{"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/probabilistic-numeric-convolutional-neural-1","title":"Probabilistic Numeric Convolutional Neural Networks","arxiv_id":"2010.10876","date":"2020-10-21","proceeding":"ICLR 2021 1","authors":["Marc Finzi","Roberto Bondesan","Max Welling"],"abstract":"Continuous input signals like images and time series that are irregularly sampled or have missing values are challenging for existing deep learning methods. Coherently defined feature representations must depend on the values in unobserved regions of the input. Drawing from the work in probabilistic numerics, we propose Probabilistic Numeric Convolutional Neural Networks which represent features as Gaussian processes (GPs), providing a probabilistic description of discretization error. We then define a convolutional layer as the evolution of a PDE defined on this GP, followed by a nonlinearity. This approach also naturally admits steerable equivariant convolutions under e.g. the rotation group. In experiments we show that our approach yields a $3\\times$ reduction of error from the previous state of the art on the SuperPixel-MNIST dataset and competitive performance on the medical time series dataset PhysioNet2012.","url_abs":"https://arxiv.org/abs/2010.10876v1","url_pdf":"https://arxiv.org/pdf/2010.10876v1.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":"probabilistic-numeric-convolutional-neural-1","repo_url":"https://github.com/Qualcomm-AI-research/ProbabilisticNumericCNNs","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"},{"task_slug":"missing-values","task_name":"Missing Values"},{"task_slug":"time-series-1","task_name":"Time Series"},{"task_slug":"time-series","task_name":"Time Series Analysis"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/superpixel-image-classification-on-75","task":"Superpixel Image Classification","dataset":"75 Superpixel MNIST","model":"PNCNN","rank_in_archive_order":2,"of":6,"metrics":{"Classification Error":"1.24"},"uses_additional_data":false}],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2010.10876","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2010.10876"}},"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/Qualcomm-AI-research/ProbabilisticNumericCNNs","reach":null}],"summary":{"ran_honours":1},"by_repo_kind":{"listed":{"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":1,"samples":[{"code_sha256_prefix":"8b89c3cb36a774f5","entry":"pthash","repo":"Qualcomm-AI-research/ProbabilisticNumericCNNs","repo_kind":"listed","path":"image_remeshing_cnn/architecture.py","file_url":"https://github.com/Qualcomm-AI-research/ProbabilisticNumericCNNs/blob/HEAD/image_remeshing_cnn/architecture.py","link_basis":"first_harvest_node","language":"python","status":"ran_honours","verification_level":1,"contract_check":"HONOURS","metamorphic_tier":"invariant","behaviour_fingerprint":true,"licence":"BSD-3-Clause-Clear","inline_ok":false,"mcp_get_code":{"code_sha256":"8b89c3cb36a774f5"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}