signals. We propose a novel unified perspective to theoretically analyse INRs. Leveraging results from harmonic analysis and deep learning theory, we show that most INR families are analogous to structured signal dictionaries whose atoms are integer harmonics of the set of initial mapping frequencies. This structure allows INRs to express signals with an exponentially increasing frequency support using a number of parameters that only grows linearly with depth. We also explore the inductive bias of INRs exploiting recent results about the empirical neural tangent kernel (NTK). Specifically, we show that the eigenfunctions of the NTK can be seen as dictionary atoms whose inner product with the target signal determines the final performance of their reconstruction. In this regard, we reveal that meta-learning has a reshaping effect on the NTK analogous to dictionary learning, building dictionary atoms as a combination of the examples seen during meta-training. Our results permit to design and tune novel INR architectures, but can also be of interest for the wider deep learning theory community.","url_abs":"https://arxiv.org/abs/2112.01917v2","url_pdf":"https://arxiv.org/pdf/2112.01917v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-structured-dictionary-perspective-on","repo_url":"https://github.com/gortizji/inr_dictionaries","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"},{"task_slug":"inductive-bias","task_name":"Inductive Bias"},{"task_slug":"learning-theory","task_name":"Learning Theory"},{"task_slug":"meta-learning","task_name":"Meta-Learning"}],"methods":[{"method_slug":"ntk","method_name":"NTK"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2112.01917","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2112.01917"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/gortizji/inr_dictionaries","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":6},"by_repo_kind":{"official":{"samples":6,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"ec4aac12840f3104","entry":"crop","repo":"gortizji/inr_dictionaries","repo_kind":"official","path":"utils/img_processing.py","file_url":"https://github.com/gortizji/inr_dictionaries/blob/HEAD/utils/img_processing.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"ec4aac12840f3104"}},{"code_sha256_prefix":"e916cd78776ee116","entry":"crop_from_right","repo":"gortizji/inr_dictionaries","repo_kind":"official","path":"utils/img_processing.py","file_url":"https://github.com/gortizji/inr_dictionaries/blob/HEAD/utils/img_processing.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"e916cd78776ee116"}},{"code_sha256_prefix":"0b5f79a436b48b57","entry":"generate_signal_with_components_equal_amplitude","repo":"gortizji/inr_dictionaries","repo_kind":"official","path":"figure_3.py","file_url":"https://github.com/gortizji/inr_dictionaries/blob/HEAD/figure_3.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"0b5f79a436b48b57"}},{"code_sha256_prefix":"db4d799a99b62a65","entry":"image_to_dataset","repo":"gortizji/inr_dictionaries","repo_kind":"official","path":"utils/img_processing.py","file_url":"https://github.com/gortizji/inr_dictionaries/blob/HEAD/utils/img_processing.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"db4d799a99b62a65"}},{"code_sha256_prefix":"1aec764310763056","entry":"input_mapping_fourier","repo":"gortizji/inr_dictionaries","repo_kind":"official","path":"models/models_flax.py","file_url":"https://github.com/gortizji/inr_dictionaries/blob/HEAD/models/models_flax.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"1aec764310763056"}},{"code_sha256_prefix":"4cd6c6c17187a12f","entry":"my_uniform","repo":"gortizji/inr_dictionaries","repo_kind":"official","path":"models/models_flax.py","file_url":"https://github.com/gortizji/inr_dictionaries/blob/HEAD/models/models_flax.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"4cd6c6c17187a12f"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}