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@@ -14,8 +14,9 @@ This section includes documentation for the following objects: * [PushTable (and PullTable)](#nnx.PushTable) : extracts a table element and inserts it later in the network; * [MultiSoftMax](#nnx.MultiSoftMax) : performs a softmax over the last dimension of a 2D or 3D input; * [SpatialReSampling](#nnx.SpatialReSampling) : performs bilinear resampling of a 3D or 4D input image; + * [QDRiemaNNLinear] (#nnx.QDRiemaNNLinear) : quasi-diagonal reduction for Riemannian gradient descent * [Recurrent](#nnx.Recurrent) : a generalized recurrent neural network container; - + <a name='nnx.SoftMaxTree'/> ### SoftMaxTree ### A hierarchy of parameterized log-softmaxes. Used for computing the likelihood of a leaf class. @@ -224,6 +225,19 @@ The re-sampled output:  +<a name='nnx.QDRiemaNNLinear'/> +### QDRiemaNNLinear ### +The Quasi-Diagonal Riemannian Neural Network Linear (QDRiemaNNLinear) module is an implementation +of the quasi-diagonal reduction of metrics, used for Riemannian gradient descent. +The algorithm is defined in Riemannian metrics for neural networks I: feedforward networks by Yann Ollivier (http://arxiv.org/abs/1303.0818) and an efficient implementation is described in Practical Riemannian Neural Networks by Yann Ollivier and Gaetan Marceau-Caron (http://arxiv.org/abs/1602.08007). +To use this module, simply replace `nn.Linear(ninput,noutput)` with `nnx.QDRiemaNNLinear(ninput,noutput)`. +As always, the step-size must be chosen accordingly. +Two additional arguments are also possible: +* gamma (default=0.01): determine the update rate of the metric for a minibatch setting, i.e., (1-gamma) * oldMetric + gamma newMetric. Smaller minibatches require a smaller gamma. A default value depending on the size of the minibatches is `gamma = 1. - torch.pow(1.-1./nTraining,miniBatchSize)` where `nTraining` is the number of training examples of the dataset and `miniBatchSize` is the number of training examples per minibatch. +* qdFlag (default=true): Whether to use the quasi-diagonal reduction (true) or only the diagonal (false). The former should be better. + +This module is a straightforward implementation of the outer product gradient descent. + ## Requirements * Torch7 (www.torch.ch) |