candidates which is based on repeating tokens or n-grams and frequent tokens [@Welleck2020Neural]. This set is updated at each time step as tokens are generated. This works at both token and sequence level and the objective tries to minimize the repetitions in generations. This is used at train time in augmentation with the maximum likelihood objective and can be used for any task.

#### Diversity-Promoting objective:

This is used to generate a varied set of sentences given similar inputs. Particularly, @li:2015 use Maximum Mutual Information (MMI) as an objective function for the dialogue response generation task. Most generation systems use maximum likelihood objective but this objective additionally tries to reduce the proportion of generic responses. It is given by: $${\mathbf{\hat{T}}} = {\mathtt{argmax}}_{T} \{ {\mathtt{log}} p({\mathbf{T}} | {\mathbf{S}}) - \lambda {\mathtt{log}} p({\mathbf{T}})\}$$ where ${\mathbf{\hat{T}}}$ is the generated target sequence, ${\mathbf{T}}$ is the reference target sequence and ${\mathbf{S}}$ is the source sequence. The second term controls the generation of the high frequency or the generic target sequences. Note that this objective is only used during the inference and the generators are trained using cross entropy loss. @zhang2018personalizing, also use a diversity encouraging objective for dialogue response generation. They train a discriminator to 