{"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/stabilizing-gradients-for-deep-neural","title":"Stabilizing Gradients for Deep Neural Networks via Efficient SVD Parameterization","arxiv_id":"1803.09327","date":"2018-03-25","proceeding":"ICML 2018 7","authors":["Jiong Zhang","Qi Lei","Inderjit S. Dhillon"],"abstract":"Vanishing and exploding gradients are two of the main obstacles in training\ndeep neural networks, especially in capturing long range dependencies in\nrecurrent neural networks~(RNNs). In this paper, we present an efficient\nparametrization of the transition matrix of an RNN that allows us to stabilize\nthe gradients that arise in its training. Specifically, we parameterize the\ntransition matrix by its singular value decomposition(SVD), which allows us to\nexplicitly track and control its singular values. We attain efficiency by using\ntools that are common in numerical linear algebra, namely Householder\nreflectors for representing the orthogonal matrices that arise in the SVD. By\nexplicitly controlling the singular values, our proposed Spectral-RNN method\nallows us to easily solve the exploding gradient problem and we observe that it\nempirically solves the vanishing gradient issue to a large extent. We note that\nthe SVD parameterization can be used for any rectangular weight matrix, hence\nit can be easily extended to any deep neural network, such as a multi-layer\nperceptron. Theoretically, we demonstrate that our parameterization does not\nlose any expressive power, and show how it controls generalization of RNN for\nthe classification task. %, and show how it potentially makes the optimization\nprocess easier. Our extensive experimental results also demonstrate that the\nproposed framework converges faster, and has good generalization, especially in\ncapturing long range dependencies, as shown on the synthetic addition and copy\ntasks, as well as on MNIST and Penn Tree Bank data sets.","url_abs":"http://arxiv.org/abs/1803.09327v1","url_pdf":"http://arxiv.org/pdf/1803.09327v1.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":"stabilizing-gradients-for-deep-neural","repo_url":"https://github.com/zhangjiong724/spectral-RNN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"svd-parameterization","method_name":"SVD Parameterization"}],"datasets_introduced":[],"methods_introduced":[{"slug":"svd-parameterization","name":"SVD Parameterization","full_name":"Singular Value Decomposition Parameterization"}],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1803.09327","atlas_url":"https://app.syntology.ai/?focus=1803.09327","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}