{"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/neural-kernels-without-tangents","title":"Neural Kernels Without Tangents","arxiv_id":"2003.02237","date":"2020-03-04","proceeding":"ICML 2020 1","authors":["Vaishaal Shankar","Alex Fang","Wenshuo Guo","Sara Fridovich-Keil","Ludwig Schmidt","Jonathan Ragan-Kelley","Benjamin Recht"],"abstract":"We investigate the connections between neural networks and simple building blocks in kernel space. In particular, using well established feature space tools such as direct sum, averaging, and moment lifting, we present an algebra for creating \"compositional\" kernels from bags of features. We show that these operations correspond to many of the building blocks of \"neural tangent kernels (NTK)\". Experimentally, we show that there is a correlation in test error between neural network architectures and the associated kernels. We construct a simple neural network architecture using only 3x3 convolutions, 2x2 average pooling, ReLU, and optimized with SGD and MSE loss that achieves 96% accuracy on CIFAR10, and whose corresponding compositional kernel achieves 90% accuracy. We also use our constructions to investigate the relative performance of neural networks, NTKs, and compositional kernels in the small dataset regime. In particular, we find that compositional kernels outperform NTKs and neural networks outperform both kernel methods.","url_abs":"https://arxiv.org/abs/2003.02237v2","url_pdf":"https://arxiv.org/pdf/2003.02237v2.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":"neural-kernels-without-tangents","repo_url":"https://github.com/Tnorm/SVM_cookietest","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"neural-kernels-without-tangents","repo_url":"https://github.com/tengandreaxu/fabr","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[{"method_slug":"relu","method_name":"ReLU"},{"method_slug":"sgd","method_name":"SGD"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2003.02237","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2003.02237"}},"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/Tnorm/SVM_cookietest","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/tengandreaxu/fabr","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"unverified":1},"by_repo_kind":{"listed":{"samples":1,"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":"e5580b0c627e219c","entry":"get_block_sizes","repo":"tengandreaxu/fabr","repo_kind":"listed","path":"models/utils.py","file_url":"https://github.com/tengandreaxu/fabr/blob/HEAD/models/utils.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":"e5580b0c627e219c"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}