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.
tfb_softplus( hinge_softness = NULL, low = NULL, validate_args = FALSE, name = "softplus" )
| hinge_softness | Nonzero floating point Tensor. Controls the softness of what would otherwise be a kink at the origin. Default is 1.0. |
|---|---|
| low | Nonzero floating point tensor, lower bound on output values.
Implicitly zero if |
| validate_args | Logical, default FALSE. Whether to validate input with asserts. If validate_args is FALSE, and the inputs are invalid, correct behavior is not guaranteed. |
| name | name prefixed to Ops created by this class. |
a bijector instance.
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.
Note: log(.) and exp(.) are applied element-wise but the Jacobian is a reduction over the event space.
[1 + exp(x / c)]: R:1%20+%20exp(x%20/%20c)
[1 + exp(x / c)]: R:1%20+%20exp(x%20/%20c)
[exp(x / c)]: R:exp(x%20/%20c)
For usage examples see tfb_forward(), tfb_inverse(), tfb_inverse_log_det_jacobian().
Other bijectors:
tfb_absolute_value(),
tfb_affine_linear_operator(),
tfb_affine_scalar(),
tfb_affine(),
tfb_ascending(),
tfb_batch_normalization(),
tfb_blockwise(),
tfb_chain(),
tfb_cholesky_outer_product(),
tfb_cholesky_to_inv_cholesky(),
tfb_correlation_cholesky(),
tfb_cumsum(),
tfb_discrete_cosine_transform(),
tfb_expm1(),
tfb_exp(),
tfb_ffjord(),
tfb_fill_scale_tri_l(),
tfb_fill_triangular(),
tfb_glow(),
tfb_gompertz_cdf(),
tfb_gumbel_cdf(),
tfb_gumbel(),
tfb_identity(),
tfb_inline(),
tfb_invert(),
tfb_iterated_sigmoid_centered(),
tfb_kumaraswamy_cdf(),
tfb_kumaraswamy(),
tfb_lambert_w_tail(),
tfb_masked_autoregressive_default_template(),
tfb_masked_autoregressive_flow(),
tfb_masked_dense(),
tfb_matrix_inverse_tri_l(),
tfb_matvec_lu(),
tfb_normal_cdf(),
tfb_ordered(),
tfb_pad(),
tfb_permute(),
tfb_power_transform(),
tfb_rational_quadratic_spline(),
tfb_rayleigh_cdf(),
tfb_real_nvp_default_template(),
tfb_real_nvp(),
tfb_reciprocal(),
tfb_reshape(),
tfb_scale_matvec_diag(),
tfb_scale_matvec_linear_operator(),
tfb_scale_matvec_lu(),
tfb_scale_matvec_tri_l(),
tfb_scale_tri_l(),
tfb_scale(),
tfb_shifted_gompertz_cdf(),
tfb_shift(),
tfb_sigmoid(),
tfb_sinh_arcsinh(),
tfb_sinh(),
tfb_softmax_centered(),
tfb_softsign(),
tfb_split(),
tfb_square(),
tfb_tanh(),
tfb_transform_diagonal(),
tfb_transpose(),
tfb_weibull_cdf(),
tfb_weibull()