上一片里，机器人学会了称重和垫底：乘权重、加偏置。可一个机器人做不了大事——把千万个排成一层层流水线，信号从一头进、另一头出。这个一路向前的流程，就叫前向传播。Last leaf, the robot learned to weigh signals and add a bias. One robot can't do much on its own — so stack thousands of them into layer after layer. A signal enters one end and exits the other. That one-way trip is called forward propagation.
第 1 步：信号进厂，一路向前Step 1: The signal enters the factory
输入卡片从左边进厂，先在机床上乘一乘、加一加，再过一道门卫——从这一站出来的，就是下一站的原料。加工完就往前走，绝不回头，所以叫『前向』传播。A card rolls in from the left: it gets multiplied, added to, then passes a gatekeeper — and what comes out of one station becomes the raw material of the next. Finished means moving forward, never back. That's why it's called forward propagation.
那这样一站站推下去，答案真的会自己浮出来吗？So if every station just does its little step, will the answer really surface on its own?
第 2 步：层层接力，数字会走Step 2: Layer by layer, the number moves
亲手推一遍：2 过第一层，按「×3 +1」的规则变成 7；7 再过第二层，按「×2」变成 14。每层规则都由三样东西组成——权重负责乘、偏置负责加、门卫决定放不放行。上一层的输出，就是下一层的输入。Push it yourself: the 2 enters layer one and follows the rule “×3 +1” to become 7; then the 7 enters layer two and follows “×2” to become 14. Every layer's rule is built from three things — weights multiply, the bias adds, and the gatekeeper decides what passes. One layer's output is the next layer's input.
回到真实的网络：一层两层可不够，几百层一起算会是什么样？Back to real networks: one or two layers won't do — what happens when hundreds run together?
第 3 步：几百层的真实网络Step 3: Real networks, hundreds of layers deep
一张猫的图片进来（在机器眼里是一大堆像素数字），穿过几十上百层：低层认出线条和边缘，中层拼出耳朵和胡须，最后一层给出答案——『猫 92%』。层数越多，网络的『深度』越深，这就是深度学习名字的由来。A cat photo goes in (just a pile of pixel numbers to the machine) and flows through dozens or hundreds of layers: early layers spot lines and edges, middle layers piece together ears and whiskers, and the final layer answers “cat 92%”. More layers means more depth — that's where deep learning gets its name.
🎮 你来推流水线（30 秒）🎮 Your turn: push the line (30 seconds)
道理讲完了。按「往前一步」，亲手把数字 2 推过两个站，看看最后出口给出几。Theory done. Hit “One more step” and push the 2 through both stations yourself — see what comes out at the end.
一句话记住它：前向传播 = 信号一路向前：上一层的输出变成下一层的输入，绝不回头。Remember it in one line: forward propagation means a signal travels forward — each layer's output becomes the next layer's input, and it never turns back.
流水线：输入进厂 → 乘一乘、加一加、过门卫 → 出口出答案The line: input enters → multiply, add, pass the gate → the answer exits层层接力：2 →（×3+1）7 →（×2）14，每层只做一小步The relay: 2 → (×3+1) 7 → (×2) 14; each layer takes one small step真实网络：图片进、答案出；层数越多，网络越『深』Real nets: a picture in, an answer out; more layers = more depth
内容参考 OpenStax 等公开教材，多来源核对 · AI 生成、人工审核 · 发现错误欢迎指正，帮这片叶子长得更好。Based on OpenStax and other open textbooks, cross-checked across sources · AI-generated, human-reviewed · Spotted a mistake? Tell us — help this leaf grow.
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