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.

#### Papers

Paper Code Results Date Stars

Image-to-Image Translation 73 13.88%
Image Generation 34 6.46%
Semantic Segmentation 23 4.37%
Style Transfer 20 3.80%
Image Segmentation 12 2.28%
Super-Resolution 12 2.28%
Object Detection 11 2.09%
Test 11 2.09%

#### Components

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