import torch
from hessQuik.activations import hessQuikActivationFunction
[docs]class quadraticActivation(hessQuikActivationFunction):
r"""
Applies the quadratic activation function to each entry of the incoming data.
Examples::
>>> import hessQuik.activations as act
>>> act_func = act.quadraticActivation()
>>> x = torch.randn(10, 4)
>>> sigma, dsigma, d2sigma = act_func(x, do_gradient=True, do_Hessian=True)
"""
def __init__(self):
super(quadraticActivation, 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}{2}x^2
"""
(dsigma, d2sigma) = (None, None)
# forward propagate
sigma = 0.5 * (x ** 2)
# compute derivatives
if do_gradient or do_Hessian:
if forward_mode is not None:
dsigma, d2sigma = self.compute_derivatives(x, do_Hessian=do_Hessian)
else:
self.ctx = (x,)
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) &= x\\
\sigma''(x) &= 1
\end{align}
"""
dsigma = args[0]
d2sigma = None
if do_Hessian:
d2sigma = torch.ones_like(dsigma)
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 = quadraticActivation()
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)