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It reduces the space of possible mapping functions by enforcing forward and backwards consistency:\r\n\r\n$$ \\mathcal{L}\\_{cyc}\\left(G, F\\right) = \\mathbb{E}\\_{x \\sim p\\_{data}\\left(x\\right)}\\left[||F\\left(G\\left(x\\right)\\right) - x||\\_{1}\\right] + \\mathbb{E}\\_{y \\sim p\\_{data}\\left(y\\right)}\\left[||G\\left(F\\left(y\\right)\\right) - y||\\_{1}\\right] $$","description_state":"present","introduced_year":null,"introduced_by":{"title":"Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks","paper":"/paper/unpaired-image-to-image-translation-using","first_author":"Jun-Yan Zhu","n_authors":4,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/unpaired-image-to-image-translation-using"},"source":{"url":"https://arxiv.org/abs/1703.10593v7","title":"Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial 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