The trunk’s summit · how an AI decides
scores → %
This is the exact moment an AI makes up its mind. It doesn’t “know” anything — it scores its options, then runs one little recipe to turn those scores into a confident choice. That recipe has a name: softmax. And it’s built entirely from rungs you’ve already climbed.
Why this quietly runs your life
Your phone finishing your sentence. A photo app tagging your dog. A spam filter binning junk mail. A self-driving car choosing brake over swerve. Every one of those is an AI hitting this exact moment — score the options, then pick with confidence. There’s no separate “decide” button hiding in there. Softmax is the decide button, and it’s just arithmetic you already know.
An AI doesn’t “know.” It scores.
Show a neural net a photo and it doesn’t announce “cat!” It spits out raw scores — say cat 3, dog 5, bird 1. Just numbers. Bigger means “more likely,” but they’re not percentages, they can be negative, and they don’t add up to anything tidy. The net needs to turn this pile of scores into an actual decision with confidence.
Step 1: make every score positive and bold — with eˣ
Remember e from last rung? Feed each score through eˣ and two magic things happen: every score becomes positive (even negative ones), and the leader gets exaggerated — because e⁵ towers over e³. The confident option pulls ahead.
Step 2: divide each by the total → shares of 100%
Add up all those eˣ values, then divide each one by the total. Now they’re shares that add up to exactly 100% — a confidence for each option. That’s the whole recipe. That’s softmax. Play with the scores and watch the decision form:
That flash of the biggest bar? That’s the decision.
The tallest share is the AI’s answer — and how tall tells you how sure it is. When you type to a chatbot, every single word it writes is a softmax over ~50,000 word-scores: eˣ, divide by the total, pick from the shares. “Making up its mind” isn’t magic — it’s this exact division, done blindingly fast.
You just finished the whole trunk
Look how far the escalator came: + gave you multiply, × gave you powers, powers gave you the exponential and e, and e just gave you a decision.
count · combine · repeat · grow continuously · decide
Next you leave the number line and ask the other half of the question: where do those scores even come from? That’s space, arrows, and machines — the rest of the map, right up to the Transformer.
Prove it · get one wrong and I’ll walk you through it
Two quick ones and the trunk is yours.
Softmax turns a pile of raw scores into…
Why run every score through eˣ first?
Answer both to finish the trunk ↓
Softmax — mastered. Trunk complete.
You just watched an AI “make up its mind” — and it was nothing but eˣ and division, both yours already. Five rungs, one clean escalator: + → × → ^ → e → decide. Next module: Space — where those scores are born.
Next module → Space (coordinates, arrows, similarity)