class

SumBackward

SumBackward

source edit

Python wrappers

pylucid.ops.sumfunction

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

The gradient broadcasts unchanged from the reduced shape back to the input shape because $\partial y / \partial x_i = 1$ for every element participating in the sum. kSavesInput = false and no output is saved — the rule is independent of both the forward input and output.

Math

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

Attributes

schema_v1OpSchema

Registered as "sum" with AmpPolicy::Promote — integer and boolean inputs are promoted to int64 before reduction so the sum cannot overflow narrow integer dtypes (parity fix found during the M4 Max training sanity check, where bool.sum() previously dropped to any() semantics on GPU).

kSavesInputbool

false. Backward depends only on shape metadata.

Notes

Dispatch: Accelerate strided reductions (CPU) / MLX sum (GPU). For empty reductions the output is $0$ (additive identity).

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_sum.

Methods

grad_formula

int grad_formula(const int & grad_out)

source edit

Backward — broadcasts grad_out back to the input shape (ones gradient).

scale_graph_grad

int scale_graph_grad(const int & g)

source edit

Graph-mode scaling helper — sum requires no scaling, so the broadcast-expanded gradient is returned unchanged.

class

SumBackward

SumBackward

source edit

Python wrappers

pylucid.ops.sumfunction

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

Math

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

Attributes

schema_v1OpSchema

kSavesInputbool

false. Backward depends only on shape metadata.

Notes

Dispatch: Accelerate strided reductions (CPU) / MLX sum (GPU). For empty reductions the output is $0$ (additive identity).

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_sum.

Methods

grad_formula

int grad_formula(const int & grad_out)

source edit

Backward — broadcasts grad_out back to the input shape (ones gradient).

scale_graph_grad

int scale_graph_grad(const int & g)

source edit

Graph-mode scaling helper — sum requires no scaling, so the broadcast-expanded gradient is returned unchanged.