Table Layers

This set of modules allows the manipulation of tables through the layers of a neural network. This allows one to build very rich architectures:

table Container Modules encapsulate sub-Modules:
- ConcatTable: applies each member module to the same input Tensor and outputs a table;
- ParallelTable: applies the i-th member module to the i-th input and outputs a table;
- MapTable: applies a single module to every input and outputs a table;
Table Conversion Modules convert between tables and Tensors or tables:
- SplitTable: splits a Tensor into a table of Tensors;
- JoinTable: joins a table of Tensors into a Tensor;
- MixtureTable: mixture of experts weighted by a gater;
- SelectTable: select one element from a table;
- NarrowTable: select a slice of elements from a table;
- FlattenTable: flattens a nested table hierarchy;
- ZipTable : zip a table of tables into a table of tables;
- ZipTableOneToMany : zip a table to a single tensor;
Pair Modules compute a measure like distance or similarity from a pair (table) of input Tensors:
- PairwiseDistance: outputs the p-norm. distance between inputs;
- DotProduct: outputs the dot product (similarity) between inputs;
- CosineDistance: outputs the cosine distance between inputs;
CMath Modules perform element-wise operations on a table of Tensors:
- CAddTable: addition of input Tensors;
- CSubTable: substraction of input Tensors;
- CMulTable: multiplication of input Tensors;
- CDivTable: division of input Tensors;
- CMaxTable: max of input Tensors;
- CMinTable: min of input Tensors;
- CAddTensorTable: adds a tensor to a table of tensors of the same size;
Table of Criteria:
- CriterionTable: wraps a Criterion so that it can accept a table of inputs.

table-based modules work by supporting forward() and backward() methods that can accept tables as inputs. It turns out that the usual Sequential module can do this, so all that is needed is other child modules that take advantage of such tables.

mlp = nn.Sequential()
t = {x, y, z}
pred = mlp:forward(t)
pred = mlp:forward{x, y, z}      -- This is equivalent to the line before

ConcatTable

module = nn.ConcatTable()

ConcatTable is a container module that applies each member module to the same input Tensor or table.

                  +-----------+
             +----> {member1, |
+-------+    |    |           |
| input +----+---->  member2, |
+-------+    |    |           |
   or        +---->  member3} |
 {input}          +-----------+

Example 1

mlp = nn.ConcatTable()
mlp:add(nn.Linear(5, 2))
mlp:add(nn.Linear(5, 3))

pred = mlp:forward(torch.randn(5))
for i, k in ipairs(pred) do print(i, k) end

which gives the output:

1
-0.4073
 0.0110
[torch.Tensor of dimension 2]

2
 0.0027
-0.0598
-0.1189
[torch.Tensor of dimension 3]

Example 2

mlp = nn.ConcatTable()
mlp:add(nn.Identity())
mlp:add(nn.Identity())

pred = mlp:forward{torch.randn(2), {torch.randn(3)}}
print(pred)

which gives the output (using th):

{
  1 :
    {
      1 : DoubleTensor - size: 2
      2 :
        {
          1 : DoubleTensor - size: 3
        }
    }
  2 :
    {
      1 : DoubleTensor - size: 2
      2 :
        {
          1 : DoubleTensor - size: 3
        }
    }
}

ParallelTable

module = nn.ParallelTable()

ParallelTable is a container module that, in its forward() method, applies the i-th member module to the i-th input, and outputs a table of the set of outputs.

+----------+         +-----------+
| {input1, +---------> {member1, |
|          |         |           |
|  input2, +--------->  member2, |
|          |         |           |
|  input3} +--------->  member3} |
+----------+         +-----------+

Example

mlp = nn.ParallelTable()
mlp:add(nn.Linear(10, 2))
mlp:add(nn.Linear(5, 3))

x = torch.randn(10)
y = torch.rand(5)

pred = mlp:forward{x, y}
for i, k in pairs(pred) do print(i, k) end

which gives the output:

1
 0.0331
 0.7003
[torch.Tensor of dimension 2]

2
 0.0677
-0.1657
-0.7383
[torch.Tensor of dimension 3]

MapTable

module = nn.MapTable(m, share)

MapTable is a container for a single module which will be applied to all input elements. The member module is cloned as necessary to process all input elements. Call resize(n) to set the number of clones manually or call clearState() to discard all clones.

