speechbrain.nnet.quaternion_networks.q_linear module

Library implementing quaternion-valued linear transformation.

Authors

  • Titouan Parcollet 2020

Summary

Classes:

QLinear

This function implements a fully connected quaternion-valued linear layer: y = Wx + b.

Reference

class speechbrain.nnet.quaternion_networks.q_linear.QLinear(n_neurons, input_shape, bias=True, init_criterion='glorot', weight_init='quaternion', autograd=True, spinor=False, vector_scale=False)[source]

Bases: Module

This function implements a fully connected quaternion-valued linear layer: y = Wx + b. y, W, x and b are thus quaternion numbers. A quaternion number is written as: r + xi + yj + zk. A tensor of quaternion numbers x = [batch, 32] can be understood as [batch, 0:7] = R, [batch, 8:15] = Xi, [batch, 16:23] = Yi, and [batch, 24:31] = Xi. Thus the features dimension is cut in four (must be divisible by 4).

Parameters

  • n_neurons (int) – It is the number of output neurons (i.e, the dimensionality of the output). Please note that these are quaternion-valued neurons. If 256 neurons are specified, the output dimension will be 1024.

  • input_shape (tuple) – Expected size of the input.

  • bias (bool) – If True, the additive bias b is adopted.

  • init_criterion (str , optional) – (glorot, he). This parameter controls the initialization criterion of the weights. It is combined with weights_init to build the initialization method of the quaternion-valued weights (default “glorot”).

  • weight_init (str, optional) – (quaternion, unitary). This parameter defines the initialization procedure of the quaternion-valued weights. “quaternion” will generate quaternion-valued weights following the init_criterion and the quaternion polar form. “unitary” will normalize the weights to lie on the unit circle (default “quaternion”). More details in: “Quaternion recurrent neural networks”, Parcollet T.

  • autograd (bool, optional) – When True, the default PyTorch autograd will be used. When False, a custom backpropagation will be used, reducing by a factor 3 to 4 the memory consumption. It is also 2x slower. This only works with spinor = False (default True).

  • spinor (bool, optional) – When True, the layer will be turned into a spinor layer. More precisely W*x will be turned into W*x*W-1. The input x will be rotated by W such as in a spinor neural network. However, x MUST be a quaternion with the real part equal to zero. (0 + xi + yj + zk). Indeed, the rotation operation only acts on the vector part. Note that W will always be normalized before the rotation to ensure the quaternion algebra (default False). More details in: “Quaternion neural networks”, Parcollet T.

  • vector_scale (bool, optional) – The vector_scale is only used when spinor = True. In the context of a spinor neural network, multiple rotations of the input vector x are performed and summed. Hence, the norm of the output vector always increases with the number of layers, making the neural network instable with deep configurations. The vector_scale parameters are learnable parameters that acts like gates by multiplying the output vector with a small trainable parameter (default False).

Example

>>> inputs = torch.rand(10, 50, 40)
>>> lin = QLinear(n_neurons=100, input_shape=inputs.shape, weight_init='unitary')
>>> output = lin(inputs)
>>> output.shape
torch.Size([10, 50, 400])
training: bool
forward(x)[source]

Returns the linear transformation of input tensor.

Parameters

x (torch.Tensor) – Input to transform linearly.