{"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/zero-stability-well-predicts-performance-of","title":"Zero Stability Well Predicts Performance of Convolutional Neural Networks","arxiv_id":"2206.13100","date":"2022-06-27","proceeding":null,"authors":["Liangming Chen","Long Jin","Mingsheng Shang"],"abstract":"The question of what kind of convolutional neural network (CNN) structure performs well is fascinating. In this work, we move toward the answer with one more step by connecting zero stability and model performance. Specifically, we found that if a discrete solver of an ordinary differential equation is zero stable, the CNN corresponding to that solver performs well. We first give the interpretation of zero stability in the context of deep learning and then investigate the performance of existing first- and second-order CNNs under different zero-stable circumstances. Based on the preliminary observation, we provide a higher-order discretization to construct CNNs and then propose a zero-stable network (ZeroSNet). To guarantee zero stability of the ZeroSNet, we first deduce a structure that meets consistency conditions and then give a zero stable region of a training-free parameter. By analyzing the roots of a characteristic equation, we theoretically obtain the optimal coefficients of feature maps. Empirically, we present our results from three aspects: We provide extensive empirical evidence of different depth on different datasets to show that the moduli of the characteristic equation's roots are the keys for the performance of CNNs that require historical features; Our experiments show that ZeroSNet outperforms existing CNNs which is based on high-order discretization; ZeroSNets show better robustness against noises on the input. The source code is available at \\url{https://github.com/LongJin-lab/ZeroSNet}.","url_abs":"https://arxiv.org/abs/2206.13100v1","url_pdf":"https://arxiv.org/pdf/2206.13100v1.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":"zero-stability-well-predicts-performance-of","repo_url":"https://github.com/longjin-lab/zerosnet","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2206.13100","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2206.13100"}},"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/logichen/ZeroSNet","reach":null}],"summary":{"unverified":1},"by_repo_kind":{"found_in_text":{"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":"c7d2bb1242937dcd","entry":"ZeroSNet_Tra","repo":"logichen/ZeroSNet","repo_kind":"found_in_text","path":"CIFAR/models/ZeroSNet.py","file_url":"https://github.com/logichen/ZeroSNet/blob/HEAD/CIFAR/models/ZeroSNet.py","link_basis":"first_harvest_node","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":"c7d2bb1242937dcd"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}