PositiveT

class brainstate.nn.PositiveT

Transformation constraining parameters to be strictly positive (0, +∞).

This is a convenience class that provides a simple positive constraint using the exponential transformation with lower bound of 0.

The transformation is defined by:

\[\text{forward}(x) = e^x\]

The inverse transformation is:

\[\text{inverse}(y) = \log(y)\]

Notes

Important

forward uses save_exp(), which clips the exponent at max_value=20. Inputs with x > 20 saturate at exp(20) ≈ 4.85e8 and the transform is not invertible there; the analytic log_abs_det_jacobian (sum(x)) is only valid in the unclipped region. Keep inputs within roughly [-20, 20].

Examples

>>> transform = PositiveT()
>>> x = jnp.array([-1.0, 0.0, 1.0])
>>> y = transform.forward(x)
>>> # y ≈ [0.368, 1.0, 2.718]

forward(x)

Transform unbounded input to positive values.

Return type:

Array

inverse(y)

Transform positive input back to unbounded domain.

Return type:

Array

log_abs_det_jacobian(x, y)

For exp transform: d/dx[exp(x)] = exp(x), so log|det J| = sum(x).

Return type:

Array