Optionally, the module can be initialized with the contained module and a boolean share. It indicates whether parameters are shared across all clones or not. By default it is set to true. The shared parameters are weight, bias, gradWeight and gradBias.

+----------+         +-----------+
| {input1, +---------> {member,  |
|          |         |           |
|  input2, +--------->  clone,   |
|          |         |           |
|  input3} +--------->  clone}   |
+----------+         +-----------+

Example

map = nn.MapTable()
map:add(nn.Linear(10, 3))

x1 = torch.rand(10)
x2 = torch.rand(10)
y = map:forward{x1, x2}

for i, k in pairs(y) do print(i, k) end

which gives the output:

1
 0.0345
 0.8695
 0.6502
[torch.DoubleTensor of size 3]

2
 0.0269
 0.4953
 0.2691
[torch.DoubleTensor of size 3]

SplitTable

module = SplitTable(dimension, nInputDims)

Creates a module that takes a Tensor as input and outputs several tables, splitting the Tensor along the specified dimension. In the diagram below, dimension is equal to 1.

    +----------+         +-----------+
    | input[1] +---------> {member1, |
  +----------+-+         |           |
  | input[2] +----------->  member2, |
+----------+-+           |           |
| input[3] +------------->  member3} |
+----------+             +-----------+

The optional parameter nInputDims allows to specify the number of dimensions that this module will receive. This makes it possible to forward both minibatch and non-minibatch Tensors through the same module.

Example 1

mlp = nn.SplitTable(2)
x = torch.randn(4, 3)
pred = mlp:forward(x)
for i, k in ipairs(pred) do print(i, k) end

gives the output:

1
 1.3885
 1.3295
 0.4281
-1.0171
[torch.Tensor of dimension 4]

2
-1.1565
-0.8556
-1.0717
-0.8316
[torch.Tensor of dimension 4]

3
-1.3678
-0.1709
-0.0191
-2.5871
[torch.Tensor of dimension 4]

Example 2

mlp = nn.SplitTable(1)
pred = mlp:forward(torch.randn(4, 3))
for i, k in ipairs(pred) do print(i, k) end

gives the output:

1
 1.6114
 0.9038
 0.8419
[torch.Tensor of dimension 3]

2
 2.4742
 0.2208
 1.6043
[torch.Tensor of dimension 3]

3
 1.3415
 0.2984
 0.2260
[torch.Tensor of dimension 3]

4
 2.0889
 1.2309
 0.0983
[torch.Tensor of dimension 3]

Example 3

mlp = nn.SplitTable(1, 2)
pred = mlp:forward(torch.randn(2, 4, 3))
for i, k in ipairs(pred) do print(i, k) end
pred = mlp:forward(torch.randn(4, 3))
for i, k in ipairs(pred) do print(i, k) end

gives the output:

1
-1.3533  0.7448 -0.8818
-0.4521 -1.2463  0.0316
[torch.DoubleTensor of dimension 2x3]

2
 0.1130 -1.3904  1.4620
 0.6722  2.0910 -0.2466
[torch.DoubleTensor of dimension 2x3]

3
 0.4672 -1.2738  1.1559
 0.4664  0.0768  0.6243
[torch.DoubleTensor of dimension 2x3]

4
 0.4194  1.2991  0.2241
 2.9786 -0.6715  0.0393
[torch.DoubleTensor of dimension 2x3]


1
-1.8932
 0.0516
-0.6316
[torch.DoubleTensor of dimension 3]

2
-0.3397
-1.8881
-0.0977
[torch.DoubleTensor of dimension 3]

3
 0.0135
 1.2089
 0.5785
[torch.DoubleTensor of dimension 3]

4
-0.1758
-0.0776
-1.1013
[torch.DoubleTensor of dimension 3]

The module also supports indexing from the end using negative dimensions. This allows to use this module when the number of dimensions of the input is unknown.

