class

ErfinvBackward

ErfinvBackward

source edit

Python wrappers

pylucid.ops.erfinvfunction

Autograd node for the element-wise inverse error function $y = \mathrm{erfinv}(x)$ .

Saves the output $y$ so the backward pass can form $e^{y^2}$ without needing to invert $\mathrm{erf}$ a second time. Defined on $(-1, 1)$ ; the gradient is unbounded as $x \to \pm 1$ .

Math

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

Attributes

schema_v1OpSchema

Registered as "erfinv" with AmpPolicy::Promote.

kSavesInputbool

false.

kSavesOutputbool

true — saved tensor is

y = \mathrm{erfinv}(x)

Notes

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

Static methods

static

dispatch

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

source edit

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

Methods

grad_formula

int grad_formula(const int & g)

source edit

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

grad_formula_impl

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

source edit

Graph-mode backward: $\partial x = \tfrac{\sqrt{\pi}}{2}\,e^{\mathrm{out}^2}\,g$ using the saved output, kept inside the autograd graph.

class

ErfinvBackward

ErfinvBackward

source edit

Python wrappers

pylucid.ops.erfinvfunction

Autograd node for the element-wise inverse error function $y = \mathrm{erfinv}(x)$ .

Saves the output $y$ so the backward pass can form $e^{y^2}$ without needing to invert $\mathrm{erf}$ a second time. Defined on $(-1, 1)$ ; the gradient is unbounded as $x \to \pm 1$ .

Math

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

Attributes

schema_v1OpSchema

Registered as "erfinv" with AmpPolicy::Promote.

kSavesInputbool

false.

kSavesOutputbool

true — saved tensor is

y = \mathrm{erfinv}(x)

Notes

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

Static methods

static

dispatch

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

source edit

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

Methods

grad_formula

int grad_formula(const int & g)

source edit

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

grad_formula_impl

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

source edit

Graph-mode backward: $\partial x = \tfrac{\sqrt{\pi}}{2}\,e^{\mathrm{out}^2}\,g$ using the saved output, kept inside the autograd graph.