Functions¤
clifford_batch_norm(x, n_blades, running_mean=None, running_cov=None, weight=None, bias=None, training=True, momentum=0.1, eps=1e05)
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Clifford batch normalization for each channel across a batch of data.
Parameters:
Name  Type  Description  Default 

x 
torch.Tensor

Input tensor of shape 
required 
n_blades 
int

Number of blades of the Clifford algebra. 
required 
running_mean 
torch.Tensor

The tensor with running mean statistics having shape 
None

running_cov 
torch.Tensor

The tensor with running covariance statistics having shape 
None

weight 
Union[torch.Tensor, nn.Parameter]

Additional weight tensor which is applied post normalization, and has the shape 
None

bias 
Union[torch.Tensor, nn.Parameter]

Additional bias tensor which is applied post normalization, and has the shape 
None

training 
bool

Whether to use the running mean and variance. Defaults to True. Defaults to True. 
True

momentum 
float

Momentum for the running mean and variance. Defaults to 0.1. 
0.1

eps 
float

Epsilon for the running mean and variance. Defaults to 1e05. 
1e05

Returns:
Type  Description 

torch.Tensor

Normalized input of shape 
Source code in cliffordlayers/nn/functional/batchnorm.py
complex_batch_norm(x, running_mean=None, running_cov=None, weight=None, bias=None, training=True, momentum=0.1, eps=1e05)
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Applies complexvalued Batch Normalization as described in (Trabelsi et al., 2018) for each channel across a batch of data.
Parameters:
Name  Type  Description  Default 

x 
torch.Tensor

The input complexvalued data is expected to be at least 2d, with shape 
required 
running_mean 
Union[torch.Tensor, nn.Parameter]

The tensor with running mean statistics having shape 
None

running_cov 
Union[torch.Tensor, nn.Parameter]

The tensor with running realimaginary covariance statistics having shape 
None

weight 
torch.Tensor

Additional weight tensor which is applied post normalization, and has the shape 
None

bias 
torch.Tensor

Additional bias tensor which is applied post normalization, and has the shape 
None

training 
bool

Whether to use the running mean and variance. Defaults to 
True

momentum 
float

Momentum for the running mean and variance. Defaults to 
0.1

eps 
float

Epsilon for the running mean and variance. Defaults to 
1e05

Returns:
Type  Description 

torch.Tensor

Normalized input as complex tensor of shape 
Source code in cliffordlayers/nn/functional/batchnorm.py
whiten_data(x, training=True, running_mean=None, running_cov=None, momentum=0.1, eps=1e05)
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Jointly whiten features in tensors (B, C, *D, I)
: take n_blades(I)dim vectors
and whiten individually for each channel dimension C over (B, *D)
.
I is the number of blades in the respective Clifford algebra, e.g. I = 2 for complex numbers.
Parameters:
Name  Type  Description  Default 

x 
torch.Tensor

The tensor to whiten. 
required 
training 
bool

Wheter to update the running mean and covariance. Defaults to 
True

running_mean 
torch.Tensor

The running mean of shape 
None

running_cov 
torch.Tensor

The running covariance of shape 
None

momentum 
float

The momentum to use for the running mean and covariance. Defaults to 
0.1

eps 
float

A small number to add to the covariance. Defaults to 1e5. 
1e05

Returns:
Type  Description 

torch.Tensor

Whitened data of shape 
Source code in cliffordlayers/nn/functional/batchnorm.py
clifford_group_norm(x, n_blades, num_groups=1, running_mean=None, running_cov=None, weight=None, bias=None, training=True, momentum=0.1, eps=1e05)
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Clifford group normalization
Parameters:
Name  Type  Description  Default 

x 
torch.Tensor

Input tensor of shape 
required 
n_blades 
int

Number of blades of the Clifford algebra. 
required 
num_groups 
int

Number of groups for which normalization is calculated. Defaults to 1.
For 
1

running_mean 
torch.Tensor

The tensor with running mean statistics having shape 
None

running_cov 
torch.Tensor

The tensor with running realimaginary covariance statistics having shape 
None

weight 
Union[torch.Tensor, nn.Parameter]

Additional weight tensor which is applied post normalization, and has the shape 
None

bias 
Union[torch.Tensor, nn.Parameter]

Additional bias tensor which is applied post normalization, and has the shape 
None

training 
bool

Whether to use the running mean and variance. Defaults to True. 
True

momentum 
float

Momentum for the running mean and variance. Defaults to 0.1. 
0.1

eps 
float

Epsilon for the running mean and variance. Defaults to 1e05. 
1e05

Returns:
Type  Description 

torch.Tensor

Group normalized input of shape 
Source code in cliffordlayers/nn/functional/groupnorm.py
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complex_group_norm(x, num_groups=1, running_mean=None, running_cov=None, weight=None, bias=None, training=True, momentum=0.1, eps=1e05)
¤
Group normalization for complexvalued tensors.
Parameters:
Name  Type  Description  Default 

x 
torch.Tensor

The input complexvalued data is expected to be at least 2d, with
shape 
required 
num_groups 
int

Number of groups for which normalization is calculated. Defaults to 1.
For 
1

running_mean 
torch.Tensor

The tensor with running mean statistics having shape 
None

running_cov 
torch.Tensor

The tensor with running realimaginary covariance statistics having shape 
None

weight 
Union[torch.Tensor, nn.Parameter]

Additional weight tensor which is applied post normalization, and has the shape 
None

bias 
Union[torch.Tensor, nn.Parameter]

Additional bias tensor which is applied post normalization, and has the shape 
None

training 
bool

Whether to use the running mean and variance. Defaults to True. 
True

momentum 
float

Momentum for the running mean and variance. Defaults to 0.1. 
0.1

eps 
float

Epsilon for the running mean and variance. Defaults to 1e05. 
1e05

Returns:
Type  Description 

torch.Tensor

Normalized input as complex tensor of shape 
Source code in cliffordlayers/nn/functional/groupnorm.py
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