Example

m = nn.SplitTable(-2)
out = m:forward(torch.randn(3, 2))
for i, k in ipairs(out) do print(i, k) end
out = m:forward(torch.randn(1, 3, 2))
for i, k in ipairs(out) do print(i, k) end

gives the output:

1
 0.1420
-0.5698
[torch.DoubleTensor of size 2]

2
 0.1663
 0.1197
[torch.DoubleTensor of size 2]

3
 0.4198
-1.1394
[torch.DoubleTensor of size 2]


1
-2.4941
-1.4541
[torch.DoubleTensor of size 1x2]

2
 0.4594
 1.1946
[torch.DoubleTensor of size 1x2]

3
-2.3322
-0.7383
[torch.DoubleTensor of size 1x2]

A more complicated example

mlp = nn.Sequential()       -- Create a network that takes a Tensor as input
mlp:add(nn.SplitTable(2))
c = nn.ParallelTable()      -- The two Tensor slices go through two different Linear
c:add(nn.Linear(10, 3))     -- Layers in Parallel
c:add(nn.Linear(10, 7))
mlp:add(c)                  -- Outputing a table with 2 elements
p = nn.ParallelTable()      -- These tables go through two more linear layers separately
p:add(nn.Linear(3, 2))
p:add(nn.Linear(7, 1))
mlp:add(p)
mlp:add(nn.JoinTable(1))    -- Finally, the tables are joined together and output.

pred = mlp:forward(torch.randn(10, 2))
print(pred)

for i = 1, 100 do           -- A few steps of training such a network..
   x = torch.ones(10, 2)
   y = torch.Tensor(3)
   y:copy(x:select(2, 1):narrow(1, 1, 3))
   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(0.05)

   print(err)
end

JoinTable

module = JoinTable(dimension, nInputDims)

Creates a module that takes a table of Tensors as input and outputs a Tensor by joining them together along dimension dimension. In the diagram below dimension is set to 1.

+----------+             +-----------+
| {input1, +-------------> output[1] |
|          |           +-----------+-+
|  input2, +-----------> output[2] |
|          |         +-----------+-+
|  input3} +---------> output[3] |
+----------+         +-----------+

The optional parameter nInputDims allows to specify the number of dimensions that this module will receive. This makes it possible to forward both minibatch and non-minibatch Tensors through the same module.

Example 1

x = torch.randn(5, 1)
y = torch.randn(5, 1)
z = torch.randn(2, 1)

print(nn.JoinTable(1):forward{x, y})
print(nn.JoinTable(2):forward{x, y})
print(nn.JoinTable(1):forward{x, z})

gives the output:

 1.3965
 0.5146
-1.5244
-0.9540
 0.4256
 0.1575
 0.4491
 0.6580
 0.1784
-1.7362
[torch.DoubleTensor of dimension 10x1]

 1.3965  0.1575
 0.5146  0.4491
-1.5244  0.6580
-0.9540  0.1784
 0.4256 -1.7362
[torch.DoubleTensor of dimension 5x2]

 1.3965
 0.5146
-1.5244
-0.9540
 0.4256
-1.2660
 1.0869
[torch.Tensor of dimension 7x1]

Example 2

module = nn.JoinTable(2, 2)

x = torch.randn(3, 1)
y = torch.randn(3, 1)

mx = torch.randn(2, 3, 1)
my = torch.randn(2, 3, 1)

print(module:forward{x, y})
print(module:forward{mx, my})

gives the output:

 0.4288  1.2002
-1.4084 -0.7960
-0.2091  0.1852
[torch.DoubleTensor of dimension 3x2]

(1,.,.) =
  0.5561  0.1228
 -0.6792  0.1153
  0.0687  0.2955

(2,.,.) =
  2.5787  1.8185
 -0.9860  0.6756
  0.1989 -0.4327
[torch.DoubleTensor of dimension 2x3x2]

A more complicated example

mlp = nn.Sequential()         -- Create a network that takes a Tensor as input
c = nn.ConcatTable()          -- The same Tensor goes through two different Linear
c:add(nn.Linear(10, 3))       -- Layers in Parallel
c:add(nn.Linear(10, 7))
mlp:add(c)                    -- Outputing a table with 2 elements
p = nn.ParallelTable()        -- These tables go through two more linear layers
p:add(nn.Linear(3, 2))        -- separately.
p:add(nn.Linear(7, 1))
mlp:add(p)
mlp:add(nn.JoinTable(1))      -- Finally, the tables are joined together and output.

