def uniform_unit_scaling(tensor: torch.Tensor, nonlinearity: str = "linear"):
    """
    An initaliser which preserves output variance for approximately gaussian
    distributed inputs. This boils down to initialising layers using a uniform
    distribution in the range `(-sqrt(3/dim[0]) * scale, sqrt(3 / dim[0]) * scale)`, where
    `dim[0]` is equal to the input dimension of the parameter and the `scale`
    is a constant scaling factor which depends on the non-linearity used.

    See `Random Walk Initialisation for Training Very Deep Feedforward Networks
    <https://www.semanticscholar.org/paper/Random-Walk-Initialization-for-Training-Very-Deep-Sussillo-Abbott/be9728a0728b6acf7a485225b1e41592176eda0b>`_
    for more information.

    # Parameters

    tensor : `torch.Tensor`, required.
        The tensor to initialise.
    nonlinearity : `str`, optional (default = `"linear"`)
        The non-linearity which is performed after the projection that this
        tensor is involved in. This must be the name of a function contained
        in the `torch.nn.functional` package.

    # Returns

    The initialised tensor.
    """
    size = 1.0
    # Estimate the input size. This won't work perfectly,
    # but it covers almost all use cases where this initialiser
    # would be expected to be useful, i.e in large linear and
    # convolutional layers, as the last dimension will almost
    # always be the output size.
    for dimension in list(tensor.size())[:-1]:
        size *= dimension

    activation_scaling = torch.nn.init.calculate_gain(nonlinearity, tensor)
    max_value = math.sqrt(3 / size) * activation_scaling

    return tensor.data.uniform_(-max_value, max_value)
An initaliser which preserves output variance for approximately gaussian
distributed inputs. This boils down to initialising layers using a uniform
distribution in the range `(-sqrt(3/dim[0]) * scale, sqrt(3 / dim[0]) * scale)`, where
`dim[0]` is equal to the input dimension of the parameter and the `scale`
is a constant scaling factor which depends on the non-linearity used.

See `Random Walk Initialisation for Training Very Deep Feedforward Networks
<https://www.semanticscholar.org/paper/Random-Walk-Initialization-for-Training-Very-Deep-Sussillo-Abbott/be9728a0728b6acf7a485225b1e41592176eda0b>`_
for more information.

# Parameters

tensor : `torch.Tensor`, required.
The tensor to initialise.
nonlinearity : `str`, optional (default = `"linear"`)
The non-linearity which is performed after the projection that this
tensor is involved in. This must be the name of a function contained
in the `torch.nn.functional` package.

# Returns

The initialised tensor.
allennlp/nn/initializers.py