# 7  Modules

In the last chapter, we built a neural network for a regression task. There were two distinct types of operations: linear and non-linear.

In the non-linear category, we had ReLU activation, expressed as a straightforward function call: nnf_relu(). Activation functions are functions: Given input $$\mathbf{x}$$, they return output $$\mathbf{y}$$ every time. In other words, they are deterministic. It’s different with the linear part, though.

The linear part in the regression network was implemented as multiplication by a matrix – the weight matrix – and addition of a vector (the bias vector). With operations like that, results inevitably depend on the actual values stored in the respective tensors. Put differently, the operation is stateful.

Whenever there is state involved, it helps to encapsulate it in an object, freeing the user from manual management. This is what torch’s modules do.

Note that term, modules. In torch, a module can be of any complexity, ranging from basic layers – like the nn_linear() we are going to introduce in a minute – to complete models consisting of many such layers. Code-wise, there is no difference between “layers” and “models”. This is why in some texts, you’ll see “module” used throughout. In this book, I’ll mostly stay with the common terminology of layers and models, as it maps more closely to how things appear conceptually.

Back to the why of modules. In addition to encapsulation, there is another reason for providing layer objects: Not all often-used layers are as light-weight as nn_linear() is. We’ll quickly mention a few others at the end of the next section, reserving a complete introduction to later chapters of this book.

## 7.1 Built-in nn_module()s

In torch, a linear layer is created using nn_linear(). nn_linear() expects (at least) two arguments: in_features and out_features. Let’s say your input data has fifty observations with five features each; that is, it is of size 50 x 5. You want to build a hidden layer with sixteen units. Then in_features is 5, and out_features is 16. (The same 5 and 16 would constitute the number of rows/columns in the weight matrix if you built one yourself.)

library(torch)
l <- nn_linear(in_features = 5, out_features = 16)

l
An nn_module containing 96 parameters.
Parameters
weight: Float [1:16, 1:5]
bias: Float [1:16]

Encapsulation doesn’t keep us from inspecting the weight and bias tensors:

l$weight torch_tensor -0.2079 -0.1920 0.2926 0.0036 -0.0897 0.3658 0.0076 -0.0671 0.3981 -0.4215 0.2568 0.3648 -0.0374 -0.2778 -0.1662 0.4444 0.3851 -0.1225 0.1678 -0.3443 -0.3998 0.0207 -0.0767 0.4323 0.1653 0.3997 0.0647 -0.2823 -0.1639 -0.0225 0.0479 0.0207 -0.3426 -0.1567 0.2830 0.0925 -0.4324 0.0448 -0.0039 0.1531 -0.2924 -0.0009 -0.1841 0.2028 0.1586 -0.3064 -0.4006 -0.0553 -0.0067 0.2575 -0.0472 0.1238 -0.3583 0.4426 -0.0269 -0.0275 -0.0295 -0.2687 0.2236 0.3787 -0.2617 -0.2221 0.1503 -0.0627 0.1094 0.0122 0.2041 0.4466 0.4112 0.4168 -0.4362 -0.3390 0.3679 -0.3045 0.1358 0.2979 0.0023 0.0695 -0.1906 -0.1526 [ CPUFloatType{16,5} ] l$bias
torch_tensor
-0.2314
0.2942
0.0567
-0.1728
-0.3220
-0.1553
-0.4149
-0.2103
-0.1769
0.4219
-0.3368
0.0689
0.3625
-0.1391
-0.1411
-0.2014
[ CPUFloatType{16} ]

At this point, I need to ask for your indulgence. You’ve probably noticed that torch reports the weight matrix as being of size 16 x 5, not 5 x 16, like we said you’d create it when coding from scratch. This is due to an implementation detail inherited from the underlying C++ implementation, libtorch. For performance reasons, libtorch’s linear module stores the weight and bias tensors in transposed form. On the R side, all we can do is explicitly point you to it and thereby, hopefully, alleviate the confusion.

