Containers
Complex neural networks are easily built using container classes:
- Container : abstract class inherited by containers ;
- Sequential : plugs layers in a feed-forward fully connected manner ;
- Parallel : applies its
ithchild module to theithslice of the input Tensor ; - Concat : concatenates in one layer several modules along dimension
dim; - DepthConcat : like Concat, but adds zero-padding when non-
dimsizes don't match; - Decorator : abstract class to change the behaviour of an encapsulated module ;
- Bottle : allows any dimensionality input be forwarded through a module ;
- WeightNorm : implements the reparametrization presented in Weight Normalization ;
- DontCast : prevent encapsulated module from being casted by
Module:type(); - NaN : decorate a module to detect the source of NaN errors ;
- Profile : decorate a module to time its forwards and backwards passes ;
See also the Table Containers for manipulating tables of Tensors.
Container
This is an abstract Module class which declares methods defined in all containers. It reimplements many of the Module methods such that calls are propagated to the contained modules. For example, a call to zeroGradParameters will be propagated to all contained modules.
add(module)
Adds the given module to the container. The order is important
get(index)
Returns the contained modules at index index.
size()
Returns the number of contained modules.
Sequential
Sequential provides a means to plug layers together in a feed-forward fully connected manner.
E.g. creating a one hidden-layer multi-layer perceptron is thus just as easy as:
mlp = nn.Sequential()
mlp:add(nn.Linear(10, 25)) -- Linear module (10 inputs, 25 hidden units)
mlp:add(nn.Tanh()) -- apply hyperbolic tangent transfer function on each hidden units
mlp:add(nn.Linear(25, 1)) -- Linear module (25 inputs, 1 output)
> mlp
nn.Sequential {
[input -> (1) -> (2) -> (3) -> output]
(1): nn.Linear(10 -> 25)
(2): nn.Tanh
(3): nn.Linear(25 -> 1)
}
> print(mlp:forward(torch.randn(10)))
-0.1815
[torch.Tensor of dimension 1]
remove([index])
Remove the module at the given index. If index is not specified, remove the last layer.
model = nn.Sequential()
model:add(nn.Linear(10, 20))
model:add(nn.Linear(20, 20))
model:add(nn.Linear(20, 30))
model:remove(2)
> model
nn.Sequential {
[input -> (1) -> (2) -> output]
(1): nn.Linear(10 -> 20)
(2): nn.Linear(20 -> 30)
}
insert(module, [index])
Inserts the given module at the given index. If index is not specified, the incremented length of the sequence is used and so this is equivalent to use add(module).
model = nn.Sequential()
model:add(nn.Linear(10, 20))
model:add(nn.Linear(20, 30))
model:insert(nn.Linear(20, 20), 2)
> model
nn.Sequential {
[input -> (1) -> (2) -> (3) -> output]
(1): nn.Linear(10 -> 20)
(2): nn.Linear(20 -> 20) -- The inserted layer
(3): nn.Linear(20 -> 30)
}
Parallel
module = Parallel(inputDimension,outputDimension)
Creates a container module that applies its ith child module to the ith slice of the input Tensor by using select
on dimension inputDimension. It concatenates the results of its contained modules together along dimension outputDimension.
Example:
mlp = nn.Parallel(2,1); -- Parallel container will associate a module to each slice of dimension 2
-- (column space), and concatenate the outputs over the 1st dimension.
mlp:add(nn.Linear(10,3)); -- Linear module (input 10, output 3), applied on 1st slice of dimension 2
mlp:add(nn.Linear(10,2)) -- Linear module (input 10, output 2), applied on 2nd slice of dimension 2
-- After going through the Linear module the outputs are
-- concatenated along the unique dimension, to form 1D Tensor
> mlp:forward(torch.randn(10,2)) -- of size 5.
