{"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/understanding-convolutional-neural-networks-1","title":"Understanding Convolutional Neural Networks with A Mathematical Model","arxiv_id":"1609.04112","date":"2016-09-14","proceeding":null,"authors":["C. -C. Jay Kuo"],"abstract":"This work attempts to address two fundamental questions about the structure\nof the convolutional neural networks (CNN): 1) why a non-linear activation\nfunction is essential at the filter output of every convolutional layer? 2)\nwhat is the advantage of the two-layer cascade system over the one-layer\nsystem? A mathematical model called the \"REctified-COrrelations on a Sphere\"\n(RECOS) is proposed to answer these two questions. After the CNN training\nprocess, the converged filter weights define a set of anchor vectors in the\nRECOS model. Anchor vectors represent the frequently occurring patterns (or the\nspectral components). The necessity of rectification is explained using the\nRECOS model. Then, the behavior of a two-layer RECOS system is analyzed and\ncompared with its one-layer counterpart. The LeNet-5 and the MNIST dataset are\nused to illustrate discussion points. Finally, the RECOS model is generalized\nto a multi-layer system with the AlexNet as an example.\n  Keywords: Convolutional Neural Network (CNN), Nonlinear Activation, RECOS\nModel, Rectified Linear Unit (ReLU), MNIST Dataset.","url_abs":"http://arxiv.org/abs/1609.04112v2","url_pdf":"http://arxiv.org/pdf/1609.04112v2.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":"understanding-convolutional-neural-networks-1","repo_url":"https://github.com/krish-pinninti/api-ann-python","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":"model","task_name":"model"}],"methods":[{"method_slug":"1x1-convolution","method_name":"1x1 Convolution"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"grouped-convolution","method_name":"Grouped Convolution"},{"method_slug":"local-response-normalization","method_name":"Local Response Normalization"},{"method_slug":"max-pooling","method_name":"Max Pooling"},{"method_slug":"relu","method_name":"ReLU"},{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}