nnx: experimental 'nn' components

The original neural network from Torch7, nn, contains stable and widely used modules. 'nnx' contains more experimental, unproven modules, and optimizations. Modules that become stable and which are proven useful make their way into 'nn' (some already have).

Library Documentation

This section includes documentation for the following objects:

SoftMaxTree : a hierarchical log-softmax Module;
TreeNLLCriterion : a negative log-likelihood Criterion for the SoftMaxTree;
CTCCriterion : a Connectionist Temporal Classification Criterion based on warp-ctc;
PushTable (and PullTable) : extracts a table element and inserts it later in the network;
MultiSoftMax : performs a softmax over the last dimension of a 2D or 3D input;
SpatialReSampling : performs bilinear resampling of a 3D or 4D input image;
[QDRiemaNNLinear] (#nnx.QDRiemaNNLinear) : quasi-diagonal reduction for Riemannian gradient descent
Recurrent : a generalized recurrent neural network container;

### SoftMaxTree ### A hierarchy of parameterized log-softmaxes. Used for computing the likelihood of a leaf class. This Module should be used in conjunction with the [TreeNLLCriterion](#nnx.TreeNLLCriterion). Using this for large vocabularies (100,000 and more) greatly accelerates training and evaluation of neural network language models (NNLM). A vocabulary hierarchy is provided via the [dp](https://github.com/nicholas-leonard/dp/blob/master/README.md) package's [BillionWords](https://github.com/nicholas-leonard/dp/blob/master/doc/data.md#dp.BillionWords) [DataSource](https://github.com/nicholas-leonard/dp/blob/master/doc/data.md#dp.DataSource).

The constructor takes 2 mandatory and 4 optional arguments :

inputSize : the number of units in the input embedding representation;
hierarchy : a Tensor mapping one parent_id to many child_id (a tree);
rootId : a number identifying the root node in the hierarchy. Defaults to -1;
accUpdate : when the intent is to use backwardUpdate or accUpdateGradParameters, set this to true to save memory. Defaults to false;
static : when true (the defualt), returns parameters with keys that don't change from batch to batch;
verbose : prints some additional information concerning the hierarchy during construction.

The forward method returns an output Tensor of size 1D, while backward returns a table {gradInput, gradTarget}. The second variable is just a Tensor of zeros , such that the targets can be propagated through Containers like ParallelTable.

> input = torch.randn(5,10)
> target = torch.IntTensor{20,24,27,10,12}
> gradOutput = torch.randn(5)
> root_id = 29
> input_size = 10	
> hierarchy = {
>>    [29]=torch.IntTensor{30,1,2}, [1]=torch.IntTensor{3,4,5}, 
>>    [2]=torch.IntTensor{6,7,8}, [3]=torch.IntTensor{9,10,11},
>>    [4]=torch.IntTensor{12,13,14}, [5]=torch.IntTensor{15,16,17},
>>    [6]=torch.IntTensor{18,19,20}, [7]=torch.IntTensor{21,22,23},
>>    [8]=torch.IntTensor{24,25,26,27,28}
>> }
> smt = nn.SoftMaxTree(input_size, hierarchy, root_id)
> smt:forward{input, target}
-3.5186
-3.8950
-3.7433
-3.3071
-3.0522
[torch.DoubleTensor of dimension 5]
> smt:backward({input, target}, gradOutput)
{
  1 : DoubleTensor - size: 5x10
  2 : IntTensor - size: 5
}

### TreeNLLCriterion ### Measures the Negative log-likelihood (NLL) for [SoftMaxTrees](#nnx.SoftMaxTree). Used for maximizing the likelihood of SoftMaxTree outputs. The SoftMaxTree Module outputs a column Tensor representing the log likelihood of each target in the batch. Thus SoftMaxTree requires the targets. So this Criterion only computes the negative of those outputs, as well as its corresponding gradients. ### PushTable (and PullTable) ### PushTable and PullTable work together. The first can be put earlier in a digraph of Modules such that it can communicate with a PullTable located later in the graph. `PushTable:forward(input)` for an `input` table of Tensors to the output, excluding one, the index of which is specified by the `index` argument in the `PushTable(index)` constructor. The Tensor identified by this `index` is communicated to one or many PullTables created via the `PushTable:pull(index)` factory method. These can be inserted later in the digraph such that a call to `PushTable:forward(input)`, where `input` is a table or a Tensor, will output a table with the previously *pushed* Tensor inserted at index `index`.

