class

TanhTransform

extendsTransform

TanhTransform()

source edit

Element-wise hyperbolic tangent bijection $y = \tanh(x)$ .

Maps $\mathbb{R} \to (-1, 1)$ element-wise. Commonly used in reinforcement learning to push a Normal policy through tanh so actions live in a bounded box (SAC and friends). Monotone increasing, bijective, event_dim = 0.

Notes

Forward: $y = \tanh(x)$ .

Inverse: $x = \tfrac{1}{2}\log\!\bigl((1+y)/(1-y)\bigr)$ (the inverse hyperbolic tangent).

Log Jacobian determinant (numerically stable form):

\log\!\left|\frac{\partial y}{\partial x}\right| = \log\bigl(1 - \tanh^2(x)\bigr) = 2 \bigl(\log 2 - x - \operatorname{softplus}(-2x)\bigr)

This formulation avoids overflow / underflow when $|x|$ is large, which the naive form $\log(1 - \tanh^2 x)$ would suffer (since $\tanh(x) \to \pm 1$ ).

Examples

>>> import lucid
>>> from lucid.distributions.transforms import TanhTransform
>>> T = TanhTransform()
>>> T(lucid.tensor(0.0))  # tanh(0) = 0
Tensor(0.0)

Used by 1

lucid.distributions

Instance methods

log_abs_det_jacobian

→Tensor

log_abs_det_jacobian(x: Tensor, y: Tensor)

source edit

Numerically-stable $\log(1 - \tanh^2(x))$ .

Computed as $2\bigl(\log 2 - x - \operatorname{softplus}(-2x)\bigr)$ — the stable form used by the reference framework that avoids the catastrophic log(1 - 1) cancellation when |x| is large.

Parameters

xTensor

Pre-transform input.

yTensor

Post-transform output (tanh(x)); ignored — the log-Jacobian is expressed in x.

Returns

Tensor

Same shape as x.

class

TanhTransform

extendsTransform

TanhTransform()

source edit

Element-wise hyperbolic tangent bijection $y = \tanh(x)$ .

Notes

Forward: $y = \tanh(x)$ .

Inverse: $x = \tfrac{1}{2}\log\!\bigl((1+y)/(1-y)\bigr)$ (the inverse hyperbolic tangent).

Log Jacobian determinant (numerically stable form):

\log\!\left|\frac{\partial y}{\partial x}\right| = \log\bigl(1 - \tanh^2(x)\bigr) = 2 \bigl(\log 2 - x - \operatorname{softplus}(-2x)\bigr)

This formulation avoids overflow / underflow when $|x|$ is large, which the naive form $\log(1 - \tanh^2 x)$ would suffer (since $\tanh(x) \to \pm 1$ ).

Examples

>>> import lucid
>>> from lucid.distributions.transforms import TanhTransform
>>> T = TanhTransform()
>>> T(lucid.tensor(0.0))  # tanh(0) = 0
Tensor(0.0)

Used by 1

lucid.distributions

Instance methods

log_abs_det_jacobian

→Tensor

log_abs_det_jacobian(x: Tensor, y: Tensor)

source edit

Numerically-stable $\log(1 - \tanh^2(x))$ .

Computed as $2\bigl(\log 2 - x - \operatorname{softplus}(-2x)\bigr)$ — the stable form used by the reference framework that avoids the catastrophic log(1 - 1) cancellation when |x| is large.

Parameters

xTensor

Pre-transform input.

yTensor

Post-transform output (tanh(x)); ignored — the log-Jacobian is expressed in x.

Returns

Tensor

Same shape as x.