Let’s go on. To apply this module to input data, just “call” it like a function:

x <- torch_randn(50, 5)
output <- l(x)
output$size()  50 16 So that’s the forward pass. How about gradient computation? Previously, when creating a tensor we wanted to figure as a “source” in gradient computation, we had to let torch know explicitly, passing requires_grad = TRUE. No such thing is required for built-in nn_module()s. We can immediately check that output knows what to do on backward(): output$grad_fn
AddmmBackward0

To be sure though, let’s calculate some “dummy” loss based on output, and call backward(). We see that now, the linear module’s weight tensor has its grad field populated:

loss <- output$mean() loss$backward()
l$weight$grad
torch_tensor
0.01 *
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
-0.3064  2.4118 -0.6095  0.3419 -1.6131
[ CPUFloatType{16,5} ]

Thus, once you work with nn_modules, torch automatically assumes that you’ll want gradients computed.

nn_linear(), straightforward though it may be, is an essential building block encountered in most every model architecture. Others include:

• nn_conv1d(), nn_conv2d(), and nn_conv3d(), the so-called convolutional layers that apply filters to input data of varying dimensionality,

• nn_lstm() and nn_gru() , the recurrent layers that carry through a state,

• nn_embedding() that is used to embed categorical data in high-dimensional space,

• and more.

## 7.2 Building up a model

The built-in nn_module()s give us layers, in usual speak. How do we combine those into models? Using the “factory function” nn_module(), we can define models of arbitrary complexity. But we may not always need to go that way.

### 7.2.1 Models as sequences of layers: nn_sequential()index{nn_sequential()}

If all our model should do is propagate straight through the layers, we can use nn_sequential() to build it. Models consisting of all linear layers are known as Multi-Layer Perceptronsindex{Multi-Layer Perceptron (MLP)} (MLPs). Here is one:

mlp <- nn_sequential(
nn_linear(10, 32),
nn_relu(),
nn_linear(32, 64),
nn_relu(),
nn_linear(64, 1)
)

Take a close look at the layers involved. We’ve already seen nnf_relu(), the function that implements ReLU activation. (The f in nnf_ stands for functional.) Below, nn_relu, like nn_linear(), is a module, that is, an object. This is because nn_sequential() expects all its arguments to be modules.

Just like the built-in modules, you can apply this model to data by just calling it:

mlp(torch_randn(5, 10))
torch_tensor
0.01 *
-7.8097
-9.0363
-38.3282
5.3959
-16.4837
[ CPUFloatType{5,1} ][ grad_fn = <AddmmBackward0> ]

The single call triggered a complete forward pass through the network. Analogously, calling backward() will back-propagate through all the layers.

What if you need the model to chain execution steps in a non-sequential way?

### 7.2.2 Models with custom logic

As already hinted at, this is where you use nn_module().

nn_module() creates constructors for custom-made R6 objects. Below, my_linear() is such a constructor. When called, it will return a linear module similar to the built-in nn_linear().

Two methods should be implemented in defining a constructor: initialize() and forward(). initialize() creates the module object’s fields, that is, the objects or values it “owns” and can access from inside any of its methods. forward() defines what should happen when the module is called on the input:

my_linear <- nn_module(
initialize = function(in_features, out_features) {
self$w <- nn_parameter(torch_randn( in_features, out_features )) self$b <- nn_parameter(torch_zeros(out_features))
},
forward = function(input) {
input$mm(self$w) + self\$b
}
)

Note the use of nn_parameter(). nn_parameter() makes sure that the passed-in tensor is registered as a module parameter, and thus, is subject to backpropagation by default.

To instantiate the newly-defined module, call its constructor:

l <- my_linear(7, 1)
l
An nn_module containing 8 parameters.

Parameters ────────────────────────────────────────────────────────────────────────────────────────────
● w: Float [1:7, 1:1]
● b: Float [1:1]

Granted, in this example, there really is no custom logic we needed to define our own module for. But here, you have a template applicable to any use case. Later, we’ll see definitions of initialize() and forward() that are more complex, and we’ll encounter additional methods defined on modules. But the basic mechanism will remain the same.

At this point, you may feel like you’d like to rewrite last chapter’s neural network using modules. Feel free to do so! Or maybe wait until, in the next chapter, we’ll have learned about optimizers, and built-in loss functions. Once we’re done, we’ll return to our two examples, function minimization and the regression network. Then, we’ll be removing all do-it-yourself pieces rendered superfluous by torch.