{"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/sobolev-training-for-implicit-neural","title":"Sobolev Training for Implicit Neural Representations with Approximated Image Derivatives","arxiv_id":"2207.10395","date":"2022-07-21","proceeding":null,"authors":["Wentao Yuan","Qingtian Zhu","Xiangyue Liu","Yikang Ding","Haotian Zhang","Chi Zhang"],"abstract":"Recently, Implicit Neural Representations (INRs) parameterized by neural networks have emerged as a powerful and promising tool to represent different kinds of signals due to its continuous, differentiable properties, showing superiorities to classical discretized representations. However, the training of neural networks for INRs only utilizes input-output pairs, and the derivatives of the target output with respect to the input, which can be accessed in some cases, are usually ignored. In this paper, we propose a training paradigm for INRs whose target output is image pixels, to encode image derivatives in addition to image values in the neural network. Specifically, we use finite differences to approximate image derivatives. We show how the training paradigm can be leveraged to solve typical INRs problems, i.e., image regression and inverse rendering, and demonstrate this training paradigm can improve the data-efficiency and generalization capabilities of INRs. The code of our method is available at \\url{https://github.com/megvii-research/Sobolev_INRs}.","url_abs":"https://arxiv.org/abs/2207.10395v1","url_pdf":"https://arxiv.org/pdf/2207.10395v1.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":"sobolev-training-for-implicit-neural","repo_url":"https://github.com/megvii-research/Sobolev_INRs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"inverse-rendering","task_name":"Inverse Rendering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2207.10395","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2207.10395"}},"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":"deterministic:regex_extraction","url":"https://github.com/megvii-research/Sobolev_INRs","reach":null}],"summary":{"ran_draft_wrong":1},"by_repo_kind":{"official":{"samples":1,"ran":1,"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":"7f82f4a2e567a5ba","entry":"der_mse","repo":"megvii-research/Sobolev_INRs","repo_kind":"official","path":"Experiments/image_regression/loss.py","file_url":"https://github.com/megvii-research/Sobolev_INRs/blob/HEAD/Experiments/image_regression/loss.py","link_basis":"first_harvest_node","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"OUTPUT_MISDECLARED","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":"MIT","inline_ok":true,"mcp_get_code":{"code_sha256":"7f82f4a2e567a5ba"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}