import torch
from hessQuik.activations import hessQuikActivationFunction
[docs]class sigmoidActivation(hessQuikActivationFunction):
r"""
Applies the sigmoid activation function to each entry of the incoming data.
Examples::
>>> import hessQuik.activations as act
>>> act_func = act.sigmoidActivation()
>>> x = torch.randn(10, 4)
>>> sigma, dsigma, d2sigma = act_func(x, do_gradient=True, do_Hessian=True)
"""
def __init__(self):
super(sigmoidActivation, self).__init__()
[docs] def forward(self, x, do_gradient=False, do_Hessian=False, forward_mode=True):
r"""
Activates each entry of incoming data via
.. math::
\sigma(x) = \frac{1}{1 + e^{-x}}
"""
(dsigma, d2sigma) = (None, None)
# forward propagate
sigma = torch.sigmoid(x)
# compute derivatves
if do_gradient or do_Hessian:
if forward_mode is not None:
dsigma, d2sigma = self.compute_derivatives(sigma, do_Hessian=do_Hessian)
else:
self.ctx = (sigma,)
return sigma, dsigma, d2sigma
[docs] def compute_derivatives(self, *args, do_Hessian=False):
r"""
Computes the first and second derivatives of each entry of the incoming data via
.. math::
\begin{align}
\sigma'(x) &= \sigma(x)(1 - \sigma(x))\\
\sigma''(x) &= \sigma'(x)(1 - 2 * \sigma(x))
\end{align}
"""
sigma = args[0]
dsigma = sigma * (1 - sigma)
d2sigma = None
if do_Hessian:
d2sigma = dsigma * (1 - 2 * sigma)
return dsigma, d2sigma
if __name__ == '__main__':
from hessQuik.utils import input_derivative_check
torch.set_default_dtype(torch.float64)
nex = 11 # no. of examples
d = 4 # no. of input features
x = torch.randn(nex, d)
f = sigmoidActivation()
print('======= FORWARD =======')
input_derivative_check(f, x, do_Hessian=True, verbose=True, forward_mode=True)
print('======= BACKWARD =======')
input_derivative_check(f, x, do_Hessian=True, verbose=True, forward_mode=False)