Collection of some quick ideas that I may or may not work on later.

#### 1. Neural networks that take elements of a finite group as input

If we simply treat the input as general one-hot vectors the group structure will be lost. Could we somehow let the neural network be aware of the structure?

E.g. if the group is of order *n* then let the value of a neuron be a distribution on the *n* elements, and define a special type of neuron that takes two distributions *P* and *Q* and outputs *R* that is the distribution of *c*=*ab^-1* where *a*~*P* and *b*~*Q*. We should be able to do this with some tensor arithmetic.

**2. Iterative drawing for generating high-resolution images**

What if instead of iteratively upsampling, we draw on a large canvas with progressively finer strokes?