-0.5300
-1.1015
0.7764
0.2819
-0.6026
[torch.Tensor of dimension 5]
A more complicated example:
mlp = nn.Sequential();
c = nn.Parallel(1,2) -- Parallel container will associate a module to each slice of dimension 1
-- (row space), and concatenate the outputs over the 2nd dimension.
for i=1,10 do -- Add 10 Linear+Reshape modules in parallel (input = 3, output = 2x1)
local t=nn.Sequential()
t:add(nn.Linear(3,2)) -- Linear module (input = 3, output = 2)
t:add(nn.Reshape(2,1)) -- Reshape 1D Tensor of size 2 to 2D Tensor of size 2x1
c:add(t)
end
mlp:add(c) -- Add the Parallel container in the Sequential container
pred = mlp:forward(torch.randn(10,3)) -- 2D Tensor of size 10x3 goes through the Sequential container
-- which contains a Parallel container of 10 Linear+Reshape.
-- Each Linear+Reshape module receives a slice of dimension 1
-- which corresponds to a 1D Tensor of size 3.
-- Eventually all the Linear+Reshape modules' outputs of size 2x1
-- are concatenated alond the 2nd dimension (column space)
-- to form pred, a 2D Tensor of size 2x10.
> pred
-0.7987 -0.4677 -0.1602 -0.8060 1.1337 -0.4781 0.1990 0.2665 -0.1364 0.8109
-0.2135 -0.3815 0.3964 -0.4078 0.0516 -0.5029 -0.9783 -0.5826 0.4474 0.6092
[torch.DoubleTensor of size 2x10]
for i = 1, 10000 do -- Train for a few iterations
x = torch.randn(10,3);
y = torch.ones(2,10);
pred = mlp:forward(x)
criterion = nn.MSECriterion()
local err = criterion:forward(pred,y)
local gradCriterion = criterion:backward(pred,y);
mlp:zeroGradParameters();
mlp:backward(x, gradCriterion);
mlp:updateParameters(0.01);
print(err)
end
Concat
module = nn.Concat(dim)
Concat concatenates the output of one layer of "parallel" modules along the
provided dimension dim: they take the same inputs, and their output is
concatenated.
mlp = nn.Concat(1);
mlp:add(nn.Linear(5,3))
mlp:add(nn.Linear(5,7))
> print(mlp:forward(torch.randn(5)))
0.7486
0.1349
0.7924
-0.0371
-0.4794
0.3044
-0.0835
-0.7928
0.7856
-0.1815
[torch.Tensor of dimension 10]
DepthConcat
module = nn.DepthConcat(dim)
DepthConcat concatenates the output of one layer of "parallel" modules along the
provided dimension dim: they take the same inputs, and their output is
concatenated. For dimensions other than dim having different sizes,
the smaller tensors are copied in the center of the output tensor,
effectively padding the borders with zeros.
The module is particularly useful for concatenating the output of Convolutions
along the depth dimension (i.e. nOutputFrame).
This is used to implement the DepthConcat layer
of the Going deeper with convolutions article.
The normal Concat Module can't be used since the spatial
dimensions (height and width) of the output Tensors requiring concatenation
may have different values. To deal with this, the output uses the largest
spatial dimensions and adds zero-padding around the smaller Tensors.
