# Model Building Basics

## The Model

*... Initialising Photon Beams ...*

The core concept in Flux is the *model*. A model (or "layer") is simply a function with parameters. For example, in plain Julia code, we could define the following function to represent a logistic regression (or simple neural network):

```julia
W = randn(3,5)
b = randn(3)
affine(x) = W * x + b

x1 = rand(5) # [0.581466,0.606507,0.981732,0.488618,0.415414]
y1 = softmax(affine(x1)) # [0.32676,0.0974173,0.575823]
```

`affine` is simply a function which takes some vector `x1` and outputs a new one `y1`. For example, `x1` could be data from an image and `y1` could be predictions about the content of that image. However, `affine` isn't static. It has *parameters* `W` and `b`, and if we tweak those parameters we'll tweak the result – hopefully to make the predictions more accurate.

This is all well and good, but we usually want to have more than one affine layer in our network; writing out the above definition to create new sets of parameters every time would quickly become tedious. For that reason, we want to use a *template* which creates these functions for us:

```julia
affine1 = Affine(5, 5)
affine2 = Affine(5, 5)

softmax(affine1(x1)) # [0.167952, 0.186325, 0.176683, 0.238571, 0.23047]
softmax(affine2(x1)) # [0.125361, 0.246448, 0.21966, 0.124596, 0.283935]
```

We just created two separate `Affine` layers, and each contains its own (randomly initialised) version of `W` and `b`, leading to a different result when called with our data. It's easy to define templates like `Affine` ourselves (see [templates](templates.html)), but Flux provides `Affine` out of the box, so we'll use that for now.

## Combining Models

*... Inflating Graviton Zeppelins ...*

A more complex model usually involves many basic layers like `affine`, where we use the output of one layer as the input to the next:

```julia
mymodel1(x) = softmax(affine2(σ(affine1(x))))
mymodel1(x1) # [0.187935, 0.232237, 0.169824, 0.230589, 0.179414]
```

This syntax is again a little unwieldy for larger networks, so Flux provides another template of sorts to create the function for us:

```julia
mymodel2 = Chain(affine1, σ, affine2, softmax)
mymodel2(x2) # [0.187935, 0.232237, 0.169824, 0.230589, 0.179414]
```

`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:

```julia
mymodel3 = Chain(
  Affine(5, 5), σ,
  Affine(5, 5), softmax)
```

You now know enough to take a look at the [logistic regression](../examples/logreg.md) example, if you haven't already.

## A Function in Model's Clothing

*... Booting Dark Matter Transmogrifiers ...*

We noted above that a "model" is a function with some number of trainable parameters. This goes both ways; a normal Julia function like `exp` is effectively a model with 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:

```julia
foo = Chain(exp, sum, log)
foo([1,2,3]) == 3.408 == log(sum(exp([1,2,3])))
```