pred = mlp:forward(torch.randn(10))
print(pred)

for i = 1, 100 do             -- A few steps of training such a network..
   x = torch.ones(10)
   y = torch.Tensor(3); y:copy(x:narrow(1, 1, 3))
   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(0.05)

   print(err)
end

MixtureTable

module = MixtureTable([dim])

Creates a module that takes a table {gater, experts} as input and outputs the mixture of experts (a Tensor or table of Tensors) using a gater Tensor. When dim is provided, it specifies the dimension of the experts Tensor that will be interpolated (or mixed). Otherwise, the experts should take the form of a table of Tensors. This Module works for experts of dimension 1D or more, and for a 1D or 2D gater, i.e. for single examples or mini-batches.

Considering an input = {G, E} with a single example, then the mixture of experts Tensor E with gater Tensor G has the following form:

output = G[1]*E[1] + G[2]*E[2] + ... + G[n]*E[n]

where dim = 1, n = E:size(dim) = G:size(dim) and G:dim() == 1. Note that E:dim() >= 2, such that output:dim() = E:dim() - 1.

Example 1: Using this Module, an arbitrary mixture of n 2-layer experts by a 2-layer gater could be constructed as follows:

experts = nn.ConcatTable()
for i = 1, n do
   local expert = nn.Sequential()
   expert:add(nn.Linear(3, 4))
   expert:add(nn.Tanh())
   expert:add(nn.Linear(4, 5))
   expert:add(nn.Tanh())
   experts:add(expert)
end

gater = nn.Sequential()
gater:add(nn.Linear(3, 7))
gater:add(nn.Tanh())
gater:add(nn.Linear(7, n))
gater:add(nn.SoftMax())

trunk = nn.ConcatTable()
trunk:add(gater)
trunk:add(experts)

moe = nn.Sequential()
moe:add(trunk)
moe:add(nn.MixtureTable())

Forwarding a batch of 2 examples gives us something like this:

> =moe:forward(torch.randn(2, 3))
-0.2152  0.3141  0.3280 -0.3772  0.2284
 0.2568  0.3511  0.0973 -0.0912 -0.0599
[torch.DoubleTensor of dimension 2x5]

Example 2: In the following, the MixtureTable expects experts to be a Tensor of size = {1, 4, 2, 5, n}:

experts = nn.Concat(5)
for i = 1, n do
   local expert = nn.Sequential()
   expert:add(nn.Linear(3, 4))
   expert:add(nn.Tanh())
   expert:add(nn.Linear(4, 4*2*5))
   expert:add(nn.Tanh())
   expert:add(nn.Reshape(4, 2, 5, 1))
   experts:add(expert)
end

gater = nn.Sequential()
gater:add(nn.Linear(3, 7))
gater:add(nn.Tanh())
gater:add(nn.Linear(7, n))
gater:add(nn.SoftMax())

trunk = nn.ConcatTable()
trunk:add(gater)
trunk:add(experts)

moe = nn.Sequential()
moe:add(trunk)
moe:add(nn.MixtureTable(5))

Forwarding a batch of 2 examples gives us something like this:

> =moe:forward(torch.randn(2, 3)):size()
 2
 4
 2
 5
[torch.LongStorage of size 4]

SelectTable

module = SelectTable(index)

Creates a module that takes a (nested) table as input and outputs the element at index index. index can be strings or integers (positive or negative). This can be either a table or a Tensor.

The gradients of the non-index elements are zeroed Tensors of the same size. This is true regardless of the depth of the encapsulated Tensor as the function used internally to do so is recursive.

