---
library_name: kernels
license: apache-2.0
tags:
- kernel
- webgpu
- wgsl
---
# ai.onnx.ReduceSumSquare

`ai.onnx`  ·  standard ONNX operator  ·  ONNX opset ≥ 18

## Description

Computes the sum of squared elements of the input tensor along the specified axes. The output rank matches the input if `keepdims` is 1; otherwise the reduced dimensions are pruned. Reduction over an empty set of values yields 0.

See the [ONNX `ReduceSumSquare` spec](https://onnx.ai/onnx/operators/onnx__ReduceSumSquare.html) for the reference semantics.

## Inputs

| Name | Bind key | Logical dtype | Rank | Shape | Description | Presence |
| --- | --- | --- | --- | --- | --- | --- |
| `data` | `x` | `T` | — | — | The input tensor to reduce. | required |

## Outputs

| Name | Bind key | Logical dtype | Rank | Shape | Description | Presence |
| --- | --- | --- | --- | --- | --- | --- |
| `reduced` | `y` | `T` | derived | — | The reduced output tensor containing the sum of squares. | required |

## Attributes

Default values (overridable per request):

| Attribute | Default | Description |
| --- | --- | --- |
| `keepdims` | `1` | If 1 (default in spec), retain the reduced dimensions with size 1; if 0, remove them. |
| `noop_with_empty_axes` | `0` | If 1 and axes is empty, acts as a no-op that squares each element without reducing; if 0 (default), reduces over all axes when axes is empty. |
| `axes` | `[]` | Values of the optional ONNX `axes` tensor input, supplied through this request attribute; an empty list follows `noop_with_empty_axes`. |

## Type constraints

| Variable | Allowed dtypes |
| --- | --- |
| `T` | `float32`, `float16`, `int32` |

## Device requirements

Some implementation variants require `subgroups`. These are route-specific capabilities, not package-wide requirements; availability also depends on the request shape and dtype.

## Files

- [`metadata.json`](build/webgpu/metadata.json) — kernel metadata (id, digests, provenance)
- [`manifest.json`](build/webgpu/manifest.json) — the op contract (source of truth)
- [`test.json`](build/webgpu/test.json) — correctness cases
- [`bench.json`](build/webgpu/bench.json) — benchmark + tuning cases
- [`reduce-axis-split-reduce.wgsl.jinja`](build/webgpu/reduce-axis-split-reduce.wgsl.jinja)
- [`reduce-axis0-splitk-combine.wgsl.jinja`](build/webgpu/reduce-axis0-splitk-combine.wgsl.jinja)
- [`reduce-axis0-splitk-reduce.wgsl.jinja`](build/webgpu/reduce-axis0-splitk-reduce.wgsl.jinja)
- [`reduce-axis0-tilecols.wgsl.jinja`](build/webgpu/reduce-axis0-tilecols.wgsl.jinja)
- [`reduce-flat-partial.wgsl.jinja`](build/webgpu/reduce-flat-partial.wgsl.jinja)
- [`reduce-noop-empty-axes.wgsl.jinja`](build/webgpu/reduce-noop-empty-axes.wgsl.jinja)
- [`reduce-row-subgroup.wgsl.jinja`](build/webgpu/reduce-row-subgroup.wgsl.jinja)
- [`reduce-row-tree.wgsl.jinja`](build/webgpu/reduce-row-tree.wgsl.jinja)
- [`reduce-serial-axis.wgsl.jinja`](build/webgpu/reduce-serial-axis.wgsl.jinja)

## Use with `@huggingface/kernels`

The loader automatically allocates outputs whose metadata it can derive from the manifest contract and this call.

The explicit `outputs` entries provide shape and logical dtype metadata for the results listed below:

- `y`

Each entry either requests an optional result or supplies metadata that cannot be inferred from the inputs.

The `version: 1` option selects the published kernel contract; it is independent of any operator opset, contrib `since_version`, or model version.

Replace each `*Data` placeholder with a typed array containing the corresponding input data.

```js
import { getKernel } from "@huggingface/kernels";

const kernel = await getKernel("webgpu-kernels/ai.onnx.ReduceSumSquare", { version: 1 });
// Explicit destinations request optional results or supply metadata that cannot be inferred.
const { y } = await kernel({ x: { data: xData, shape: [] } }, {
  outputs: { y: { shape: [], dtype: "float32" } },
});
```