This paper nicely describes a rather specific situation when the preparatory work for optimizing a generative adversarial network $($GAN$)$ on a mobile device is done with a high$-$resolution image dataset; the trade$-$off between the batch size and learning rate settings in this case is rather unique. Based on this, you ascertain that reduced batch sizes have stable convergence but slow learning rates, while on the other hand, increased batch sizes speed up learning, but the downside is that it causes mode collapse. Based on this background, what values of batch size and learning rate would protect from mode collapse while boosting convergence at the same time? Evaluate the following scenarios, considering both stability and learning dynamics: