{"url":"/method/fractal-block","slug":"fractal-block","name":"Fractal Block","full_name":"Fractal Block","full_name_withheld":false,"description_markdown":"A **Fractal Block** is an image model block that utilizes an expansion rule that yields a structural layout of truncated fractals. For the base case where $f\\_{1}\\left(z\\right) = \\text{conv}\\left(z\\right)$ is a convolutional layer, we then have recursive fractals of the form:\r\n\r\n$$ f\\_{C+1}\\left(z\\right) = \\left[\\left(f\\_{C}\\circ{f\\_{C}}\\right)\\left(z\\right)\\right] \\oplus \\left[\\text{conv}\\left(z\\right)\\right]$$\r\n\r\nWhere $C$ is the number of columns. For the join layer (green in Figure), we use the element-wise mean rather than concatenation or addition.","description_state":"present","introduced_year":null,"introduced_by":{"title":"FractalNet: Ultra-Deep Neural Networks without Residuals","paper":"/paper/fractalnet-ultra-deep-neural-networks-without","first_author":"Gustav Larsson","n_authors":3,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/fractalnet-ultra-deep-neural-networks-without"},"source":{"url":"http://arxiv.org/abs/1605.07648v4","title":"FractalNet: Ultra-Deep Neural Networks without Residuals","url_on_a_paper_host":true},"code_snippet_url":"https://github.com/osmr/imgclsmob/blob/68335927ba27f2356093b985bada0bc3989836b1/pytorch/pytorchcv/models/fractalnet_cifar.py#L103","code_snippet_url_on_a_code_host":true,"categories":[{"area":"Computer Vision","area_id":"computer-vision","collection":"Image Model Blocks","url":"/methods/category/image-model-blocks","pwc_aliases":[]}],"n_papers_tagged":6,"archive_num_papers":6,"papers_newest_first":[{"paper":"/paper/handwritten-bangla-character-recognition","title":"Handwritten Bangla Character Recognition Using The State-of-Art Deep Convolutional Neural Networks","date":"2017-12-28","arxiv_id":"1712.09872","n_code_links":1,"syntology":null},{"paper":null,"title":"CrescendoNet: A Simple Deep Convolutional Neural Network with Ensemble Behavior","date":"2017-10-30","arxiv_id":"1710.11176","n_code_links":0,"syntology":null},{"paper":null,"title":"Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations","date":"2017-10-27","arxiv_id":"1710.10121","n_code_links":0,"syntology":null},{"paper":"/paper/smash-one-shot-model-architecture-search","title":"SMASH: One-Shot Model Architecture Search through HyperNetworks","date":"2017-08-17","arxiv_id":"1708.05344","n_code_links":1,"syntology":null},{"paper":"/paper/deep-convolutional-neural-network-design","title":"Deep Convolutional Neural Network Design Patterns","date":"2016-11-02","arxiv_id":"1611.00847","n_code_links":1,"syntology":null},{"paper":"/paper/fractalnet-ultra-deep-neural-networks-without","title":"FractalNet: Ultra-Deep Neural Networks without Residuals","date":"2016-05-24","arxiv_id":"1605.07648","n_code_links":4,"syntology":{"ran":4,"of":6,"unverified":2,"pointer_only":1}}],"papers_shown":6,"tasks":[{"task":"/task/deep-learning","name":"Deep Learning","papers":1},{"task":"/task/image-classification","name":"Image Classification","papers":1},{"task":"/task/architecture-search","name":"Neural Architecture Search","papers":1},{"task":"/task/object-recognition","name":"Object Recognition","papers":1},{"task":"/task/translation","name":"Translation","papers":1},{"task":"/task/model","name":"model","papers":1}],"tasks_shown":6,"n_tasks":6,"usage_by_year":[{"year":"2016","papers":2},{"year":"2017","papers":4}],"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/fractal-block"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}