hardsigmoid

→Tensor

hardsigmoid(x: Tensor)

source

Hard sigmoid — piecewise linear approximation of sigmoid.

Avoids the cost of an exponential by clipping a scaled-and-shifted identity to $[0, 1]$ . Widely used as the gating function inside quantised mobile networks (MobileNetV3 Squeeze-and-Excitation blocks).

Parameters

xTensor

Input tensor of any shape; activation is element-wise.

Returns

Tensor

Activated tensor with the same shape as x, values in $[0, 1]$ .

Notes

\text{HardSigmoid}(x) = \begin{cases} 0 & x \le -3 \\ x/6 + 1/2 & -3 < x < 3 \\ 1 & x \ge 3 \end{cases}

Matches sigmoid exactly at $x = 0$ (both return 0.5) but is only piecewise-linear. Derivative is $1/6$ in the linear region and $0$ in the saturated regions.

Examples

>>> import lucid
>>> from lucid.nn.functional import hardsigmoid
>>> x = lucid.tensor([-4.0, -1.0, 0.0, 1.0, 4.0])
>>> hardsigmoid(x)
Tensor([0.0000, 0.3333, 0.5000, 0.6667, 1.0000])