class

SqrtBackward

SqrtBackward

source edit

Python wrappers

pylucid.ops.sqrtfunction

Autograd node for the element-wise square root $y = \sqrt{x}$ .

Saves the output $y$ because the backward formula $\partial y / \partial x = 1 / (2y)$ is cheaper and numerically identical to recomputing $\sqrt{x}$ . Defined for $x \geq 0$ ; negative inputs produce NaN.

Math

\frac{\partial y}{\partial x} = \frac{1}{2\sqrt{x}} = \frac{1}{2y}, \qquad \frac{\partial \mathcal{L}}{\partial x} = \frac{1}{2y}\,\frac{\partial \mathcal{L}}{\partial y}, \quad x \geq 0.$$

Attributes

schema_v1OpSchema

Registered as "sqrt" with AmpPolicy::Promote.

kSavesInputbool

false.

kSavesOutputbool

true — saved tensor is

y = \sqrt{x}

Notes

Dispatch: Accelerate vvsqrtf/vvsqrt (CPU) / MLX sqrt (GPU). Gradient is unbounded as $x \to 0^+$ .

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::sqrt to compute $y = \sqrt{x}$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

Backward — $\partial y/\partial x = 1/(2y)$ , scaled by grad_out.

grad_formula_impl

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

source edit

Graph-mode backward: $\partial x = g / (2y)$ where $y = \sqrt{x}$ is the saved output; kept inside the autograd graph.

class

SqrtBackward

SqrtBackward

source edit

Python wrappers

pylucid.ops.sqrtfunction

Autograd node for the element-wise square root $y = \sqrt{x}$ .

Math

\frac{\partial y}{\partial x} = \frac{1}{2\sqrt{x}} = \frac{1}{2y}, \qquad \frac{\partial \mathcal{L}}{\partial x} = \frac{1}{2y}\,\frac{\partial \mathcal{L}}{\partial y}, \quad x \geq 0.$$

Attributes

schema_v1OpSchema

Registered as "sqrt" with AmpPolicy::Promote.

kSavesInputbool

false.

kSavesOutputbool

true — saved tensor is

y = \sqrt{x}

Notes

Dispatch: Accelerate vvsqrtf/vvsqrt (CPU) / MLX sqrt (GPU). Gradient is unbounded as $x \to 0^+$ .

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::sqrt to compute $y = \sqrt{x}$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

Backward — $\partial y/\partial x = 1/(2y)$ , scaled by grad_out.

grad_formula_impl

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

source edit

Graph-mode backward: $\partial x = g / (2y)$ where $y = \sqrt{x}$ is the saved output; kept inside the autograd graph.