class

SigmoidBackward

SigmoidBackward

source edit

Python wrappers

Autograd node for the logistic sigmoid $y = 1 / (1 + e^{-x})$ .

Saves the output $y$ rather than the input because the gradient formula $y(1 - y)$ depends only on $y$ . This avoids a redundant forward pass and keeps the saved tensor at the same dtype as the activation.

Math

$y = \frac{1}{1 + e^{-x}}, \qquad \frac{\partial y}{\partial x} = y\,(1 - y)$

Attributes

schema_v1OpSchema

"sigmoid", AmpPolicy::Promote — half-precision inputs are promoted to float32 to keep

e^{-x}

from underflowing for large

|x|

Notes

The eager backward builds $(1 - y)$ via mul_scalar(-1) + add_scalar(1) to reuse the existing storage primitives rather than introducing a dedicated subtract kernel.

Static methods

static

dispatch

int dispatch(backend::IBackend & be, const int & a, const int & s, Dtype dt)

source edit

Forward — calls IBackend::sigmoid to compute $y = 1 / (1 + e^{-x})$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

Eager-mode backward: $\partial L/\partial x = y(1 - y) \cdot \partial L/\partial y$ using the saved output $y$ .

grad_formula_impl

int grad_formula_impl(const int & g, const int &, const int & out)

source edit

Graph-mode backward: out * (1 - out) * g expressed as composable ops so the chain remains differentiable.

class

SigmoidBackward

SigmoidBackward

source edit

Python wrappers

Autograd node for the logistic sigmoid $y = 1 / (1 + e^{-x})$ .

Math

$y = \frac{1}{1 + e^{-x}}, \qquad \frac{\partial y}{\partial x} = y\,(1 - y)$

Attributes

schema_v1OpSchema

"sigmoid", AmpPolicy::Promote — half-precision inputs are promoted to float32 to keep

e^{-x}

from underflowing for large

|x|

Notes

The eager backward builds $(1 - y)$ via mul_scalar(-1) + add_scalar(1) to reuse the existing storage primitives rather than introducing a dedicated subtract kernel.

Static methods

static

dispatch

int dispatch(backend::IBackend & be, const int & a, const int & s, Dtype dt)

source edit

Forward — calls IBackend::sigmoid to compute $y = 1 / (1 + e^{-x})$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

Eager-mode backward: $\partial L/\partial x = y(1 - y) \cdot \partial L/\partial y$ using the saved output $y$ .

grad_formula_impl

int grad_formula_impl(const int & g, const int &, const int & out)

source edit

Graph-mode backward: out * (1 - out) * g expressed as composable ops so the chain remains differentiable.