逐层应用链式法则
在网络中组合各层的导数
逐层应用链式法则 是 CoddyKit 上的免费 Deep Learning Academy 课时。 这是第 1 节课，共 4 节。 你可以在下方免费阅读本课时的完整内容 — 然后在浏览器中使用内置代码编辑器和全天候 AI 导师进行实践。 这是 Deep Learning Academy 学习路径的一部分，你的进度在网页和 CoddyKit 应用中同步。 Deep Learning Academy 课程共包含 4 节课。
本课时的部分内容尚未翻译，以英文显示。
A Net Is Nested Functions
A neural network is just functions wrapped inside functions: each layer feeds its output into the next. Backprop needs the derivative of that whole stack.
The Chain Rule in One Line
The chain rule says the derivative of nested functions multiplies the derivatives of each piece. That single fact is the engine behind all of backprop. ⛓️
dy/dx = dy/du * du/dxA Tiny Composition
Say z depends on y, and y depends on x. To get how z changes with x, you multiply dz/dy by dy/dx. Each link passes its slope along.
Layers Are Links in a Chain
Every layer is one link. The loss sits at the far end, the input at the near end, and gradients flow back link by link as a chain of multiplications.
Start From the Loss
Backprop begins at the loss and asks: how does loss change if this layer output nudges a bit? That answer is the first derivative in the chain.
Pass the Gradient Backward
Each layer receives the gradient from the layer above, multiplies by its own local derivative, and hands the result to the layer below.
grad_below = grad_above * local_derivativeLocal Derivative of a Layer
A layer only needs to know its own local derivative: how its output changes with its input and weights. It never needs the whole network at once.
Weights Get Their Own Gradient
At each layer the incoming gradient also tells you how the loss changes with that layer's weights. That is exactly what the optimizer will use to update them.
Why Order Matters
You multiply derivatives in reverse order, from loss back to input. Going forward computes values; going backward computes how to improve them.
It Scales to Any Depth
Add ten more layers and nothing changes: you just multiply ten more local derivatives into the chain. Depth is no problem for the chain rule.
The Whole Idea, Compressed
Backprop is the chain rule applied layer by layer, from the loss back to the inputs, multiplying local slopes to find each weight's gradient.
Quick Check
Let's check the core rule.
Recap
A network is nested functions, so its derivative is a chain of multiplied local slopes. Backprop walks that chain from loss back to input. ⛓️
常见问题解答
「逐层应用链式法则」课时是免费的吗？
是的 — 「逐层应用链式法则」的完整文本可在网页上免费阅读。要进行交互式练习（内置代码编辑器和全天候 AI 导师）并解锁 Deep Learning Academy 课程的其余内容，请升级到 CoddyKit PRO。 Deep Learning Academy 课程共包含 4 节课。
「逐层应用链式法则」这节课中我会学到什么？
在网络中组合各层的导数 你通过在浏览器中直接运行的动手代码来练习 Deep Learning Academy，全天候 AI 导师会在你学习这节课的过程中回答你的问题。
学习 Deep Learning Academy 需要有经验吗？
无需任何先前经验。CoddyKit 上的 Deep Learning Academy 课程适合初学者到高级学习者，你可以从这里开始或从头开始，按照自己的节奏学习。 这是第 1 节课，共 4 节。
「逐层应用链式法则」课时需要多长时间？
大多数 CoddyKit 课程大约需要 5–10 分钟。每节课都很精短且互动，所以你能稳步进步，并在网页和应用中从离开的地方继续。
我能在这节 Deep Learning Academy 课中编写并运行代码吗？
能。每节 Deep Learning Academy 课都包含内置代码编辑器，你可以在浏览器中直接编写并运行真实代码，并获得即时 AI 反馈 — 无需本地设置。