Median#

class byzfl.Median[source]#

Description#

Compute the coordinate-wise median along the first axis [1]:

\[\big[\mathrm{Median} \ (x_1, \dots, x_n)\big]_k = \mathrm{median} \big(\big[x_1\big]_k, \dots, \big[x_n\big]_k\big)\]

where

  • \(x_1, \dots, x_n\) are the input vectors, which conceptually correspond to gradients submitted by honest and Byzantine participants during a training iteration.

  • \(\big[\cdot\big]_k\) refers to the \(k\)-th coordinate.

  • \(\mathrm{median}\) refers to the median of \(n\) scalars.

Initialization parameters:

None

Calling the instance

Input parameters:

vectors (numpy.ndarray, torch.Tensor, list of numpy.ndarray or list of torch.Tensor) – A set of vectors, matrix or tensors.

Returns:

numpy.ndarray or torch.Tensor – The data type of the output will be the same as the input.

Examples

>>> import byzfl
>>> agg = byzfl.Median()

Using numpy arrays

>>> import numpy as np
>>> x = np.array([[1., 2., 3.],       # np.ndarray
>>>               [4., 5., 6.],
>>>               [7., 8., 9.]])
>>> agg(x)
array([4. 5. 6.])

Using torch tensors

>>> import torch
>>> x = torch.tensor([[1., 2., 3.],   # torch.tensor
>>>                   [4., 5., 6.],
>>>                   [7., 8., 9.]])
>>> agg(x)
tensor([4., 5., 6.])

Using list of numpy arrays

>>> import numpy as np
>>> x = [np.array([1., 2., 3.]),      # list of np.ndarray
>>>      np.array([4., 5., 6.]),
>>>      np.array([7., 8., 9.])]
>>> agg(x)
array([4., 5., 6.])

Using list of torch tensors

>>> import torch
>>> x = [torch.tensor([1., 2., 3.]),  # list of torch.tensor
>>>      torch.tensor([4., 5., 6.]),
>>>      torch.tensor([7., 8., 9.])]
>>> agg(x)
tensor([4., 5., 6.])

References

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