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# Transfer Function Layers # Transfer functions are normally used to introduce a non-linearity after a parameterized layer like [Linear](simple.md#nn.Linear) and [SpatialConvolution](convolution.md#nn.SpatialConvolution). Non-linearities allows for dividing the problem space into more complex regions than what a simple logistic regressor would permit. ## HardTanh ##

Applies the HardTanh function element-wise to the input Tensor, thus outputting a Tensor of the same dimension.

HardTanh is defined as:

  • f(x) = 1, if x > 1,
  • f(x) = -1, if x < -1,
  • f(x) = x, otherwise.
ii=torch.linspace(-2,2)
m=nn.HardTanh()
oo=m:forward(ii)
go=torch.ones(100)
gi=m:backward(ii,go)
gnuplot.plot({'f(x)',ii,oo,'+-'},{'df/dx',ii,gi,'+-'})
gnuplot.grid(true)

 ## HardShrink ##

module = nn.HardShrink(lambda)

Applies the hard shrinkage function element-wise to the input Tensor. The output is the same size as the input.

HardShrinkage operator is defined as:

  • f(x) = x, if x > lambda
  • f(x) = -x, if x < -lambda
  • f(x) = 0, otherwise
ii=torch.linspace(-2,2)
m=nn.HardShrink(0.85)
oo=m:forward(ii)
go=torch.ones(100)
gi=m:backward(ii,go)
gnuplot.plot({'f(x)',ii,oo,'+-'},{'df/dx',ii,gi,'+-'})
gnuplot.grid(true)

## SoftShrink ##

module = nn.SoftShrink(lambda)

Applies the hard shrinkage function element-wise to the input Tensor. The output is the same size as the input.

HardShrinkage operator is defined as:

  • f(x) = x-lambda, if x > lambda
  • f(x) = -x+lambda, if x < -lambda
  • f(x) = 0, otherwise
ii=torch.linspace(-2,2)
m=nn.SoftShrink(0.85)
oo=m:forward(ii)
go=torch.ones(100)
gi=m:backward(ii,go)
gnuplot.plot({'f(x)',ii,oo,'+-'},{'df/dx',ii,gi,'+-'})
gnuplot.grid(true)

## SoftMax ##

Applies the Softmax function to an n-dimensional input Tensor, rescaling them so that the elements of the n-dimensional output Tensor lie in the range (0,1) and sum to 1.

Softmax is defined as f_i(x) = exp(x_i-shift) / sum_j exp(x_j-shift), where shift = max_i x_i.

ii=torch.exp(torch.abs(torch.randn(10)))
m=nn.SoftMax()
oo=m:forward(ii)
gnuplot.plot({'Input',ii,'+-'},{'Output',oo,'+-'})
gnuplot.grid(true)

Note that this module doesn't work directly with ClassNLLCriterion, which expects the nn.Log to be computed between the SoftMax and itself. Use LogSoftMax instead (it's faster).

## SoftMin ##

Applies the Softmin function to an n-dimensional input Tensor, rescaling them so that the elements of the n-dimensional output Tensor lie in the range (0,1) and sum to 1.

Softmin is defined as f_i(x) = exp(-x_i-shift) / sum_j exp(-x_j-shift), where shift = max_i x_i.

ii=torch.exp(torch.abs(torch.randn(10)))
m=nn.SoftMin()
oo=m:forward(ii)
gnuplot.plot({'Input',ii,'+-'},{'Output',oo,'+-'})
gnuplot.grid(true)

 ### SoftPlus ###

Applies the SoftPlus function to an n-dimensioanl input Tensor. Can be used to constrain the output of a machine to always be positive.

SoftPlus is defined as f_i(x) = 1/beta * log(1 + exp(beta * x_i)).

ii=torch.randn(10)
m=nn.SoftPlus()
oo=m:forward(ii)
go=torch.ones(10)
gi=m:backward(ii,go)
gnuplot.plot({'Input',ii,'+-'},{'Output',oo,'+-'},{'gradInput',gi,'+-'})
gnuplot.grid(true)

 ## SoftSign ##

Applies the SoftSign function to an n-dimensioanl input Tensor.