Example 1:

> input = {torch.randn(2, 3), torch.randn(2, 1)}
> =nn.SelectTable(1):forward(input)
-0.3060  0.1398  0.2707
 0.0576  1.5455  0.0610
[torch.DoubleTensor of dimension 2x3]

> =nn.SelectTable(-1):forward(input)
 2.3080
-0.2955
[torch.DoubleTensor of dimension 2x1]

> =table.unpack(nn.SelectTable(1):backward(input, torch.randn(2, 3)))
-0.4891 -0.3495 -0.3182
-2.0999  0.7381 -0.5312
[torch.DoubleTensor of dimension 2x3]

0
0
[torch.DoubleTensor of dimension 2x1]

Exmaple 2:

> input = { A=torch.randn(2, 3), B=torch.randn(2, 1) }
> =nn.SelectTable("A"):forward(input)
-0.3060  0.1398  0.2707
 0.0576  1.5455  0.0610
[torch.DoubleTensor of dimension 2x3]

> gradInput = nn.SelectTable("A"):backward(input, torch.randn(2, 3))

> gradInput
{
  A : DoubleTensor - size: 2x3
  B : DoubleTensor - size: 2x1
}

> gradInput["A"]
-0.4891 -0.3495 -0.3182
-2.0999  0.7381 -0.5312
[torch.DoubleTensor of dimension 2x3]

> gradInput["B"]
0
0
[torch.DoubleTensor of dimension 2x1]

Example 3:

> input = {torch.randn(2, 3), {torch.randn(2, 1), {torch.randn(2, 2)}}}

> =nn.SelectTable(2):forward(input)
{
  1 : DoubleTensor - size: 2x1
  2 :
    {
      1 : DoubleTensor - size: 2x2
    }
}

> =table.unpack(nn.SelectTable(2):backward(input, {torch.randn(2, 1), {torch.randn(2, 2)}}))
0 0 0
0 0 0
[torch.DoubleTensor of dimension 2x3]

{
  1 : DoubleTensor - size: 2x1
  2 :
    {
      1 : DoubleTensor - size: 2x2
    }
}

> gradInput = nn.SelectTable(1):backward(input, torch.randn(2, 3))

> =gradInput
{
  1 : DoubleTensor - size: 2x3
  2 :
    {
      1 : DoubleTensor - size: 2x1
      2 :
        {
          1 : DoubleTensor - size: 2x2
        }
    }
}

> =gradInput[1]
-0.3400 -0.0404  1.1885
 1.2865  0.4107  0.6506
[torch.DoubleTensor of dimension 2x3]

> gradInput[2][1]
0
0
[torch.DoubleTensor of dimension 2x1]

> gradInput[2][2][1]
0 0
0 0
[torch.DoubleTensor of dimension 2x2]

NarrowTable

module = NarrowTable(offset [, length])

Creates a module that takes a table as input and outputs the subtable starting at index offset having length elements (defaults to 1 element). The elements can be either a table or a Tensor.

The gradients of the elements not included in the subtable are zeroed Tensors of the same size. This is true regardless of the depth of the encapsulated Tensor as the function used internally to do so is recursive.

Example:

> input = {torch.randn(2, 3), torch.randn(2, 1), torch.randn(1, 2)}
> =nn.NarrowTable(2,2):forward(input)
{
  1 : DoubleTensor - size: 2x1
  2 : DoubleTensor - size: 1x2
}

> =nn.NarrowTable(1):forward(input)
{
  1 : DoubleTensor - size: 2x3
}

> =table.unpack(nn.NarrowTable(1,2):backward(input, {torch.randn(2, 3), torch.randn(2, 1)}))
 1.9528 -0.1381  0.2023
 0.2297 -1.5169 -1.1871
[torch.DoubleTensor of size 2x3]

-1.2023
-0.4165
[torch.DoubleTensor of size 2x1]

 0  0
[torch.DoubleTensor of size 1x2]

FlattenTable

module = FlattenTable()

Creates a module that takes an arbitrarily deep table of Tensors (potentially nested) as input and outputs a table of Tensors, where the output Tensor in index i is the Tensor with post-order DFS index i in the input table.

This module is particularly useful in combination with nn.Identity() to create networks that can append to their input table.

Example:

x = {torch.rand(1), {torch.rand(2), {torch.rand(3)}}, torch.rand(4)}
print(x)
print(nn.FlattenTable():forward(x))

gives the output:

{
  1 : DoubleTensor - size: 1
  2 :
    {
      1 : DoubleTensor - size: 2
      2 :
        {
          1 : DoubleTensor - size: 3
        }
    }
  3 : DoubleTensor - size: 4
}
{
  1 : DoubleTensor - size: 1
  2 : DoubleTensor - size: 2
  3 : DoubleTensor - size: 3
  4 : DoubleTensor - size: 4
}

ZipTable

module = nn.ZipTable()

Zips a table of tables into a table of tables.

