S2-07 · 基础S2-07 · Foundation

神经元 · 把三路信号汇成一个输出Artificial Neuron · Combine Three Signals into One Output

inputs × weights → weighted sum → activation → output

人工神经元是对输入做加权求和并经过激活函数的最小计算单元。它不是会思考的细胞,而是一段清楚的乘、加、开关计算。An artificial neuron is a small computation that forms a weighted sum of inputs and passes it through an activation. It is not a thinking cell; it is explicit multiply, add, and gate logic.

01 · 三票不会同权01 · Three votes need not count equally

三个信号一起投票时,为什么一票能推亮灯,另一票却把结果往回拉?When three signals vote together, why can one push the lamp on while another pulls the result back?

02三路输入神经元Three-Input Neuron

乘加过阈值Multiply, add, threshold
加权和 zWeighted sum z
Σ xiwi
阈值Threshold
0.60
必须严格超过must strictly exceed
输出灯Output lamp
activation(z)

每条边显示自己的乘积。试着把某个权重变成负数:它会把加权和往反方向拉。Each edge shows its product. Make one weight negative and watch it pull the weighted sum in the opposite direction.

03神经元里的 4 个零件Four Parts Inside a Neuron

乘 · 加 · 开关Multiply · add · gate
PART 01

输入Inputs

x1、x2、x3 是进入单元的三路数值。x1, x2, and x3 are incoming values.

PART 02

权重Weights

w 决定每路信号的方向与影响强度。Each w sets a signal's direction and influence.

PART 03

加权和Weighted sum

三个乘积在汇总槽里加成 z。The three products add into z in the sum slot.

PART 04

激活输出Activated output

阈值函数把 z 变成灯亮或灯灭。The threshold function turns z into lamp on or off.

04最小机制:先逐路乘,再统一加Minimal Mechanism: Multiply Each Path, Then Add

y = f(Σ xiwi)
z = x1w1 + x2w2 + x3w3; y = step(z)
上方每条边标出一个乘积,汇总槽显示 z,灯显示 step(z > 0.60)。三处读数可以逐项核对。Every edge above shows a product, the sum slot shows z, and the lamp shows step(z > 0.60). You can verify the calculation term by term.
改变输入或权重Change x or w对应乘积改变Its product changes
乘积相加Add products汇总槽得到新 zThe slot gets a new z
检查阈值Check threshold过线后灯才翻转Lamp flips only after crossing

05边界实验:把所有权重清零Boundary Test: Zero Every Weight

主动制造失败Create a failure

输入全开,影响全无Full inputs, zero influence

把三路输入都设成 1,却把权重全部设成 0。信号再大,乘积仍为 0,灯不会亮。Set every input to one but every weight to zero. No matter how large the inputs are, every product remains zero and the lamp stays off.

尚未执行。当前三路权重并不相同。Not run yet. The current three weights differ.
神经元会理解输入的含义。A neuron understands what inputs mean. → ✓ 它只执行确定的乘、加和激活计算。It performs fixed multiply, add, and activation operations.
输入大就一定影响大。A large input always has a large effect. → ✓ 实际影响由输入与权重的乘积决定。Actual influence is the input-weight product.
只要有正输入,输出灯就会亮。Any positive input turns the lamp on. → ✓ 所有加权项相加后还必须越过激活门槛。The full weighted sum must still cross the activation threshold.
06 · 一句话带走06 · One line to keep

人工神经元把输入逐路乘权重、相加,再经过激活函数产生输出;拖动任一路 x 或 w,就能核对乘积、加权和与灯的因果链。An artificial neuron multiplies inputs by weights, adds them, then applies an activation. Move any x or w to verify the chain from product to weighted sum to lamp.