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convert second table
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breandan committed Apr 11, 2023
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Expand Up @@ -147,11 +147,11 @@ Kotlin∇ operators are [higher-order functions](https://en.wikipedia.org/wiki/H

Kotlin∇ supports derivatives between tensors of up to rank 2. The shape of a tensor derivative depends on (1) the shape of the function under differentiation and (2) the shape of the variable with respect to which we are differentiating.

| I/O Shape | ℝ<sup>?</sup>→ℝ | ℝ<sup>?</sup>→ℝ<sup>m</sup> | ℝ<sup>?</sup>→ℝ<sup>j×k</sup> |
|:------------------------------------:|:-----------------------------:|:-----------------------------:|:-----------------------------:|
| <b>ℝ<sup>?</sup>→ℝ</b> | ℝ<sup>?</sup>→ℝ | ℝ<sup>?</sup>→ℝ<sup>m</sup> | ℝ<sup>?</sup>→ℝ<sup>j×k</sup> |
| <b>ℝ<sup>?</sup>→ℝ<sup>n</sup></b> | ℝ<sup>?</sup>→ℝ<sup>n</sup> | ℝ<sup>?</sup>→ℝ<sup>m×n</sup> | :x: |
| <b>ℝ<sup>?</sup>→ℝ<sup>h×i</sup></b> | ℝ<sup>?</sup>→ℝ<sup>h×i</sup> | :x: | :x: |
| I/O Shape | $$ℝ^{?}→ℝ$$ | $$ℝ^{?}→ℝ^{m}$$ | $$ℝ^{?}→ℝ^{j×k}$$ |
|:-----------------:|:-----------------:|:------------------:|:-----------------:|
| $$ℝ^{?}→ℝ$$ | $$ℝ^{?}→ℝ$$ | $$ℝ^{?}→ℝ^{m}$$ | $$ℝ^{?}→ℝ^{j×k}$$ |
| $$ℝ^{?}→ℝ^{n}$$ | $$ℝ^{?}→ℝ^{n}$$ | $$ℝ^{?}→ℝ^{m×n}$$ | :x: |
| $$ℝ^{?}→ℝ^{h×i}$$ | $$ℝ^{?}→ℝ^{h×i}$$ | :x: | :x: |

Matrix-by-vector, vector-by-matrix, and matrix-by-matrix derivatives require rank 3+ tensors and are currently unsupported.

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