Example:

print(module:forward{ {'a1','a2'}, {'b1','b2'}, {'c1','c2'} })
{ {'a1','b1','c1'}, {'a2','b2','c2'} }

ZipTableOneToMany

module = nn.ZipTableOneToMany()

Zips a table of element el and table of elements tab into a table of tables, where the i-th table contains the element el and the i-th element in table tab

Example:

print(module:forward{ 'el', {'a','b','c'} })
{ {'el','a'}, {'el','b'}, {'el','c'} }

PairwiseDistance

module = PairwiseDistance(p) creates a module that takes a table of two vectors as input and outputs the distance between them using the p-norm.

Example:

mlp_l1 = nn.PairwiseDistance(1)
mlp_l2 = nn.PairwiseDistance(2)
x = torch.Tensor({1, 2, 3})
y = torch.Tensor({4, 5, 6})
print(mlp_l1:forward({x, y}))
print(mlp_l2:forward({x, y}))

gives the output:

 9
[torch.Tensor of dimension 1]

 5.1962
[torch.Tensor of dimension 1]

A more complicated example:

-- imagine we have one network we are interested in, it is called "p1_mlp"
p1_mlp= nn.Sequential(); p1_mlp:add(nn.Linear(5, 2))

-- But we want to push examples towards or away from each other
-- so we make another copy of it called p2_mlp
-- this *shares* the same weights via the set command, but has its own set of temporary gradient storage
-- that's why we create it again (so that the gradients of the pair don't wipe each other)
p2_mlp= nn.Sequential(); p2_mlp:add(nn.Linear(5, 2))
p2_mlp:get(1).weight:set(p1_mlp:get(1).weight)
p2_mlp:get(1).bias:set(p1_mlp:get(1).bias)

-- we make a parallel table that takes a pair of examples as input. they both go through the same (cloned) mlp
prl = nn.ParallelTable()
prl:add(p1_mlp)
prl:add(p2_mlp)

-- now we define our top level network that takes this parallel table and computes the pairwise distance between
-- the pair of outputs
mlp= nn.Sequential()
mlp:add(prl)
mlp:add(nn.PairwiseDistance(1))

-- and a criterion for pushing together or pulling apart pairs
crit = nn.HingeEmbeddingCriterion(1)

-- lets make two example vectors
x = torch.rand(5)
y = torch.rand(5)


-- Use a typical generic gradient update function
function gradUpdate(mlp, x, y, criterion, learningRate)
local pred = mlp:forward(x)
local err = criterion:forward(pred, y)
local gradCriterion = criterion:backward(pred, y)
mlp:zeroGradParameters()
mlp:backward(x, gradCriterion)
mlp:updateParameters(learningRate)
end

-- push the pair x and y together, notice how then the distance between them given
-- by  print(mlp:forward({x, y})[1]) gets smaller
for i = 1, 10 do
gradUpdate(mlp, {x, y}, 1, crit, 0.01)
print(mlp:forward({x, y})[1])
end


-- pull apart the pair x and y, notice how then the distance between them given
-- by  print(mlp:forward({x, y})[1]) gets larger

for i = 1, 10 do
gradUpdate(mlp, {x, y}, -1, crit, 0.01)
print(mlp:forward({x, y})[1])
end

DotProduct

module = DotProduct() creates a module that takes a table of two vectors (or matrices if in batch mode) as input and outputs the dot product between them.

