Viet-Anh on Software Logo

What is: GAN Least Squares Loss?

SourceLeast Squares Generative Adversarial Networks
Year2000
Data SourceCC BY-SA - https://paperswithcode.com

GAN Least Squares Loss is a least squares loss function for generative adversarial networks. Minimizing this objective function is equivalent to minimizing the Pearson χ2\chi^{2} divergence. The objective function (here for LSGAN) can be defined as:

min_DV_LS(D)=12E_xp_data(x)[(D(x)b)2]+12E_zp_data(z)[(D(G(z))a)2]\min\_{D}V\_{LS}\left(D\right) = \frac{1}{2}\mathbb{E}\_{\mathbf{x} \sim p\_{data}\left(\mathbf{x}\right)}\left[\left(D\left(\mathbf{x}\right) - b\right)^{2}\right] + \frac{1}{2}\mathbb{E}\_{\mathbf{z}\sim p\_{data}\left(\mathbf{z}\right)}\left[\left(D\left(G\left(\mathbf{z}\right)\right) - a\right)^{2}\right]

min_GV_LS(G)=12E_zp_z(z)[(D(G(z))c)2]\min\_{G}V\_{LS}\left(G\right) = \frac{1}{2}\mathbb{E}\_{\mathbf{z} \sim p\_{\mathbf{z}}\left(\mathbf{z}\right)}\left[\left(D\left(G\left(\mathbf{z}\right)\right) - c\right)^{2}\right]

where aa and bb are the labels for fake data and real data and cc denotes the value that GG wants DD to believe for fake data.