class

ErfBackward

ErfBackward

source edit

Python wrappers

pylucid.ops.erffunction

Autograd node for the element-wise error function $y = \mathrm{erf}(x) = (2/\sqrt{\pi})\int_0^x e^{-t^2}\,dt$ .

Saves the input x so the backward pass can build $e^{-x^2}$ . Defined on all of $\mathbb{R}$ with range $(-1, 1)$ .

Math

\frac{\partial y}{\partial x} = \frac{2}{\sqrt{\pi}}\,e^{-x^2}, \qquad \frac{\partial \mathcal{L}}{\partial x} = \frac{2}{\sqrt{\pi}}\,e^{-x^2}\,\frac{\partial \mathcal{L}}{\partial y}.$$

Attributes

schema_v1OpSchema

Registered as "erf" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate erf kernel (CPU) / MLX erf (GPU).

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::erf to compute $y = \mathrm{erf}(x)$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

Backward — $\partial y/\partial x = (2/\sqrt{\pi})\,e^{-x^2}$ , scaled by grad_out.

grad_formula_impl

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

source edit

Graph-mode backward: $\partial x = (2/\sqrt{\pi})\,e^{-x^2}\,g$ kept inside the autograd graph.

class

ErfBackward

ErfBackward

source edit

Python wrappers

pylucid.ops.erffunction

Autograd node for the element-wise error function $y = \mathrm{erf}(x) = (2/\sqrt{\pi})\int_0^x e^{-t^2}\,dt$ .

Saves the input x so the backward pass can build $e^{-x^2}$ . Defined on all of $\mathbb{R}$ with range $(-1, 1)$ .

Math

\frac{\partial y}{\partial x} = \frac{2}{\sqrt{\pi}}\,e^{-x^2}, \qquad \frac{\partial \mathcal{L}}{\partial x} = \frac{2}{\sqrt{\pi}}\,e^{-x^2}\,\frac{\partial \mathcal{L}}{\partial y}.$$

Attributes

schema_v1OpSchema

Registered as "erf" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate erf kernel (CPU) / MLX erf (GPU).

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::erf to compute $y = \mathrm{erf}(x)$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

Backward — $\partial y/\partial x = (2/\sqrt{\pi})\,e^{-x^2}$ , scaled by grad_out.

grad_formula_impl

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

source edit

Graph-mode backward: $\partial x = (2/\sqrt{\pi})\,e^{-x^2}\,g$ kept inside the autograd graph.