# tf.contrib.distributions.bijectors.Softplus

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| [![](https://www.tensorflow.org/images/GitHub-Mark-32px.png) View source on GitHub](https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/contrib/distributions/python/ops/bijectors/softplus.py#L36-L150) |

Bijector which computes `Y = g(X) = Log[1 + exp(X)]`.

Inherits From: [`Bijector`](https://www.tensorflow.org/versions/r1.15/api_docs/python/tf/contrib/distributions/bijectors/Bijector)

    tf.contrib.distributions.bijectors.Softplus(
        hinge_softness=None, validate_args=False, name='softplus'
    )

The softplus `Bijector` has the following two useful properties:

- The domain is the positive real numbers
- `softplus(x) approx x`, for large `x`, so it does not overflow as easily as the `Exp` `Bijector`.

The optional nonzero `hinge_softness` parameter changes the transition at
zero. With `hinge_softness = c`, the bijector is:

For large `x >> 1`, `c * Log[1 + exp(x / c)] approx c * Log[exp(x / c)] = x`,
so the behavior for large `x` is the same as the standard softplus.

As `c > 0` approaches 0 from the right, `f_c(x)` becomes less and less soft,
approaching `max(0, x)`.

- `c = 1` is the default.
- `c > 0` but small means `f(x) approx ReLu(x) = max(0, x)`.
- `c < 0` flips sign and reflects around the `y-axis`: `f_{-c}(x) = -f_c(-x)`.
- `c = 0` results in a non-bijective transformation and triggers an exception.

  Example Use:

>     # Create the Y=g(X)=softplus(X) transform which works only on Tensors with 1
>     # batch ndim and 2 event ndims (i.e., vector of matrices).
>     softplus = Softplus()
>     x = [[[1., 2],
>           [3, 4]],
>          [[5, 6],
>           [7, 8]]]
>     log(1 + exp(x)) == softplus.forward(x)
>     log(exp(x) - 1) == softplus.inverse(x)

> [!NOTE]
> **Note:** log(.) and exp(.) are applied element-wise but the Jacobian is a reduction over the event space.

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| ## Attributes ||
|---|---|
| `dtype` | dtype of `Tensor`s transformable by this distribution. |
| `forward_min_event_ndims` | Returns the minimal number of dimensions bijector.forward operates on. |
| `graph_parents` | Returns this `Bijector`'s graph_parents as a Python list. |
| `hinge_softness` | <br /> <br /> |
| `inverse_min_event_ndims` | Returns the minimal number of dimensions bijector.inverse operates on. |
| `is_constant_jacobian` | Returns true iff the Jacobian matrix is not a function of x. <br /> > [!NOTE] > **Note:** Jacobian matrix is either constant for both forward and inverse or neither. |
| `name` | Returns the string name of this `Bijector`. |
| `validate_args` | Returns True if Tensor arguments will be validated. |

## Methods

### `forward`

[View source](https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L753-L768)

    forward(
        x, name='forward'
    )

Returns the forward `Bijector` evaluation, i.e., X = g(Y).

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| Args ||
|---|---|
| `x` | `Tensor`. The input to the "forward" evaluation. |
| `name` | The name to give this op. |

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| Returns ||
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| `Tensor`. ||

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| Raises ||
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| `TypeError` | if `self.dtype` is specified and `x.dtype` is not `self.dtype`. |
| `NotImplementedError` | if `_forward` is not implemented. |

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### `forward_event_shape`

[View source](https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L677-L690)

    forward_event_shape(
        input_shape
    )

Shape of a single sample from a single batch as a `TensorShape`.

Same meaning as `forward_event_shape_tensor`. May be only partially defined.

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| Args ||
|---|---|
| `input_shape` | `TensorShape` indicating event-portion shape passed into `forward` function. |

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| Returns ||
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| `forward_event_shape_tensor` | `TensorShape` indicating event-portion shape after applying `forward`. Possibly unknown. |

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### `forward_event_shape_tensor`

[View source](https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L653-L670)

    forward_event_shape_tensor(
        input_shape, name='forward_event_shape_tensor'
    )

Shape of a single sample from a single batch as an `int32` 1D `Tensor`.

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| Args ||
|---|---|
| `input_shape` | `Tensor`, `int32` vector indicating event-portion shape passed into `forward` function. |
| `name` | name to give to the op |

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| Returns ||
|---|---|
| `forward_event_shape_tensor` | `Tensor`, `int32` vector indicating event-portion shape after applying `forward`. |

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### `forward_log_det_jacobian`

[View source](https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L973-L997)

    forward_log_det_jacobian(
        x, event_ndims, name='forward_log_det_jacobian'
    )

Returns both the forward_log_det_jacobian.

