Loss Functions

GAN Least Squares Loss

Introduced by Mao et al. in Least Squares Generative Adversarial Networks

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

$$ \min_{D}V_{LS}\left(D\right) = \frac{1}{2}\mathbb{E}_{\mathbf{x} \sim p_{data}\left(\mathbf{x}\right)}\left[\left(D\left(\mathbf{x}\right) - b\right)^{2}\right] + \frac{1}{2}\mathbb{E}_{\mathbf{z}\sim p_{data}\left(\mathbf{z}\right)}\left[\left(D\left(G\left(\mathbf{z}\right)\right) - a\right)^{2}\right] $$

$$ \min_{G}V_{LS}\left(G\right) = \frac{1}{2}\mathbb{E}_{\mathbf{z} \sim p_{\mathbf{z}}\left(\mathbf{z}\right)}\left[\left(D\left(G\left(\mathbf{z}\right)\right) - c\right)^{2}\right] $$

where $a$ and $b$ are the labels for fake data and real data and $c$ denotes the value that $G$ wants $D$ to believe for fake data.

Source: Least Squares Generative Adversarial Networks

Papers


Paper Code Results Date Stars

Tasks


Task Papers Share
Translation 94 14.37%
Image-to-Image Translation 80 12.23%
Image Generation 42 6.42%
Domain Adaptation 32 4.89%
Semantic Segmentation 23 3.52%
Style Transfer 22 3.36%
Image Segmentation 12 1.83%
Super-Resolution 12 1.83%
Object Detection 11 1.68%

Components


Component Type
🤖 No Components Found You can add them if they exist; e.g. Mask R-CNN uses RoIAlign

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