Layer Normalization: Normalizing Per Example
LayerNorm answers BatchNorm's batch-coupling problem: standardize each sample's own features, so no batch statistics and no train/eval switch are needed. This topic shows the math, why LayerNorm became the normalization of transformers, and what pre-LN vs post-LN costs.
01.The Problem: BatchNorm Ties Samples Together
Batch Normalization (topic 91) standardizes each channel using the whole batch. In one plain sentence: BN looks at all the samples together to decide what "normal" means.
That works great for images. But it creates three headaches:
- An output depends on which other samples share its batch (batch coupling).
- You must keep two modes: live batch stats while training, memorized running stats at inference.
- A batch of size 1 has no meaningful mean or spread.
Now imagine a language model. Data comes as sequences of tokens with different lengths. Padding, streaming one token at a time, changing batch composition every generation step — BN's batch-based statistics become a nightmare.
So the question becomes:
What if a sample could normalize itself, using only its own numbers?
That is Layer Normalization (LN) — Ba, Kiros & Hinton, 2016.
LN Statistics and Block Placement
LN Statistics and Block Placement
LN normalizes across the feature dimension of each sample independently. In transformers, where you put it — post vs pre residual — changes trainability at depth.
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