# SoftmaxTransform¶

Softmax transformation with mapping \(y=\exp(x)\) then normalizing.

It’s generally used to convert unconstrained space to simplex. This mapping is not injective, so `forward_log_det_jacobian` and `inverse_log_det_jacobian` are not implemented.

Examples

```>>> import paddle

>>> print(t.forward(x))
[[0.33333334, 0.33333334, 0.33333334],
[0.33333334, 0.33333334, 0.33333334]])
>>> print(t.inverse(t.forward(x)))
[[-1.09861231, -1.09861231, -1.09861231],
[-1.09861231, -1.09861231, -1.09861231]])
```
forward ( x )

Forward transformation with mapping \(y = f(x)\).

Useful for turning one random outcome into another.

Parameters

x (Tensor) – Input parameter, generally is a sample generated from `Distribution`.

Returns

Outcome of forward transformation.

Return type

Tensor

forward_log_det_jacobian ( x )

The log of the absolute value of the determinant of the matrix of all first-order partial derivatives of the inverse function.

Parameters

x (Tensor) – Input tensor, generally is a sample generated from `Distribution`

Returns

The log of the absolute value of Jacobian determinant.

Return type

Tensor

forward_shape ( shape )

Infer the shape of forward transformation.

Parameters

shape (Sequence[int]) – The input shape.

Returns

The output shape.

Return type

Sequence[int]

inverse ( y )

Inverse transformation \(x = f^{-1}(y)\). It’s useful for “reversing” a transformation to compute one probability in terms of another.

Parameters

y (Tensor) – Input parameter for inverse transformation.

Returns

Outcome of inverse transform.

Return type

Tensor

inverse_log_det_jacobian ( y )

Compute \(log|det J_{f^{-1}}(y)|\). Note that `forward_log_det_jacobian` is the negative of this function, evaluated at \(f^{-1}(y)\).

Parameters

y (Tensor) – The input to the `inverse` Jacobian determinant evaluation.

Returns

The value of \(log|det J_{f^{-1}}(y)|\).

Return type

Tensor

inverse_shape ( shape )

Infer the shape of inverse transformation.

Parameters

shape (Sequence[int]) – The input shape of inverse transformation.

Returns

The output shape of inverse transformation.

Return type

Sequence[int]