inputSize = 3
outputSize = 2
input = torch.randn(inputSize,7,7)
mlp=nn.DepthConcat(1);
mlp:add(nn.SpatialConvolutionMM(inputSize, outputSize, 1, 1))
mlp:add(nn.SpatialConvolutionMM(inputSize, outputSize, 3, 3))
mlp:add(nn.SpatialConvolutionMM(inputSize, outputSize, 4, 4))
> print(mlp:forward(input))
(1,.,.) =
-0.2874 0.6255 1.1122 0.4768 0.9863 -0.2201 -0.1516
0.2779 0.9295 1.1944 0.4457 1.1470 0.9693 0.1654
-0.5769 -0.4730 0.3283 0.6729 1.3574 -0.6610 0.0265
0.3767 1.0300 1.6927 0.4422 0.5837 1.5277 1.1686
0.8843 -0.7698 0.0539 -0.3547 0.6904 -0.6842 0.2653
0.4147 0.5062 0.6251 0.4374 0.3252 0.3478 0.0046
0.7845 -0.0902 0.3499 0.0342 1.0706 -0.0605 0.5525
(2,.,.) =
-0.7351 -0.9327 -0.3092 -1.3395 -0.4596 -0.6377 -0.5097
-0.2406 -0.2617 -0.3400 -0.4339 -0.3648 0.1539 -0.2961
-0.7124 -1.2228 -0.2632 0.1690 0.4836 -0.9469 -0.7003
-0.0221 0.1067 0.6975 -0.4221 -0.3121 0.4822 0.6617
0.2043 -0.9928 -0.9500 -1.6107 0.1409 -1.3548 -0.5212
-0.3086 -0.0298 -0.2031 0.1026 -0.5785 -0.3275 -0.1630
0.0596 -0.6097 0.1443 -0.8603 -0.2774 -0.4506 -0.5367
(3,.,.) =
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 -0.7326 0.3544 0.1821 0.4796 1.0164 0.0000
0.0000 -0.9195 -0.0567 -0.1947 0.0169 0.1924 0.0000
0.0000 0.2596 0.6766 0.0939 0.5677 0.6359 0.0000
0.0000 -0.2981 -1.2165 -0.0224 -1.1001 0.0008 0.0000
0.0000 -0.1911 0.2912 0.5092 0.2955 0.7171 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
(4,.,.) =
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 -0.8263 0.3646 0.6750 0.2062 0.2785 0.0000
0.0000 -0.7572 0.0432 -0.0821 0.4871 1.9506 0.0000
0.0000 -0.4609 0.4362 0.5091 0.8901 -0.6954 0.0000
0.0000 0.6049 -0.1501 -0.4602 -0.6514 0.5439 0.0000
0.0000 0.2570 0.4694 -0.1262 0.5602 0.0821 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
(5,.,.) =
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.3158 0.4389 -0.0485 -0.2179 0.0000 0.0000
0.0000 0.1966 0.6185 -0.9563 -0.3365 0.0000 0.0000
0.0000 -0.2892 -0.9266 -0.0172 -0.3122 0.0000 0.0000
0.0000 -0.6269 0.5349 -0.2520 -0.2187 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
(6,.,.) =
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 1.1148 0.2324 -0.1093 0.5024 0.0000 0.0000
0.0000 -0.2624 -0.5863 0.3444 0.3506 0.0000 0.0000
0.0000 0.1486 0.8413 0.6229 -0.0130 0.0000 0.0000
0.0000 0.8446 0.3801 -0.2611 0.8140 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
[torch.DoubleTensor of dimension 6x7x7]
Note how the last 2 of 6 filter maps have 1 column of zero-padding
on the left and top, as well as 2 on the right and bottom.
This is inevitable when the component
module output tensors non-dim sizes aren't all odd or even.
Such that in order to keep the mappings aligned, one need
only ensure that these be all odd (or even).
Decorator
dmodule = nn.Decorator(module)
This module is an abstract class used to decorate a module. This means
that method calls to dmodule will call the same method on the encapsulated
module, and return its results.
Bottle
module = nn.Bottle(module, [nInputDim], [nOutputDim])
Bottle allows varying dimensionality input to be forwarded through any module that accepts input of nInputDim dimensions, and generates output of nOutputDim dimensions.
Bottle can be used to forward a 4D input of varying sizes through a 2D module b x n. The module Bottle(module, 2) will accept input of shape p x q x r x n and outputs with the shape p x q x r x m. Internally Bottle will view the input of module as p*q*r x n, and view the output as p x q x r x m. The numbers p x q x r are inferred from the input and can change for every forward/backward pass.
input = torch.Tensor(4, 5, 3, 10)
mlp = nn.Bottle(nn.Linear(10, 2))
> print(input:size())
4
5
3
10
[torch.LongStorage of size 4]
> print(mlp:forward(input):size())
4
5
3
2
[torch.LongStorage of size 4]
Weight Normalization
module = nn.WeightNorm(module)
WeightNorm implements the reparametrization presented in Weight Normalization, which decouples the length of neural network weight vectors from their direction. The weight vector w is determined instead by parameters g and v such that w = g * v / ||v||, where ||v|| is the euclidean norm of vector v. This container can wrap nn layers with weights.
