Flux's core feature is the `@net` macro, which adds some superpowers to regular ol' Julia functions. Consider this simple function with the `@net` annotation applied:
```julia
@net f(x) = x .* x
f([1,2,3]) == [1,4,9]
```
This behaves as expected, but we have some extra features. For example, we can convert the function to run on [TensorFlow](https://www.tensorflow.org/) or [MXNet](https://github.com/dmlc/MXNet.jl):
```julia
f_mxnet = mxnet(f)
f_mxnet([1,2,3]) == [1.0, 4.0, 9.0]
```
Simples! Flux took care of a lot of boilerplate for us and just ran the multiplication on MXNet. MXNet can optimise this code for us, taking advantage of parallelism or running the code on a GPU.
Using MXNet, we can get the gradient of the function, too:
`f` is effectively `x^2`, so the gradient is `2x` as expected.
For TensorFlow users this may seem similar to building a graph as usual. The difference is that Julia code still behaves like Julia code. Error messages give you helpful stacktraces that pinpoint mistakes. You can step through the code in the debugger. The code runs when it's called, as usual, rather than running once to build the graph and then again to execute it.
The core concept in Flux is the *model*. This corresponds to what might be called a "layer" or "module" in other frameworks. A model is simply a differentiable function with parameters. Given a model `m` we can do things like:
```julia
m(x) # See what the model does to an input vector `x`
back!(m, Δ, x) # backpropogate the gradient `Δ` through `m`
update!(m, η) # update the parameters of `m` using the gradient
We can implement a model however we like as long as it fits this interface. But as hinted above, `@net` is a particularly easy way to do it, as `@net` functions are models already.
## Parameters
Consider how we'd write a logistic regression. We just take the Julia code and add `@net`.
Bigger networks contain many affine transformations like `W * x + b`. We don't want to write out the definition every time we use it. Instead, we can factor this out by making a function that produces models:
```julia
function create_affine(in, out)
W = randn(out,in)
b = randn(out)
@net x -> W * x + b
end
affine1 = create_affine(3,2)
affine1([1,2,3])
```
Flux has a [more powerful syntax](templates.html) for this pattern, but also provides a bunch of layers out of the box. So we can instead write:
`mymodel2` is exactly equivalent to `mymodel1` because it simply calls the provided functions in sequence. We don't have to predefine the affine layers and can also write this as:
We noted above that a model is a function with trainable parameters. Normal functions like `exp` are actually models too – they just happen to have 0 parameters. Flux doesn't care, and anywhere that you use one, you can use the other. For example, `Chain` will happily work with regular functions:
