Type Softplus
Namespace tensorflow.contrib.distributions.bijectors
Parent Bijector
Interfaces ISoftplus
Bijector which computes `Y = g(X) = Log[1 + exp(X)]`. 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: ```f_c(x) := c * g(x / c) = c * Log[1 + exp(x / c)].``` 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:
Note: log(.) and exp(.) are applied element-wise but the Jacobian is a
reduction over the event space.
Show Example
# 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)