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| Args ||
|---|---|
| `x` | `Tensor`. The input to the "forward" Jacobian determinant evaluation. |
| `event_ndims` | Number of dimensions in the probabilistic events being transformed. Must be greater than or equal to `self.forward_min_event_ndims`. The result is summed over the final dimensions to produce a scalar Jacobian determinant for each event, i.e. it has shape `x.shape.ndims - event_ndims` dimensions. |
| `name` | The name to give this op. |

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| Returns ||
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| `Tensor`, if this bijector is injective. If not injective this is not implemented. ||

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| Raises ||
|---|---|
| `TypeError` | if `self.dtype` is specified and `y.dtype` is not `self.dtype`. |
| `NotImplementedError` | if neither `_forward_log_det_jacobian` nor {`_inverse`, `_inverse_log_det_jacobian`} are implemented, or this is a non-injective bijector. |

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### `inverse`

[View source](https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L787-L804)

    inverse(
        y, name='inverse'
    )

Returns the inverse `Bijector` evaluation, i.e., X = g\^{-1}(Y).

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| Args ||
|---|---|
| `y` | `Tensor`. The input to the "inverse" evaluation. |
| `name` | The name to give this op. |

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| Returns ||
|---|---|
| `Tensor`, if this bijector is injective. If not injective, returns the k-tuple containing the unique `k` points `(x1, ..., xk)` such that `g(xi) = y`. ||

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| Raises ||
|---|---|
| `TypeError` | if `self.dtype` is specified and `y.dtype` is not `self.dtype`. |
| `NotImplementedError` | if `_inverse` is not implemented. |

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### `inverse_event_shape`

[View source](https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L721-L734)

    inverse_event_shape(
        output_shape
    )

Shape of a single sample from a single batch as a `TensorShape`.

Same meaning as `inverse_event_shape_tensor`. May be only partially defined.

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| Args ||
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| `output_shape` | `TensorShape` indicating event-portion shape passed into `inverse` function. |

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| Returns ||
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| `inverse_event_shape_tensor` | `TensorShape` indicating event-portion shape after applying `inverse`. Possibly unknown. |

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### `inverse_event_shape_tensor`

[View source](https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L697-L714)

    inverse_event_shape_tensor(
        output_shape, name='inverse_event_shape_tensor'
    )

Shape of a single sample from a single batch as an `int32` 1D `Tensor`.

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| Args ||
|---|---|
| `output_shape` | `Tensor`, `int32` vector indicating event-portion shape passed into `inverse` function. |
| `name` | name to give to the op |

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| Returns ||
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| `inverse_event_shape_tensor` | `Tensor`, `int32` vector indicating event-portion shape after applying `inverse`. |

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### `inverse_log_det_jacobian`

[View source](https://github.com/tensorflow/tensorflow/blob/v1.15.0/tensorflow/python/ops/distributions/bijector_impl.py#L871-L900)

    inverse_log_det_jacobian(
        y, event_ndims, name='inverse_log_det_jacobian'
    )

Returns the (log o det o Jacobian o inverse)(y).

Mathematically, returns: `log(det(dX/dY))(Y)`. (Recall that: `X=g^{-1}(Y)`.)

Note that `forward_log_det_jacobian` is the negative of this function,
evaluated at `g^{-1}(y)`.

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| Args ||
|---|---|
| `y` | `Tensor`. The input to the "inverse" Jacobian determinant evaluation. |
| `event_ndims` | Number of dimensions in the probabilistic events being transformed. Must be greater than or equal to `self.inverse_min_event_ndims`. The result is summed over the final dimensions to produce a scalar Jacobian determinant for each event, i.e. it has shape `y.shape.ndims - event_ndims` dimensions. |
| `name` | The name to give this op. |

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| Returns ||
|---|---|
| `Tensor`, if this bijector is injective. If not injective, returns the tuple of local log det Jacobians, `log(det(Dg_i^{-1}(y)))`, where `g_i` is the restriction of `g` to the `ith` partition `Di`. ||

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| Raises ||
|---|---|
| `TypeError` | if `self.dtype` is specified and `y.dtype` is not `self.dtype`. |
| `NotImplementedError` | if `_inverse_log_det_jacobian` is not implemented. |

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