{"url":"/method/g-gln-neuron","slug":"g-gln-neuron","name":"G-GLN Neuron","full_name":"G-GLN Neuron","full_name_withheld":false,"description_markdown":"A **G-GLN Neuron** is a type of neuron used in the [G-GLN](https://paperswithcode.com/method/g-gln) architecture. G-GLN. The key idea is that further representational power can be added to a weighted product of Gaussians via a contextual gating procedure. This is achieved by extending a weighted product of Gaussians model with an additional type of input called side information. The side information will be used by a neuron to select a weight vector to apply for a given example from a table of weight vectors. In typical applications to regression, the side information is defined as the (normalized) input features for an input example: i.e. $z=(x-\\bar{x}) / \\sigma\\_{x}$.\r\n\r\nMore formally, associated with each neuron is a context function $c: \\mathcal{Z} \\rightarrow \\mathcal{C}$, where $\\mathcal{Z}$ is the set of possible side information and $\\mathcal{C}=\\{0, \\ldots, k-1\\}$ for some $k \\in \\mathbb{N}$ is the context space. Each neuron $i$ is now parameterized by a weight matrix $W\\_{i}=\\left[w\\_{i, 0} \\ldots w\\_{i, k-1}\\right]^{\\top}$ with each row vector $w\\_{i j} \\in \\mathcal{W}$ for $0 \\leq j<k$. The context function $c$ is responsible for mapping side information $z \\in \\mathcal{Z}$ to a particular row $w\\_{i, c(z)}$ of $W_{i}$, which we then use to weight the Product of Gaussians. In other words, a G-GLN neuron can be defined by:\r\n\r\n$$\r\n\\operatorname{PoG}\\_{W}^{c}\\left(y ; f_{1}(\\cdot), \\ldots, f\\_{m}(\\cdot), z\\right):=\\operatorname{PoG}\\_{w^{c(z)}}\\left(y ; f\\_{1}(\\cdot), \\ldots, f\\_{m}(\\cdot)\\right)\r\n$$\r\n\r\nwith the associated loss function $-\\log \\left(\\operatorname{PoG}\\_{W}^{c}\\left(y ; f\\_{1}(y), \\ldots, f\\_{m}(y), z\\right)\\right)$ inheriting all the properties needed to apply Online Convex Programming.","description_state":"present","introduced_year":null,"introduced_by":{"title":"Gaussian Gated Linear Networks","paper":"/paper/gaussian-gated-linear-networks","first_author":"David Budden","n_authors":6,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/gaussian-gated-linear-networks"},"source":{"url":"https://arxiv.org/abs/2006.05964v2","title":"Gaussian Gated Linear Networks","url_on_a_paper_host":true},"code_snippet_url":null,"code_snippet_url_on_a_code_host":false,"categories":[{"area":"General","area_id":"general","collection":"Gated Linear Networks","url":"/methods/category/gated-linear-networks","pwc_aliases":[]}],"n_papers_tagged":1,"archive_num_papers":1,"papers_newest_first":[{"paper":"/paper/gaussian-gated-linear-networks","title":"Gaussian Gated Linear Networks","date":"2020-06-10","arxiv_id":"2006.05964","n_code_links":3,"syntology":null}],"papers_shown":1,"tasks":[{"task":"/task/denoising","name":"Denoising","papers":1},{"task":"/task/density-estimation","name":"Density Estimation","papers":1},{"task":"/task/multi-armed-bandits","name":"Multi-Armed Bandits","papers":1},{"task":"/task/regression-1","name":"regression","papers":1}],"tasks_shown":4,"n_tasks":4,"usage_by_year":[{"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/g-gln-neuron"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}