class

MinimumBackward

MinimumBackward

source edit

Python wrappers

pylucid.ops.minimumfunction

Autograd node for elementwise minimum $y = \min(a, b)$ with NumPy broadcasting.

Saves both inputs a and b (kSavesInputs = true inherited from BinaryKernel) so the backward pass can reconstruct the indicator masks for the comparison. Gradient flows only through whichever operand "won" the elementwise comparison; ties are broken in favour of a (gradient assigned entirely to a when $a_i = b_i$ ).

Math

y_i = \min(a_i, b_i)

\frac{\partial L}{\partial a_i} = \mathbb{1}\{a_i \leq b_i\} \cdot \frac{\partial L}{\partial y_i}

\frac{\partial L}{\partial b_i} = \mathbb{1}\{a_i > b_i\} \cdot \frac{\partial L}{\partial y_i}

Shape

Inputs a, b follow NumPy broadcasting rules; the output takes the broadcast shape. Both gradient branches are sum-reduced back to their original input shapes by sum_to_shape in the apply trampoline.

See Also

MaximumBackward : Elementwise maximum (mirror operation).

Attributes

schema_v1OpSchema

"minimum", version 1, AmpPolicy::Promote, deterministic.

Notes

Internally the masks are computed with the operand order reversed relative to MaximumBackward: ge_mask(b, a) and lt_mask(b, a) instead of ge_mask(a, b) / lt_mask(a, b). This yields the same tie resolution (all gradient to a) while flipping the comparison direction. The two masks partition the index set, so their sum is exactly $1$ at every position.

Static methods

static

dispatch

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

source edit

Route the forward computation through the backend's minimum primitive.

Methods

grad_formula

int grad_formula(const int & grad_out)

source edit

Compute the gradients for both inputs given the output gradient.

class

MinimumBackward

MinimumBackward

source edit

Python wrappers

pylucid.ops.minimumfunction

Autograd node for elementwise minimum $y = \min(a, b)$ with NumPy broadcasting.

Math

y_i = \min(a_i, b_i)

\frac{\partial L}{\partial a_i} = \mathbb{1}\{a_i \leq b_i\} \cdot \frac{\partial L}{\partial y_i}

\frac{\partial L}{\partial b_i} = \mathbb{1}\{a_i > b_i\} \cdot \frac{\partial L}{\partial y_i}

Shape

See Also

MaximumBackward : Elementwise maximum (mirror operation).

Attributes

schema_v1OpSchema

"minimum", version 1, AmpPolicy::Promote, deterministic.

Notes

Static methods

static

dispatch

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

source edit

Route the forward computation through the backend's minimum primitive.

Methods

grad_formula

int grad_formula(const int & grad_out)

source edit

Compute the gradients for both inputs given the output gradient.