The **Two Time-scale Update Rule (TTUR)** is an update rule for generative adversarial networks trained with stochastic gradient descent. TTUR has an individual learning rate for both the discriminator and the generator. The main premise is that the discriminator converges to a local minimum when the generator is fixed. If the generator changes slowly enough, then the discriminator still converges, since the generator perturbations are small. Besides ensuring convergence, the performance may also improve since the discriminator must first learn new patterns before they are transferred to the generator. In contrast, a generator which is overly fast, drives the discriminator steadily into new regions without capturing its gathered information.

**Sigmoid Activations** are a type of activation function for neural networks:

$$f\left(x\right) = \frac{1}{\left(1+\exp\left(-x\right)\right)}$$

Some drawbacks of this activation that have been noted in the literature are: sharp damp gradients during backpropagation from deeper hidden layers to inputs, gradient saturation, and slow convergence.

Sigmoid Activation

TTUR

GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium

The  overhead  cost  of  training  multiple  deep  neural networks  could  be  very  high  in  terms  of  the  training  time, hardware, and computational resource requirement and often acts  as  obstacle  for  creating  deep  ensembles.  To  overcome these barriers Huang et al. proposed a unique method to create  ensemble  which  at  the  cost  of  training  one  model, yields  multiple  constituent  model  snapshots  that  can  be ensembled together to create a strong learner. The core idea behind the concept is to make the model converge to several local minima along the optimization path and save the model parameters at these local minima points. During the training phase, a neural network would traverse through many such points. The lowest of all such local minima is known as the Global Minima. The larger the model, more are the number of parameters and larger the number of local minima points. This implies, there are discrete sets of weights and biases, at which  the  model  is  making  fewer  errors.  So,  every  such minimum  can  be  considered a  weak  but  a  potential learner model for the problem being solved. Multiple such snapshot of  weights  and  biases  are  recorded  which  can  later  be ensembled to get a better generalized model which makes the least amount of mistakes.

Source	GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium
Year	2000
Data Source	CC BY-SA - https://paperswithcode.com