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Then, we show that the infinite wide limit of the NN, under suitable scaling on the weights, is a stochastic process whose finite-dimensional distributions are multivariate stable distributions. The limiting process is referred to as the stable process, and it generalizes the class of Gaussian processes recently obtained as infinite wide limits of NNs (Matthews at al., 2018b). Parameters of the stable process can be computed via an explicit recursion over the layers of the network. Our result contributes to the theory of fully connected feed-forward deep NNs, and it paves the way to expand recent lines of research that rely on Gaussian infinite wide limits.","url_abs":"https://arxiv.org/abs/2003.00394v1","url_pdf":"https://arxiv.org/pdf/2003.00394v1.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":"stable-behaviour-of-infinitely-wide-deep","repo_url":"https://github.com/stepelu/deep-stable","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"gaussian-processes","task_name":"Gaussian Processes"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2003.00394","atlas_url":"https://app.syntology.ai/?focus=2003.00394","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2003.00394"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+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. 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