{"url":"/method/pelu","slug":"pelu","name":"PELU","full_name":"Parametric Exponential Linear Unit","full_name_withheld":false,"description_markdown":"**Parameterized Exponential Linear Units**, or **PELU**, is an activation function for neural networks. It involves learning a parameterization of [ELU](https://paperswithcode.com/method/elu) in order to learn the proper activation shape at each layer in a CNN. \r\n\r\nThe PELU has two additional parameters over the ELU:\r\n\r\n$$ f\\left(x\\right) = cx \\text{ if } x > 0 $$\r\n$$ f\\left(x\\right) = \\alpha\\exp^{\\frac{x}{b}} - 1 \\text{ if } x \\leq 0 $$\r\n\r\nWhere $a$, $b$, and $c > 0$. Here $c$ causes a change in the slope in the positive quadrant, $b$ controls the scale of the [exponential decay](https://paperswithcode.com/method/exponential-decay), and $\\alpha$ controls the saturation in the negative quadrant.\r\n\r\nSource: [Activation Functions](https://arxiv.org/pdf/1811.03378.pdf)","description_state":"present","introduced_year":null,"introduced_by":{"title":"Parametric Exponential Linear Unit for Deep Convolutional Neural Networks","paper":"/paper/parametric-exponential-linear-unit-for-deep","first_author":"Ludovic Trottier","n_authors":3,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/parametric-exponential-linear-unit-for-deep"},"source":{"url":"http://arxiv.org/abs/1605.09332v4","title":"Parametric Exponential Linear Unit for Deep Convolutional Neural Networks","url_on_a_paper_host":true},"code_snippet_url":"https://github.com/InzamamRahaman/PELU/blob/ee2598c32f3596f18d957417c97c03e8862086bf/pelu.py#L6","code_snippet_url_on_a_code_host":true,"categories":[{"area":"General","area_id":"general","collection":"Adaptive Activation Functions","url":"/methods/category/adaptive-activation-functions","pwc_aliases":[]},{"area":"General","area_id":"general","collection":"Activation Functions","url":"/methods/category/activation-functions","pwc_aliases":[]}],"n_papers_tagged":2,"archive_num_papers":2,"papers_newest_first":[{"paper":"/paper/recurrent-rational-networks","title":"Adaptive Rational Activations to Boost Deep Reinforcement Learning","date":"2021-02-18","arxiv_id":"2102.09407","n_code_links":4,"syntology":{"ran":6,"of":6,"unverified":0,"pointer_only":3}},{"paper":"/paper/parametric-exponential-linear-unit-for-deep","title":"Parametric Exponential Linear Unit for Deep Convolutional Neural Networks","date":"2016-05-30","arxiv_id":"1605.09332","n_code_links":0,"syntology":null}],"papers_shown":2,"tasks":[{"task":"/task/atari-games","name":"Atari Games","papers":1},{"task":"/task/deep-reinforcement-learning","name":"Deep Reinforcement Learning","papers":1},{"task":"/task/general-reinforcement-learning","name":"General Reinforcement Learning","papers":1},{"task":"/task/image-classification","name":"Image Classification","papers":1},{"task":"/task/object-recognition","name":"Object Recognition","papers":1},{"task":"/task/reinforcement-learning","name":"Reinforcement Learning","papers":1},{"task":"/task/reinforcement-learning-1","name":"Reinforcement Learning (RL)","papers":1},{"task":"/task/scene-understanding","name":"Scene Understanding","papers":1},{"task":"/task/reinforcement-learning-2","name":"reinforcement-learning","papers":1}],"tasks_shown":9,"n_tasks":9,"usage_by_year":[{"year":"2016","papers":1},{"year":"2021","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/pelu"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}