SoftSign is defined as f_i(x) = x_i / (1+|x_i|)

ii=torch.linspace(-5,5)
m=nn.SoftSign()
oo=m:forward(ii)
go=torch.ones(100)
gi=m:backward(ii,go)
gnuplot.plot({'f(x)',ii,oo,'+-'},{'df/dx',ii,gi,'+-'})
gnuplot.grid(true)

 ## LogSigmoid ##

Applies the LogSigmoid function to an n-dimensional input Tensor.

LogSigmoid is defined as f_i(x) = log(1/(1+ exp(-x_i))).

ii=torch.randn(10)
m=nn.LogSigmoid()
oo=m:forward(ii)
go=torch.ones(10)
gi=m:backward(ii,go)
gnuplot.plot({'Input',ii,'+-'},{'Output',oo,'+-'},{'gradInput',gi,'+-'})
gnuplot.grid(true)

 ## LogSoftMax ##

Applies the LogSoftmax function to an n-dimensional input Tensor.

LogSoftmax is defined as f_i(x) = log(1/a exp(x_i)), where a = sum_j exp(x_j).

ii=torch.randn(10)
m=nn.LogSoftMax()
oo=m:forward(ii)
go=torch.ones(10)
gi=m:backward(ii,go)
gnuplot.plot({'Input',ii,'+-'},{'Output',oo,'+-'},{'gradInput',gi,'+-'})
gnuplot.grid(true)

 ## Sigmoid ##

Applies the Sigmoid function element-wise to the input Tensor, thus outputting a Tensor of the same dimension.

Sigmoid is defined as f(x) = 1/(1+exp(-x)).

ii=torch.linspace(-5,5)
m=nn.Sigmoid()
oo=m:forward(ii)
go=torch.ones(100)
gi=m:backward(ii,go)
gnuplot.plot({'f(x)',ii,oo,'+-'},{'df/dx',ii,gi,'+-'})
gnuplot.grid(true)

 ## Tanh ##

Applies the Tanh function element-wise to the input Tensor, thus outputting a Tensor of the same dimension.

ii=torch.linspace(-3,3)
m=nn.Tanh()
oo=m:forward(ii)
go=torch.ones(100)
gi=m:backward(ii,go)
gnuplot.plot({'f(x)',ii,oo,'+-'},{'df/dx',ii,gi,'+-'})
gnuplot.grid(true)

 ## ReLU ##

Applies the rectified linear unit (ReLU) function element-wise to the input Tensor, thus outputting a Tensor of the same dimension.

Can optionally do it's operation in-place without using extra state memory:

m=nn.ReLU(true) -- true = in-place, false = keeping separate state.
ii=torch.linspace(-3,3)
m=nn.ReLU()
oo=m:forward(ii)
go=torch.ones(100)
gi=m:backward(ii,go)
gnuplot.plot({'f(x)',ii,oo,'+-'},{'df/dx',ii,gi,'+-'})
gnuplot.grid(true)

 ## PReLU ##

Applies parametric ReLU, which parameter varies the slope of the negative part:

max(0,y_i) + a_i * min(0,y_i)

When called without a number on input as nn.PReLU() uses shared version, meaning has only one parameter. Otherwise if called nn.PReLU(nOutputPlane) has nOutputPlane parameters, one for each input map. The output dimension is always equal to input dimension. Note that weight decay should not be used on it. For reference see http://arxiv.org/abs/1502.01852

## AddConstant ##

Adds a (non-learnable) scalar constant. This module is sometimes useful for debuggging purposes: f(x) = x + k, where k is a scalar.

Can optionally do it's operation in-place without using extra state memory:

m=nn.AddConstant(k,true) -- true = in-place, false = keeping separate state.

In-place mode restores the original input value after the backward pass, allowing it's use after other in-place modules, like MulConstant.

## MulConstant ##

Multiplies input tensor by a (non-learnable) scalar constant. This module is sometimes useful for debuggging purposes: f(x) = k * x, where k is a scalar.

Can optionally do it's operation in-place without using extra state memory:

m=nn.MulConstant(k,true) -- true = in-place, false = keeping separate state.

In-place mode restores the original input value after the backward pass, allowing it's use after other in-place modules, like AddConstant.