{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T15:04:39Z","timestamp":1773414279600,"version":"3.50.1"},"reference-count":59,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"}],"funder":[{"name":"NSF Graduate Research Fellowships","award":["DGE-1745016"],"award-info":[{"award-number":["DGE-1745016"]}]},{"name":"NSF Graduate Research Fellowships","award":["DGE-2140739"],"award-info":[{"award-number":["DGE-2140739"]}]},{"name":"NSF","award":["CCF-2327905"],"award-info":[{"award-number":["CCF-2327905"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Signal Process."],"published-print":{"date-parts":[[2025]]},"DOI":"10.1109\/tsp.2024.3496692","type":"journal-article","created":{"date-parts":[[2024,11,13]],"date-time":"2024-11-13T18:59:31Z","timestamp":1731524371000},"page":"324-339","source":"Crossref","is-referenced-by-count":4,"title":["Gradient Networks"],"prefix":"10.1109","volume":"73","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2294-1453","authenticated-orcid":false,"given":"Shreyas","family":"Chaudhari","sequence":"first","affiliation":[{"name":"Electrical and Computer Engineering Department, Carnegie Mellon University, Pittsburgh, PA, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4159-4098","authenticated-orcid":false,"given":"Srinivasa","family":"Pranav","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering Department, Carnegie Mellon University, Pittsburgh, PA, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9822-8294","authenticated-orcid":false,"given":"Jos\u00e9 M.F.","family":"Moura","sequence":"additional","affiliation":[{"name":"Electrical and Computer Engineering Department, Carnegie Mellon University, Pittsburgh, PA, USA"}]}],"member":"263","reference":[{"key":"ref1","article-title":"ImageNet classification with deep convolutional neural networks","volume":"25","author":"Krizhevsky","year":"2012","journal-title":"Adv. Neur. Inf. Process. Syst."},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.48550\/ARXIV.1706.03762"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1038\/nature14236"},{"issue":"4","key":"ref4","first-page":"695","article-title":"Estimation of non-normalized statistical models by score matching.\u201d","volume":"6","author":"Hyv\u00e4rinen","year":"2005","journal-title":"J. Mach. Learn. Res."},{"key":"ref5","article-title":"Generative modeling by estimating gradients of the data distribution","volume":"32","author":"Song","year":"2019","journal-title":"Adv. Neur. Inf. Process. Syst."},{"key":"ref6","article-title":"Score-based generative modeling through stochastic differential equations","volume-title":"Proc. 9th Int. Conf. Learn. Represent. (ICLR)","author":"Song","year":"2021"},{"key":"ref7","first-page":"12438","article-title":"Improved techniques for training score-based generative models","volume":"33","author":"Song","year":"2020","journal-title":"Adv. Neur. Inf. Process. Syst."},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-58580-8_22"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160440402"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-20828-2"},{"key":"ref11","first-page":"14593","article-title":"Do neural optimal transport solvers work? A continuous Wasserstein-2 benchmark","volume":"34","author":"Korotin","year":"2021","journal-title":"Adv. Neur. Inf. Process. Syst."},{"key":"ref12","first-page":"6859","article-title":"Supervised training of conditional Monge maps","volume":"35","author":"Bunne","year":"2022","journal-title":"Adv. Neur. Inf. Process. Syst."},{"key":"ref13","first-page":"6672","article-title":"Optimal transport mapping via input convex neural networks","volume-title":"Int. Conf. Mach. Learn.","author":"Makkuva","year":"2020"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP49357.2023.10097266"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2018.2826536"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/16M1102884"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/TCI.2018.2880326"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/GlobalSIP.2013.6737048"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2022.3199595"},{"key":"ref20","first-page":"18152","article-title":"It has potential: Gradient-driven denoisers for convergent solutions to inverse problems","volume":"34","author":"Cohen","year":"2021","journal-title":"Adv. Neur. Inf. Process. Syst."},{"key":"ref21","article-title":"Gradient step denoiser for convergent plug-and-play","volume-title":"Proc. Int. Conf. Learn. Represent. (ICLR)","author":"Hurault","year":"2022"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2021.3075092"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1137\/22M1490843"},{"key":"ref24","article-title":"Learning to learn by gradient descent by gradient descent","volume":"29","author":"Andrychowicz","year":"2016","journal-title":"Adv. Neur. Inf. Process. Syst."