Sigmoid

Activation series · 2 of 12

Apr 30, 2026

Activation › Sigmoid

Sigmoid squashes any real number into a probability between 0 and 1: the classic activation for binary classification, and still the gating function inside LSTMs and GRUs.

QQ Activation (2 of 3)

When a new boba shop opens, I'd go try it. After the first cup, the question hits: what's the chance I'll come back? It depends on how the new shop stacks up against my baseline: the average shop back in Taiwan, chewiness zero on my QQ scale.

Now imagine you're in the same spot. You try a new shop and mentally apply the same QQ scale, giving the new place a score `x`, with your baseline (whatever you've calibrated to) sitting at chewiness zero. What's the chance you'll come back?

Sigmoid turns that single x into a probability between 0 and 1: the chance the new place earns a return visit. It's softmax narrowed to just two options: the new shop on one side, the average of everyone else on the other.

Walking through the Math

1. Input: the new shop's chewiness x and the fixed baseline 0 for the usual.

2. Exp: exponentiate both, eˣ and e⁰ = 1.

3. Sum: total Z = eˣ + 1.

4. Sigmoid: probability P = eˣ / Z for the new shop, 1 − P for the usual.

The two probabilities add up to one. The new shop earns a higher chance of your next visit when its pearls get chewier; your usual keeps the rest. Sigmoid turns one chewiness score into a clean 0-to-1 odds of trying the new place.

Reading the Numbers

What does sigmoid forecast across the QQ scale?

| chewiness x | meaning | σ(x) | what it says about your next visit |
|---|---|---|---|
| +3 | perfect QQ | 0.95 | almost certain return |
| +2 | very chewy | 0.88 | very likely |
| +1 | pleasantly ch

Notice sigmoid never says "definitely yes" or "definitely no" — even at chewiness +3, there's a 5% chance you don't return (you got busy, the shop closed early). And even at chewiness -3, there's a 5% chance you do (you happened to be in the area). That bounded honesty is sigmoid's signature.