{"url":"/method/weight-demodulation","slug":"weight-demodulation","name":"Weight Demodulation","full_name":"Weight Demodulation","full_name_withheld":false,"description_markdown":"**Weight Modulation** is an alternative to [adaptive instance normalization](https://paperswithcode.com/method/adaptive-instance-normalization) for use in generative adversarial networks, specifically it is introduced in [StyleGAN2](https://paperswithcode.com/method/stylegan2). The purpose of [instance normalization](https://paperswithcode.com/method/instance-normalization) is to remove the effect of $s$ - the scales of the features maps - from the statistics of the [convolution](https://paperswithcode.com/method/convolution)’s output feature maps. Weight modulation tries to achieve this goal more directly. Assuming that input activations are i.i.d. random variables with unit standard deviation. After modulation and convolution, the output activations have standard deviation of:\r\n\r\n$$ \\sigma\\_{j} = \\sqrt{{\\sum\\_{i,k}w\\_{ijk}'}^{2}} $$\r\n\r\ni.e., the outputs are scaled by the $L\\_{2}$ norm of the corresponding weights. The subsequent normalization aims to restore the outputs back to unit standard deviation. This can be achieved if we scale (“demodulate”) each output feature map $j$ by $1/\\sigma\\_{j}$ . Alternatively, we can again bake this into the convolution weights:\r\n\r\n$$ w''\\_{ijk} = w'\\_{ijk} / \\sqrt{{\\sum\\_{i, k}w'\\_{ijk}}^{2} + \\epsilon} $$\r\n\r\nwhere $\\epsilon$ is a small constant to avoid numerical issues.","description_state":"present","introduced_year":null,"introduced_by":{"title":null,"paper":null,"first_author":null,"n_authors":0,"url_abs":null,"archive_paper_url":null},"source":{"url":"https://arxiv.org/abs/1912.04958v2","title":"Analyzing and Improving the Image Quality of StyleGAN","url_on_a_paper_host":true},"code_snippet_url":"https://github.com/NVlabs/stylegan2/blob/4874628c7dfffaae01f89558c476842b475f54d5/metrics/perceptual_path_length.py#L18","code_snippet_url_on_a_code_host":true,"categories":[{"area":"General","area_id":"general","collection":"Normalization","url":"/methods/category/normalization","pwc_aliases":[]}],"n_papers_tagged":182,"archive_num_papers":null,"papers_newest_first":[{"paper":null,"title":"Pose and Facial Expression Transfer by using StyleGAN","date":"2025-04-17","arxiv_id":"2504.13021","n_code_links":0,"syntology":null},{"paper":"/paper/the-gan-is-dead-long-live-the-gan-a-modern","title":"The GAN is dead; long live the GAN! 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