Example:

mlp = nn.DotProduct()
x = torch.Tensor({1, 2, 3})
y = torch.Tensor({4, 5, 6})
print(mlp:forward({x, y}))

gives the output:

 32
[torch.Tensor of dimension 1]

A more complicated example:

-- Train a ranking function so that mlp:forward({x, y}, {x, z}) returns a number
-- which indicates whether x is better matched with y or z (larger score = better match), or vice versa.

mlp1 = nn.Linear(5, 10)
mlp2 = mlp1:clone('weight', 'bias')

prl = nn.ParallelTable();
prl:add(mlp1); prl:add(mlp2)

mlp1 = nn.Sequential()
mlp1:add(prl)
mlp1:add(nn.DotProduct())

mlp2 = mlp1:clone('weight', 'bias')

mlp = nn.Sequential()
prla = nn.ParallelTable()
prla:add(mlp1)
prla:add(mlp2)
mlp:add(prla)

x = torch.rand(5);
y = torch.rand(5)
z = torch.rand(5)


print(mlp1:forward{x, x})
print(mlp1:forward{x, y})
print(mlp1:forward{y, y})


crit = nn.MarginRankingCriterion(1);

-- Use a typical generic gradient update function
function gradUpdate(mlp, x, y, criterion, learningRate)
   local pred = mlp:forward(x)
   local err = criterion:forward(pred, y)
   local gradCriterion = criterion:backward(pred, y)
   mlp:zeroGradParameters()
   mlp:backward(x, gradCriterion)
   mlp:updateParameters(learningRate)
end

inp = {{x, y}, {x, z}}

math.randomseed(1)

-- make the pair x and y have a larger dot product than x and z

for i = 1, 100 do
   gradUpdate(mlp, inp, 1, crit, 0.05)
   o1 = mlp1:forward{x, y}[1];
   o2 = mlp2:forward{x, z}[1];
   o = crit:forward(mlp:forward{{x, y}, {x, z}}, 1)
   print(o1, o2, o)
end

print "________________**"

-- make the pair x and z have a larger dot product than x and y

for i = 1, 100 do
   gradUpdate(mlp, inp, -1, crit, 0.05)
   o1 = mlp1:forward{x, y}[1];
   o2 = mlp2:forward{x, z}[1];
   o = crit:forward(mlp:forward{{x, y}, {x, z}}, -1)
   print(o1, o2, o)
end

CosineDistance

module = CosineDistance() creates a module that takes a table of two vectors (or matrices if in batch mode) as input and outputs the cosine distance between them.

Examples:

mlp = nn.CosineDistance()
x = torch.Tensor({1, 2, 3})
y = torch.Tensor({4, 5, 6})
print(mlp:forward({x, y}))

gives the output:

 0.9746
[torch.Tensor of dimension 1]

CosineDistance also accepts batches:

mlp = nn.CosineDistance()
x = torch.Tensor({{1,2,3},{1,2,-3}})
y = torch.Tensor({{4,5,6},{-4,5,6}})
print(mlp:forward({x,y}))

gives the output:

 0.9746
-0.3655
[torch.DoubleTensor of size 2]

A more complicated example:

-- imagine we have one network we are interested in, it is called "p1_mlp"
p1_mlp= nn.Sequential(); p1_mlp:add(nn.Linear(5, 2))

-- But we want to push examples towards or away from each other
-- so we make another copy of it called p2_mlp
-- this *shares* the same weights via the set command, but has its own set of temporary gradient storage
-- that's why we create it again (so that the gradients of the pair don't wipe each other)
p2_mlp= p1_mlp:clone('weight', 'bias')

-- we make a parallel table that takes a pair of examples as input. they both go through the same (cloned) mlp
prl = nn.ParallelTable()
prl:add(p1_mlp)
prl:add(p2_mlp)

-- now we define our top level network that takes this parallel table and computes the cosine distance between
-- the pair of outputs
mlp= nn.Sequential()
mlp:add(prl)
mlp:add(nn.CosineDistance())


-- lets make two example vectors
x = torch.rand(5)
y = torch.rand(5)

-- Grad update function..
function gradUpdate(mlp, x, y, learningRate)
    local pred = mlp:forward(x)
    if pred[1]*y < 1 then
        gradCriterion = torch.Tensor({-y})
        mlp:zeroGradParameters()
        mlp:backward(x, gradCriterion)
        mlp:updateParameters(learningRate)
    end
end

-- push the pair x and y together, the distance should get larger..
for i = 1, 1000 do
 gradUpdate(mlp, {x, y}, 1, 0.1)
 if ((i%100)==0) then print(mlp:forward({x, y})[1]);end
end


-- pull apart the pair x and y, the distance should get smaller..

for i = 1, 1000 do
 gradUpdate(mlp, {x, y}, -1, 0.1)
 if ((i%100)==0) then print(mlp:forward({x, y})[1]);end
end

CriterionTable

module = CriterionTable(criterion)

Creates a module that wraps a Criterion module so that it can accept a table of inputs. Typically the table would contain two elements: the input and output x and y that the Criterion compares.

