Neural Network Layer

01 · 像面团过压面机 01 · Like dough through rollers

同一批点每过一道机器，为什么形状会变，数量却可以不变？ Why can the same points change shape after each machine while their count stays fixed?

02 逐层推动固定点云 Advance a Fixed Point Cloud

逐层变换型 Layer-by-layer

已通过 Passed

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层 layers

点的数量 Point count

保持不变 unchanged

当前形状 Current shape

[6 × 2]

点云代表一批输入表示；画面只演示“层会变换表示”，不对应某个真实网络。 The cloud stands for a batch of representations. This only demonstrates that layers transform representations; it is not a real network.

03 一层里的 3 个零件 Three Parts Inside a Layer

并行处理整批 Batch in parallel

PART 01

一批输入 Input batch

6 个点一起进入，每个点都是一个二维表示。 Six points enter together; each point is a two-dimensional representation.

PART 02

共享变换 Shared transform

同一层用同一套规则并行处理这一批点。 The layer applies the same rule across the batch in parallel.

PART 03

一批输出 Output batch

点的位置改变，形成供下一层继续处理的新表示。 Point positions change into new representations for the next layer.

CHECK

形状标签 Shape labels

[6 × 2] 表示 6 个对象、每个对象 2 个分量。 [6 × 2] means six objects with two components each.

04 最小机制：输出成为下一层输入 Minimal Mechanism: Output Becomes the Next Input

H^(l+1) = f(H^(l)W^(l) + b^(l))

[6 × 2] → layer → [6 × 2]

这里让宽度保持为 2，方便盯住形状变化；真实层也可以改变表示维度。 Width stays at 2 here so the shape change is easy to see. A real layer may also change representation width.

读取一批表示 Read a batch 当前点坐标进入层 Current coordinates enter

并行应用规则 Apply one rule 每个点都被变换 Every point transforms

交给下一层 Hand off output 新坐标成为新输入 New coordinates become input

05 边界实验：跳过中间层 Boundary Test: Skip the Middle Layer

主动制造失败 Create a failure

后一层没有预期输入 The later layer lacks its expected input

从原始点云直接索要第 3 层结果。第 3 层本来应该读取第 2 层输出，因果链因此断开。 Demand layer 3 output directly from the original cloud. Layer 3 expected layer 2 output, so the causal chain breaks.

尚未执行。按顺序通过每一层。 Not run yet. Pass through each layer in order.

✗ 层只是数据停靠的盒子。 A layer is only a storage box. → ✓ 层对表示执行一次变换。 A layer performs one transformation.

✗ 一层只处理一个点。 A layer handles one point only. → ✓ 一组单元可并行处理一批表示。 A set of units can process a batch in parallel.

✗ 可以越层拿到中间结果。 Intermediate layers can be skipped. → ✓ 后一层读取前一层的输出。 Each later layer reads the prior output.

06 · 一句话带走 06 · One line to keep

网络层用一组并行计算把一批输入表示变成下一批表示；逐层点击，就能检验输出如何接成下一层输入。 A neural network layer uses parallel computation to turn one batch of representations into the next. Advance layer by layer to verify how each output becomes the next input.