class

SquareBackward

SquareBackward

source edit

Python wrappers

pylucid.ops.squarefunction

Autograd node for the element-wise square $y = x^2$ .

Saves the input x so the backward pass can scale the upstream gradient by $2x$ .

Math

\frac{\partial y}{\partial x} = 2x, \qquad \frac{\partial \mathcal{L}}{\partial x} = 2x\,\frac{\partial \mathcal{L}}{\partial y}.$$

Attributes

schema_v1OpSchema

Registered as "square" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate vDSP_vsq (CPU) / MLX square (GPU).

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::square to compute $y = x^2$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

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

grad_formula_impl

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

source edit

Graph-mode backward: $\partial x = 2x \cdot g$ kept inside the autograd graph.

class

SquareBackward

SquareBackward

source edit

Python wrappers

pylucid.ops.squarefunction

Autograd node for the element-wise square $y = x^2$ .

Saves the input x so the backward pass can scale the upstream gradient by $2x$ .

Math

\frac{\partial y}{\partial x} = 2x, \qquad \frac{\partial \mathcal{L}}{\partial x} = 2x\,\frac{\partial \mathcal{L}}{\partial y}.$$

Attributes

schema_v1OpSchema

Registered as "square" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate vDSP_vsq (CPU) / MLX square (GPU).

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::square to compute $y = x^2$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

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

grad_formula_impl

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

source edit

Graph-mode backward: $\partial x = 2x \cdot g$ kept inside the autograd graph.