{"url":"/method/rrelu","slug":"rrelu","name":"RReLU","full_name":"Randomized Leaky Rectified Linear Units","full_name_withheld":false,"description_markdown":"**Randomized Leaky Rectified Linear Units**, or **RReLU**, are an activation function that randomly samples the negative slope for activation values. It was first proposed and used in the Kaggle NDSB Competition. During training, $a\\_{ji}$ is a random number sampled from a uniform distribution $U\\left(l, u\\right)$. Formally:\r\n\r\n$$ y\\_{ji} = x\\_{ji} \\text{   if } x\\_{ji} \\geq{0} $$\r\n$$ y\\_{ji} = a\\_{ji}x\\_{ji} \\text{   if } x\\_{ji} < 0 $$\r\n\r\nwhere\r\n\r\n$$\\alpha\\_{ji} \\sim U\\left(l, u\\right), l < u \\text{ and } l, u \\in \\left[0,1\\right)$$\r\n\r\nIn the test phase, we take average of all the $a\\_{ji}$ in training similar to [dropout](https://paperswithcode.com/method/dropout), and thus set $a\\_{ji}$ to $\\frac{l+u}{2}$ to get a deterministic result. As suggested by the NDSB competition winner, $a\\_{ji}$ is sampled from $U\\left(3, 8\\right)$. \r\n\r\nAt test time, we use:\r\n\r\n$$ y\\_{ji} = \\frac{x\\_{ji}}{\\frac{l+u}{2}} $$","description_state":"present","introduced_year":null,"introduced_by":{"title":"Empirical Evaluation of Rectified Activations in Convolutional Network","paper":"/paper/empirical-evaluation-of-rectified-activations","first_author":"Bing Xu","n_authors":4,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/empirical-evaluation-of-rectified-activations"},"source":{"url":"http://arxiv.org/abs/1505.00853v2","title":"Empirical Evaluation of Rectified Activations in Convolutional Network","url_on_a_paper_host":true},"code_snippet_url":"https://github.com/pytorch/pytorch/blob/96aaa311c0251d24decb9dc5da4957b7c590af6f/torch/nn/modules/activation.py#L109","code_snippet_url_on_a_code_host":true,"categories":[{"area":"General","area_id":"general","collection":"Activation Functions","url":"/methods/category/activation-functions","pwc_aliases":[]}],"n_papers_tagged":3,"archive_num_papers":3,"papers_newest_first":[{"paper":null,"title":"Non-Linearities Improve OrigiNet based on Active Imaging for Micro Expression Recognition","date":"2020-05-16","arxiv_id":"2005.07991","n_code_links":0,"syntology":null},{"paper":null,"title":"Towards Single-phase Single-stage Detection of Pulmonary Nodules in Chest CT Imaging","date":"2018-07-16","arxiv_id":"1807.05972","n_code_links":0,"syntology":null},{"paper":"/paper/empirical-evaluation-of-rectified-activations","title":"Empirical Evaluation of Rectified Activations in Convolutional Network","date":"2015-05-05","arxiv_id":"1505.00853","n_code_links":2,"syntology":null}],"papers_shown":3,"tasks":[{"task":"/task/classification","name":"General Classification","papers":1},{"task":"/task/image-classification","name":"Image Classification","papers":1},{"task":"/task/micro-expression-recognition-1","name":"Micro Expression Recognition","papers":1},{"task":"/task/micro-expression-recognition","name":"Micro-Expression Recognition","papers":1},{"task":"/task/transfer-learning","name":"Transfer Learning","papers":1},{"task":"/task/image-classification","name":"image-classification","papers":1}],"tasks_shown":6,"n_tasks":6,"usage_by_year":[{"year":"2015","papers":1},{"year":"2018","papers":1},{"year":"2020","papers":1}],"row_source":"methods_table","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/rrelu"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}