Sigmoid

Quantized lucid.nn.Sigmoid — sigmoid(x) then output fake-quant.

The inference-time replacement for a calibrated float nn.Sigmoid sitting inside a quantized region, installed by lucid.quantization.convert / from_float. Under the sidecar representation (design B) a quantized activation is simply the float activation followed by a fake-quantize to the calibrated output grid, so a standalone sigmoid is requantized rather than left at full precision between two int8 layers.

Because $\sigma(x) \in [0, 1]$ the output range is known a priori, this is the archetypal fixed-qparams activation: instead of calibrating the range from data, pair it with a lucid.quantization.FixedQParamsObserver in the qconfig, which pins the grid to the constant $[0, 1]$ mapping.

so the quint8 codes 0 .. 255 tile $[0, 1]$ uniformly with step $S$. $\operatorname{fake\_quant}(t) = (\operatorname{clamp}( \operatorname{round}(t/S) + Z, q_{\min}, q_{\max}) - Z)\, S$.