It accepts a parameter outputDim that represents the output dimension of the module weight it wraps, which defaults to 1. If the outputDim is not 1 the container will transpose the weight appropriately. If the module weight is not 2D, e.g. in the case of convolutional layers, the container will view the weight into an appropriate 2D shape based on the outputDim specified by the user.
An optimised version of nn.WeightNorm(nn.Linear(inputDimension, outputDimension)) is available as nn.LinearWeightNorm(inputDimension, outputDimension, [bias = true]). This layer occupies less memory and is faster through the use of fewer tensor copy operations, it also stores and updates a dirty flag to avoid unnecessary computation of the weight matrix.
DontCast
dmodule = nn.DontCast(module)
This module is a decorator. Use it to decorate a module that you don't
want to be cast when the type() method is called.
module = nn.DontCast(nn.Linear(3,4):float())
module:double()
th> print(module:forward(torch.FloatTensor{1,2,3}))
1.0927
-1.9380
-1.8158
-0.0805
[torch.FloatTensor of size 4]
NaN
dmodule = nn.NaN(module, [id])
The NaN module asserts that the output and gradInput of the decorated module do not contain NaNs.
This is useful for locating the source of those pesky NaN errors.
The id defaults to automatically incremented values of 1,2,3,....
For example :
linear = nn.Linear(3,4)
mlp = nn.Sequential()
mlp:add(nn.NaN(nn.Identity()))
mlp:add(nn.NaN(linear))
mlp:add(nn.NaN(nn.Linear(4,2)))
print(mlp)
As you can see the NaN layers are have unique ids :
nn.Sequential {
[input -> (1) -> (2) -> (3) -> output]
(1): nn.NaN(1) @ nn.Identity
(2): nn.NaN(2) @ nn.Linear(3 -> 4)
(3): nn.NaN(3) @ nn.Linear(4 -> 2)
}
And if we fill the bias of the linear module with NaNs and call forward:
nan = math.log(math.log(0)) -- this is a nan value
linear.bias:fill(nan)
mlp:forward(torch.randn(2,3))
We get a nice error message:
/usr/local/share/lua/5.1/nn/NaN.lua:39: NaN found in parameters of module :
nn.NaN(2) @ nn.Linear(3 -> 4)
For a quick one-liner to catch NaNs anywhere inside a model (for example, a nn.Sequential or any other nn.Container), we can use this with the nn.Module.replace function:
model:replace(function(module) return nn.NaN(module) end)
Profile
dmodule = nn.Profile(module, [print_interval, [name] ])
The Profile module times each forward and backward pass of the decorated module. It prints this information after print_interval passes, which is 100 by default. For timing multiple modules, the name argument allows this information to be printed accompanied by a name, which by default is the type of the decorated module.
This is useful for profiling new modules you develop, and tracking down bottlenecks in the speed of a network.
The timer and print statement can add a small amount of overhead to the overall speed.
As an example:
mlp = nn.Sequential()
mlp:add(nn.Identity())
mlp:add(nn.Linear(1000,1000))
mlp:add(nn.Tanh())
mlp:replace(function(module) return nn.Profile(module, 1000) end)
inp = torch.randn(1000)
gradOutput = torch.randn(1000)
for i=1,1000 do
mlp:forward(inp)
mlp:backward(inp, gradOutput)
end
results in the following profile information:
nn.Identity took 0.026 seconds for 1000 forward passes
nn.Linear took 0.119 seconds for 1000 forward passes
nn.Tanh took 0.061 seconds for 1000 forward passes
nn.Tanh took 0.032 seconds for 1000 backward passes
nn.Linear took 0.161 seconds for 1000 backward passes
nn.Identity took 0.026 seconds for 1000 backward passes
It's good practice to profile modules after a single forwards and backwards pass, since the initial pass often has to allocate memory. Thus, in the example above, you would run another 1000 forwards and backwards passes to time the modules in their normal mode of operation:
for i=1,1000 do
mlp:forward(inp)
mlp:backward(inp, gradOutput)
end
Table Containers
While the above containers are used for manipulating input Tensors, table containers are used for manipulating tables : * ConcatTable * ParallelTable
These, along with all other modules for manipulating tables can be found here.