An example utilizing the above SoftMaxTree Module and a Linear Module demonstrates how the PushTable can be used to forward the target Tensor without any other Table Modules:

> mlp = nn.Sequential()
> linear = nn.Linear(50,100)
> push = nn.PushTable(2)
> pull = push:pull(2)
> mlp:add(push)
> mlp:add(nn.SelectTable(1))
> mlp:add(linear)
> mlp:add(pull)
> mlp:add(smt) --smt is a SoftMaxTree instance
> mlp:forward{input, target} -- input and target are defined above
-3.5186
-3.8950
-3.7433
-3.3071
-3.0522
[torch.DoubleTensor of dimension 5]
> mlp:backward({input, target}, gradOutput) -- so is gradOutput
{
  1 : DoubleTensor - size: 5x10
  2 : IntTensor - size: 5
}

The above code is equivalent to the following:

> mlp2 = nn.Sequential()
> para = nn.ParallelTable()
> para:add(linear)
> para:add(nn.Identity())
> mlp2:add(para)
> mlp2:add(smt)
> mlp2:forward{input, target}
-3.5186
-3.8950
-3.7433
-3.3071
-3.0522
[torch.DoubleTensor of dimension 5]
> mlp2:backward({input, target}, gradOutput)
{
  1 : DoubleTensor - size: 5x10
  2 : IntTensor - size: 5
}

In some cases, this can simplify the digraph of Modules. Note that a PushTable can be associated to many PullTables, but each PullTable is associated to only one PushTable.

### CTCCriterion ### ``` criterion = nn.CTCCriterion() ``` Creates a Criterion based on Baidus' [warp-ctc](https://github.com/baidu-research/warp-ctc) implementation. This Module measures the loss between a 3D output of (batch x time x inputdim) and a target without needing alignment of inputs and labels. Must have installed warp-ctc which can be installed via luarocks: ``` luarocks install http://raw.githubusercontent.com/baidu-research/warp-ctc/master/torch_binding/rocks/warp-ctc-scm-1.rockspec ``` Supports cuda via: ``` criterion = nn.CTCCriterion():cuda() ``` Example: ``` output = torch.Tensor({{{1,2,3,4,5},{6,7,8,9,10}}}) -- Tensor of size 1x1x5 (batch x time x inputdim). label = {{1,3}} ctcCriterion = nn.CTCCriterion()

print(ctcCriterion:forward(output,label))

ctcCriterion = ctcCriterion:cuda() -- Switch to cuda implementation. output = output:cuda()

print(ctcCriterion:forward(output,label))


gives the output:

4.9038286209106 4.9038290977478

<a name='nnx.MultiSoftMax'/>
### MultiSoftMax ###
This Module takes 2D or 3D input and performs a softmax over the last dimension. 
It uses the existing [SoftMax](https://github.com/torch/nn/blob/master/doc/transfer.md#nn.SoftMax) 
CUDA/C code to do so such that the Module can be used on both GPU and CPU. 
This can be useful for [keypoint detection](https://github.com/nicholas-leonard/dp/blob/master/doc/facialkeypointstutorial.md#multisoftmax).

<a name='nnx.SpatialReSampling'/>
### SpatialReSampling ###
Applies a 2D re-sampling over an input image composed of
several input planes (or channels, colors). The input tensor in `forward(input)` is 
expected to be a 3D or 4D tensor of size : `[batchSize x] nInputPlane x width x height`. 
The number of output planes will be the same as the number of input
planes.

The re-sampling is done using [bilinear interpolation](http://en.wikipedia.org/wiki/Bilinear_interpolation). 
For a simple nearest-neihbor upsampling, use `nn.SpatialUpSampling()`,
and for a simple average-based down-sampling, use 
`nn.SpatialDownSampling()`.

If the input image is a 3D tensor of size `nInputPlane x height x width`,
the output image size will be `nInputPlane x oheight x owidth` where
`owidth` and `oheight` are given to the constructor.

Instead of `owidth` and `oheight`, one can provide `rwidth` and `rheight`, 
such that `owidth = iwidth*rwidth` and `oheight = iheight*rheight`.

As an example, we can run the following code on the famous Lenna image:
```lua
require 'image'                                                           
require 'nnx'
input = image.loadPNG('doc/image/Lenna.png')
l = nn.SpatialReSampling{owidth=150,oheight=150}
output = l:forward(input)
image.save('doc/image/Lenna-150x150-bilinear.png', output)

The input:

Lenna