class

PowScalarBackward

PowScalarBackward

source edit

Autograd node for scalar-exponent power: $y = x^{\text{exp}}$ .

The exponent is a Python float (here promoted to double) captured on the node at forward time; the input tensor is saved so the backward pass can reconstruct $x^{\text{exp}-1}$ via the same backend kernel.

Math

Forward

$y_i = x_i^{\text{exp}}$

Backward

\cdot \frac{\partial L}{\partial y_i}$$ **See Also** `RPowScalarBackward`, `pow_scalar_op`.

Attributes

exp_double

Scalar exponent captured at forward; reused inside grad_formula to compute

x^{\text{exp}-1}

and the leading multiplier.

schema_v1OpSchema

Op name "pow_scalar" with AmpPolicy::ForceFP32 (integer / half precision are unsafe for arbitrary exponents).

Notes

Capturing only the scalar (rather than baking it into the op name) keeps the op table small. pow_scalar is reused inside grad_formula to compute $x^{\text{exp}-1}$ — no separate "decrement-exponent" kernel.

Static methods

static

forward

→TensorImplPtr

int forward(const int & a, double exp)

source edit

Forward dispatch with scalar capture — computes $y = x^{\text{exp}}$ and wires the backward node manually so exp is persisted.

Parameters

aconst TensorImplPtr&

Input tensor (must be non-null; promoted to FP32 by the schema).

expdouble

Scalar exponent.

Returns

TensorImplPtr

Output tensor with the same shape and (post-promotion) dtype as a; the backward node carries exp.

Methods

grad_formula

→Storage

int grad_formula(const int & g)

source edit

Computes $\partial L/\partial x = \text{exp} \cdot x^{\text{exp}-1} \cdot g$ from the saved input and the captured exp_.

Parameters

gconst Storage&

Upstream gradient

\partial L/\partial y

Returns

Storage

Gradient with respect to x — same shape, dtype, and device as the saved input.

grad_formula_impl

→TensorImplPtr

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

source edit

Graph-mode equivalent of grad_formula used when higher-order autograd is enabled — produces a fresh TensorImpl whose own backward chain remains intact.

Math

$\frac{\partial}{\partial x}(x^e) = e \cdot x^{e-1}$

Parameters

gconst TensorImplPtr&

Upstream gradient tensor

\partial L/\partial y

aconst TensorImplPtr&

Saved input tensor.

/* out */const TensorImplPtr&

Saved output tensor (unused; preserved for signature parity with other grad_formula_impl overrides).

Returns

TensorImplPtr

Tensor representing $\text{exp} \cdot x^{\text{exp}-1} \cdot g$ with a live autograd graph.

class

PowScalarBackward

PowScalarBackward

source edit

Autograd node for scalar-exponent power: $y = x^{\text{exp}}$ .

Math

Forward

$y_i = x_i^{\text{exp}}$

Backward

\cdot \frac{\partial L}{\partial y_i}$$ **See Also** `RPowScalarBackward`, `pow_scalar_op`.

Attributes

exp_double

Scalar exponent captured at forward; reused inside grad_formula to compute

x^{\text{exp}-1}

and the leading multiplier.

schema_v1OpSchema

Op name "pow_scalar" with AmpPolicy::ForceFP32 (integer / half precision are unsafe for arbitrary exponents).

Notes

Static methods

static

forward

→TensorImplPtr

int forward(const int & a, double exp)

source edit

Forward dispatch with scalar capture — computes $y = x^{\text{exp}}$ and wires the backward node manually so exp is persisted.

Parameters

aconst TensorImplPtr&

Input tensor (must be non-null; promoted to FP32 by the schema).

expdouble

Scalar exponent.

Returns

TensorImplPtr

Output tensor with the same shape and (post-promotion) dtype as a; the backward node carries exp.

Methods

grad_formula

→Storage

int grad_formula(const int & g)

source edit

Computes $\partial L/\partial x = \text{exp} \cdot x^{\text{exp}-1} \cdot g$ from the saved input and the captured exp_.

Parameters

gconst Storage&

Upstream gradient

\partial L/\partial y

Returns

Storage

Gradient with respect to x — same shape, dtype, and device as the saved input.

grad_formula_impl

→TensorImplPtr

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

source edit

Graph-mode equivalent of grad_formula used when higher-order autograd is enabled — produces a fresh TensorImpl whose own backward chain remains intact.

Math

$\frac{\partial}{\partial x}(x^e) = e \cdot x^{e-1}$

Parameters

gconst TensorImplPtr&

Upstream gradient tensor

\partial L/\partial y

aconst TensorImplPtr&

Saved input tensor.

/* out */const TensorImplPtr&

Saved output tensor (unused; preserved for signature parity with other grad_formula_impl overrides).

Returns

TensorImplPtr

Tensor representing $\text{exp} \cdot x^{\text{exp}-1} \cdot g$ with a live autograd graph.