Example:

mlp = nn.CriterionTable(nn.MSECriterion())
x = torch.randn(5)
y = torch.randn(5)
print(mlp:forward{x, x})
print(mlp:forward{x, y})

gives the output:

0
1.9028918413199

Here is a more complex example of embedding the criterion into a network:

function table.print(t)
 for i, k in pairs(t) do print(i, k); end
end

mlp = nn.Sequential();                          -- Create an mlp that takes input
  main_mlp = nn.Sequential();		      -- and output using ParallelTable
  main_mlp:add(nn.Linear(5, 4))
  main_mlp:add(nn.Linear(4, 3))
 cmlp = nn.ParallelTable();
 cmlp:add(main_mlp)
 cmlp:add(nn.Identity())
mlp:add(cmlp)
mlp:add(nn.CriterionTable(nn.MSECriterion())) -- Apply the Criterion

for i = 1, 20 do                                 -- Train for a few iterations
 x = torch.ones(5);
 y = torch.Tensor(3); y:copy(x:narrow(1, 1, 3))
 err = mlp:forward{x, y}                         -- Pass in both input and output
 print(err)

 mlp:zeroGradParameters();
 mlp:backward({x, y} );
 mlp:updateParameters(0.05);
end

CAddTable

module = CAddTable([inplace])

Takes a table of Tensors and outputs summation of all Tensors. If inplace is true, the sum is written to the first Tensor.

ii = {torch.ones(5), torch.ones(5)*2, torch.ones(5)*3}
=ii[1]
 1
 1
 1
 1
 1
[torch.DoubleTensor of dimension 5]

return ii[2]
 2
 2
 2
 2
 2
[torch.DoubleTensor of dimension 5]

return ii[3]
 3
 3
 3
 3
 3
[torch.DoubleTensor of dimension 5]

m = nn.CAddTable()
=m:forward(ii)
 6
 6
 6
 6
 6
[torch.DoubleTensor of dimension 5]

CSubTable

Takes a table with two Tensor and returns the component-wise subtraction between them.

m = nn.CSubTable()
=m:forward({torch.ones(5)*2.2, torch.ones(5)})
 1.2000
 1.2000
 1.2000
 1.2000
 1.2000
[torch.DoubleTensor of dimension 5]

CMulTable

Takes a table of Tensors and outputs the multiplication of all of them.

ii = {torch.ones(5)*2, torch.ones(5)*3, torch.ones(5)*4}
m = nn.CMulTable()
=m:forward(ii)
 24
 24
 24
 24
 24
[torch.DoubleTensor of dimension 5]

CDivTable

Takes a table with two Tensor and returns the component-wise division between them.

m = nn.CDivTable()
=m:forward({torch.ones(5)*2.2, torch.ones(5)*4.4})
 0.5000
 0.5000
 0.5000
 0.5000
 0.5000
[torch.DoubleTensor of dimension 5]

CMaxTable

Takes a table of Tensors and outputs the max of all of them.

m = nn.CMaxTable()
=m:forward({{torch.Tensor{1,2,3}, torch.Tensor{3,2,1}})
 3
 2
 3
[torch.DoubleTensor of size 3]

CMinTable

Takes a table of Tensors and outputs the min of all of them.

m = nn.CMinTable()
=m:forward({{torch.Tensor{1,2,3}, torch.Tensor{3,2,1}})
 1
 2
 1
[torch.DoubleTensor of size 3]

CAddTensorTable

module = nn.CAddTensorTable()

Adds the first element el of the input table tab to each tensor contained in the second element of tab, which is itself a table

Example:

print(module:forward{ (0,1,1), {(0,0,0),(1,1,1)} })
{ (0,1,1), (1,2,2) }

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