Neural networks can grow quite large in size. This has some implications for memory use; however, efficient structures such as sparse matrices mean that we don't generally run into problems fitting a neural network in memory.

The main issue when neural networks grow large is that they take a very long time to compute. In addition, some datasets and neural networks will need to run many epochs of training to get a good fit for the dataset. The neural network we will train in this chapter takes more than 8 minutes per epoch on my reasonably powerful computer, and we expect to run dozens, potentially hundreds, of epochs. Some larger networks can take hours to train a single epoch. To get the best performance, you may be considering thousands of training cycles.

The math obviously doesn't give a nice result here.

One positive is that neural networks are, at their core, full of floating point operations. There are also a large number of operations that can be performed in parallel...