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Each reversible block takes inputs $\\left(x\\_{1}, x\\_{2}\\right)$ and produces outputs $\\left(y\\_{1}, y\\_{2}\\right)$ according to the following additive coupling rules – inspired by the transformation in [NICE](https://paperswithcode.com/method/nice) (nonlinear independent components estimation) – and residual functions $F$ and $G$ analogous to those in standard [ResNets](https://paperswithcode.com/method/resnet):\r\n\r\n$$y\\_{1} = x\\_{1} + F\\left(x\\_{2}\\right)$$\r\n$$y\\_{2} = x\\_{2} + G\\left(y\\_{1}\\right)$$\r\n\r\nEach layer’s activations can be reconstructed from the next layer’s activations as follows:\r\n\r\n$$ x\\_{2} = y\\_{2} − G\\left(y\\_{1}\\right)$$\r\n$$ x\\_{1} = y\\_{1} − F\\left(x\\_{2}\\right)$$","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":"http://arxiv.org/abs/1707.04585v1","title":"The Reversible Residual 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