},{"key":"ref25","volume-title":"Principles of Mathematical Analysis","volume":"3","author":"Rudin","year":"1964"},{"key":"ref26","article-title":"Sobolev training for neural networks","volume":"30","author":"Czarnecki","year":"2017","journal-title":"Adv. Neur. Inf. Process. Syst."},{"key":"ref27","article-title":"On approximating $\\nabla f$ with neural networks","author":"Saremi","year":"2019"},{"key":"ref28","article-title":"Gradients are not all you need","author":"Metz","year":"2021"},{"key":"ref29","article-title":"Input convex gradient networks","author":"Richter-Powell","year":"2021"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-008-0197-6"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.2307\/2337118"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2014.2299065"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-66709-6_23"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1109\/TCI.2023.3306100"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1137\/23M1565243"},{"key":"ref36","first-page":"146","article-title":"Input convex neural networks","volume-title":"Int. Conf. Mach. Learn.","author":"Amos","year":"2017"},{"key":"ref37","article-title":"Optimal control via neural networks: A convex approach","volume-title":"Proc. Int. Conf. Learn. Represent.","author":"Chen","year":"2018"},{"key":"ref38","article-title":"Convex potential flows: Universal probability distributions with optimal transport and convex optimization","volume-title":"Proc. Int. Conf. Learn. Represent.","author":"Huang","year":"2021"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-86486-6_45"},{"key":"ref40","article-title":"Principled weight initialisation for input-convex neural networks","volume":"36","author":"Hoedt","year":"2024","journal-title":"Adv. Neur. Inf. Process. Syst."},{"key":"ref41","article-title":"JacNet: Learning functions with structured Jacobians","author":"Lorraine","year":"2024"},{"key":"ref42","volume-title":"Methods of Numerical Integration","author":"Davis","year":"2007"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-10-1804-6"},{"key":"ref44","volume-title":"Variational Analysis","volume":"317","author":"Rockafellar","year":"2009"},{"key":"ref45","first-page":"5546","article-title":"Plug-and-play methods provably converge with properly trained denoisers","volume-title":"Int. Conf. Mach. Learn.","author":"Ryu","year":"2019"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP40776.2020.9054731"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511804441"},{"key":"ref48","article-title":"Learned convex regularizers for inverse problems","author":"Mukherjee","year":"2020"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1515\/9781400873173"},{"key":"ref50","volume-title":"Fundamental Concepts of Analysis","author":"Smith","year":"1966"},{"key":"ref51","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2019.2910417"},{"issue":"6","key":"ref52","doi-asserted-by":"crossref","first-page":"861","DOI":"10.1016\/S0893-6080(05)80131-5","article-title":"Multilayer feedforward networks with a nonpolynomial activation function can approximate any function","volume":"6","author":"Leshno","year":"1993","journal-title":"Neural Networks"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1162\/neco.1993.5.2.305"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1007\/BF02551274"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2016.90"},{"key":"ref56","article-title":"Visualizing the loss landscape of neural nets","volume":"31","author":"Li","year":"2018","journal-title":"Adv. Neur. Inf. Process. Syst."},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623499362822"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1017\/9781108755528"},{"key":"ref59","article-title":"Hamiltonian neural networks","volume-title":"Adv. Neur. Inf. Process. Syst.","volume":"32","author":"Greydanus","year":"2019"}],"container-title":["IEEE Transactions on Signal Processing"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx8\/78\/10807692\/10752831.pdf?arnumber=10752831","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,10]],"date-time":"2025-01-10T06:04:46Z","timestamp":1736489086000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/10752831\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":59,"URL":"https:\/\/doi.org\/10.1109\/tsp.2024.3496692","relation":{},"ISSN":["1053-587X","1941-0476"],"issn-type":[{"value":"1053-587X","type":"print"},{"value":"1941-0476","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]}}}