class

MeanBackward

MeanBackward

source edit

Python wrappers

pylucid.ops.meanfunction

Autograd node for the multi-axis reduction mean $y = \frac{1}{N} \sum_{i \in \text{axes}} x_i$ .

Backward broadcasts the upstream gradient back to the input shape and divides by $N$ , the product of the reduced dimension sizes.

Math

y = \frac{1}{N} \sum_{i \in \text{axes}} x_i, \qquad \frac{\partial \mathcal{L}}{\partial x_i} = \frac{1}{N}\,\mathrm{broadcast}\!\left( \frac{\partial \mathcal{L}}{\partial y}\right).

Attributes

schema_v1OpSchema

Registered as "mean" with AmpPolicy::Promote.

kSavesInputbool

false. Backward depends only on

N

and shape metadata.

Notes

Dispatch: Accelerate kernel (CPU) / MLX mean (GPU). Empty reductions return NaN ( $0/0$ ).

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_mean.

Methods

grad_formula

int grad_formula(const int & grad_out)

source edit

Backward — broadcasts $\mathrm{grad\_out} / N$ back to input shape.

scale_graph_grad

int scale_graph_grad(const int & g)

source edit

Graph-mode mean backward: divides the broadcast-expanded gradient by the number of reduced elements so second-order graphs flow through the division correctly.

class

MeanBackward

MeanBackward

source edit

Python wrappers

pylucid.ops.meanfunction

Autograd node for the multi-axis reduction mean $y = \frac{1}{N} \sum_{i \in \text{axes}} x_i$ .

Backward broadcasts the upstream gradient back to the input shape and divides by $N$ , the product of the reduced dimension sizes.

Math

y = \frac{1}{N} \sum_{i \in \text{axes}} x_i, \qquad \frac{\partial \mathcal{L}}{\partial x_i} = \frac{1}{N}\,\mathrm{broadcast}\!\left( \frac{\partial \mathcal{L}}{\partial y}\right).

Attributes

schema_v1OpSchema

Registered as "mean" with AmpPolicy::Promote.

kSavesInputbool

false. Backward depends only on

N

and shape metadata.

Notes

Dispatch: Accelerate kernel (CPU) / MLX mean (GPU). Empty reductions return NaN ( $0/0$ ).

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_mean.

Methods

grad_formula

int grad_formula(const int & grad_out)

source edit

Backward — broadcasts $\mathrm{grad\_out} / N$ back to input shape.

scale_graph_grad

int scale_graph_grad(const int & g)

source edit

Graph-mode mean backward: divides the broadcast-expanded gradient by the number of reduced elements so second-order graphs flow through the division correctly.