class

MinBackward

MinBackward

source edit

Python wrappers

pylucid.ops.minfunction

Autograd node for the multi-axis reduction minimum $y = \min_{i \in \text{axes}} x_i$ .

Symmetric to MaxBackward: the gradient flows to positions where $x_i$ equals the reduced minimum. Ties share gradient equally and the same composed ge/ge equality-mask trick is used.

Math

y = \min_{i \in \text{axes}} x_i, \qquad \frac{\partial \mathcal{L}}{\partial x_i} = \mathbb{1}[x_i = y]\cdot \mathrm{broadcast}\!\left(\frac{\partial \mathcal{L}}{\partial y} \right).

Attributes

schema_v1OpSchema

Registered as "min" with AmpPolicy::KeepInput.

kSavesOutputbool

true.

Static methods

static

dispatch

int dispatch(backend::IBackend & be, const int & a, const int & in_shape, const int & axes, bool keepdims, Dtype dt)

source edit

Forward — reduces a along axes via IBackend::reduce_min.

Methods

grad_formula

int grad_formula(const int & grad_out)

source edit

Backward — argmin-indicator gradient: routes grad_out only to positions where $x_i$ equals the reduced min (ties share equally).

class

MinBackward

MinBackward

source edit

Python wrappers

pylucid.ops.minfunction

Autograd node for the multi-axis reduction minimum $y = \min_{i \in \text{axes}} x_i$ .

Symmetric to MaxBackward: the gradient flows to positions where $x_i$ equals the reduced minimum. Ties share gradient equally and the same composed ge/ge equality-mask trick is used.

Math

y = \min_{i \in \text{axes}} x_i, \qquad \frac{\partial \mathcal{L}}{\partial x_i} = \mathbb{1}[x_i = y]\cdot \mathrm{broadcast}\!\left(\frac{\partial \mathcal{L}}{\partial y} \right).

Attributes

schema_v1OpSchema

Registered as "min" with AmpPolicy::KeepInput.

kSavesOutputbool

true.

Static methods

static

dispatch

int dispatch(backend::IBackend & be, const int & a, const int & in_shape, const int & axes, bool keepdims, Dtype dt)

source edit

Forward — reduces a along axes via IBackend::reduce_min.

Methods

grad_formula

int grad_formula(const int & grad_out)

source edit

Backward — argmin-indicator gradient: routes grad_out only to positions where $x_i$ equals the reduced min (ties share equally).