class

CoshBackward

CoshBackward

source edit

Python wrappers

pylucid.ops.coshfunction

Autograd node for element-wise hyperbolic cosine $y = \cosh(x)$ .

Saves the input x so the backward pass can evaluate $\sinh(x)$ . Defined on all of $\mathbb{R}$ with the identity $\cosh(x) = (e^x + e^{-x})/2 \geq 1$ .

Math

\frac{\partial y}{\partial x} = \sinh(x), \qquad \frac{\partial \mathcal{L}}{\partial x} = \sinh(x)\,\frac{\partial \mathcal{L}}{\partial y}.$$

Attributes

schema_v1OpSchema

Registered as "cosh" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate vvcoshf/vvcosh (CPU) / MLX cosh (GPU). Output magnitude grows exponentially.

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::cosh to compute $y = \cosh x$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

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

class

CoshBackward

CoshBackward

source edit

Python wrappers

pylucid.ops.coshfunction

Autograd node for element-wise hyperbolic cosine $y = \cosh(x)$ .

Saves the input x so the backward pass can evaluate $\sinh(x)$ . Defined on all of $\mathbb{R}$ with the identity $\cosh(x) = (e^x + e^{-x})/2 \geq 1$ .

Math

\frac{\partial y}{\partial x} = \sinh(x), \qquad \frac{\partial \mathcal{L}}{\partial x} = \sinh(x)\,\frac{\partial \mathcal{L}}{\partial y}.$$

Attributes

schema_v1OpSchema

Registered as "cosh" with AmpPolicy::Promote.

Notes

Dispatch: Accelerate vvcoshf/vvcosh (CPU) / MLX cosh (GPU). Output magnitude grows exponentially.

Static methods

static

dispatch

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

source edit

Forward — calls IBackend::cosh to compute $y = \cosh x$ .

Methods

grad_formula

int grad_formula(const int & g)

source edit

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