# Ops

Ops in Aesara define your ontology, i.e. the (mathematical) objects that exist in your problem space and that can be linked to one another.

In Theano, from which Aesara was forked, Ops represented simple mathematical expressions: at.log, at.exp, etc. Aesara added the concept of random variables to that.

Why is it important?

## Expressivity

Expressivity Higher-level Ops allow you to express your problem at the level of abstraction that matters to you. Take speculations around a deep learning library that we shall name Kaeras for now:

model = al.Sequential(
al.Conv2D(32, kernel_size=(3, 3)),
al.ReLu(),
al.MaxPooling2D(pool_size=(2, 2)),
layers.Conv2D(64, kernel_size=(3, 3)),
al.ReLu(),
al.MaxPooling2D(pool_size=(2, 2)),
al.Flatten(),
al.Dropout(0.5),
al.Dense(num_classes),
al.Softmax(),
)


Your ontology is not made only of tensors but also of layers: they perform an operation, have a well-defined gradient, and we can reason about them. In the same way, an entire model can become an Ops as well. And this simplifies the graph a lot. Note that in lieu of Ops we could use a function that returns a graph. But that would not allow us to do the following:

## Reasoning and rewriting

Reasoning Higher-level Ops allow you to implement rewrites that operate at a given level of abstraction. Take random variables. It is well known that the sum of two normally distributed random variables is a normally-distributed random variable:

\begin{align*} X &\sim \operatorname{N}(\mu_X, \sigma_X^2)\\ Y &\sim \operatorname{N}(\mu_Y, \sigma_Y^2)\\ Z &= X + Y \end{align*}

Then:

\begin{equation*} Z \sim \operatorname{N}(\mu_X + \mu_Y, \sigma_X^2 + \sigma_Y^2) \end{equation*}

That is something you could infer from the probability density functions, but it would be the result of a series of rewrites. Rewrites implement facts at different levels of abstractions, and it is better to do rewrites at a the highest possible level of abstraction, and then go down the hierarchy. We could imagine do the rewrites on the higher-order graph (the one we implemented) until Equality saturation, then expand the OpsFromGraph and saturate again, then expand, etc. until we've expanded the OpsFromGraph.