Nearest Neighbor Mixing (NNM)#

class byzfl.NNM(f=0)[source]#

Description#

Apply the Nearest Neighbor Mixing pre-aggregation rule [1]:

\[\mathrm{NNM}_{f} \ (x_1, \dots, x_n) = \left(\frac{1}{n-f}\sum_{i \in \mathit{N}_{1}} x_i \ \ , \ \dots \ ,\ \ \frac{1}{n-f}\sum_{i \in \mathit{N}_{n}} x_i \right)\]

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.

  • \(f\) conceptually represents the expected number of Byzantine vectors.

  • For any \(i \in \) \(\big[n\big]\), \(\mathit{N}_i\) is the set of the \(n-f\) nearest neighbors of \(x_i\) in \(\{x_1, \dots , x_n\}\).

Initialization parameters:

f (int, optional) – Number of faulty vectors. Set to 0 by default.

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.NNM(1)

Using numpy arrays

>>> import numpy as np
>>> x = np.array([[1., 2., 3.],       # np.ndarray
>>>               [4., 5., 6.],
>>>               [7., 8., 9.]])
>>> agg(x)
array([[2.5 3.5 4.5]
        [2.5 3.5 4.5]
        [5.5 6.5 7.5]])

Using torch tensors

>>> import torch
>>> x = torch.tensor([[1., 2., 3.],   # torch.tensor
>>>                   [4., 5., 6.],
>>>                   [7., 8., 9.]])
>>> agg(x)
tensor([[2.5000, 3.5000, 4.5000],
        [2.5000, 3.5000, 4.5000],
        [5.5000, 6.5000, 7.5000]])

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([[2.5 3.5 4.5]
        [2.5 3.5 4.5]
        [5.5 6.5 7.5]])

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([[2.5000, 3.5000, 4.5000],
        [2.5000, 3.5000, 4.5000],
        [5.5000, 6.5000, 7.5000]])

References

On this page