methods/bert2bert.md

---
family: architecture
introduced-in: "[[chen2021-bert2bert]]"
stores: [nothing]     # the trained source model is consumed once at initialization, then discarded; no memory is maintained during training
requires-boundaries: "no"   # no data stream — a single static corpus; the one expansion event is externally scheduled
requires-task-id: "no"
memory-growth: "constant"   # nothing accumulates; the model is enlarged once by design (source ~half the target's parameters)
tags: [method]
---

# bert2BERT

## What it does

Initializes a large Transformer LM from an existing trained smaller one, then
pretrains it normally. Width is expanded by Net2Net-style function-preserving
neuron splitting adapted to Transformers (FPI), or — better — by advanced
knowledge initialization (AKI), which deliberately breaks FPI's replica
symmetry by stacking sampled rows of the *upper* layer's widened matrix into
each layer's expansion; depth is then bridged by iteratively stacking the
widened model on itself. A two-stage schedule (a few epochs of randomly
sampled bottom-k sub-model training, then full-model training) adds further
savings. The trained small model's knowledge rides in through the
initialization, so the large model reaches the from-scratch final loss with
~45% (BERT-base) / 47% (GPT-base) fewer FLOPs.

## Aspects

- **Stores**: nothing during training. The trained source model S(Ls, Ds) is
  an input consumed at initialization (Ls ≤ Lt, Ds ≤ Dt); no replay memory,
  no snapshots kept afterward.
- **Update rule**: standard MLM/LM pretraining after initialization. FPI
  expands each weight matrix by in-dimension then out-dimension mapping
  (uniform sampling of source neurons to duplicate, duplicates rescaled by
  their multiplicity so outputs are preserved), with head-wise expansion for
  MHA and constraints tying the mappings of adjacent modules so residual
  connections stay consistent; layer-norm statistics break exact preservation
  by a small, ignored gap. AKI builds each expanded matrix from the widened
  current-layer matrix stacked with sampled rows of the widened upper-layer
  matrix — worse initial loss than FPI, faster convergence. Two-stage
  training: for Eb epochs, sample a bottom-{lb, 2lb, …, Lt} sub-model per
  step and update only its top lb layers plus a shared head; then train the
  full model.
- **Requires**: an existing pretrained smaller model of compatible family
  (source/target layer and width choices are hand-set; effect of source size
  and architecture left to future work); no task boundaries, identities, or
  stream structure — the setting is a single static corpus.
- **Costs**: the point is negative cost — 45.2% of BERT-base pretraining
  FLOPs saved (AKI + two-stage, S(12,512)→T(12,768)), 47% for GPT; savings
  shrink to 23.9% with a half-depth source S(6,512). No inference-time
  overhead; the initialization itself is a one-shot transformation.

## Documented behavior

- [[chen2021-bert2bert]] (introduces): FPI-expanded models reproduce the
  source's MLM loss at initialization (1.89/1.70 vs sources' 1.89/1.67)
  where DirectCopy lands at 9.05/6.45 and random init at 10.40; FPI alone
  saves 30.4%, AKI 38.4%, AKI + two-stage 45.2% (avg GLUE 85.7 vs 85.5 from
  scratch); DirectCopy saves 12.2% with a half-width source and 0% with a
  half-depth one, where bert2BERT keeps 23.9%. Over-long sub-model training
  destroys the inherited knowledge (Eb=20: saving collapses to 25.4%, GLUE
  84.3, baseline loss never reached). FPI's loss curve initially *rises* —
  read as optimization having to break the replica symmetry — while AKI
  avoids this; attention-pattern analyses show FPI preserving the source's
  patterns, AKI additionally carrying upper-layer patterns, and DirectCopy
  destroying them.
- [[qin2022-elle]] (adopts the width expansion): uses bert2BERT's FPI to
  grow the model at each corpus arrival in lifelong pretraining, but adds
  Gaussian noise to the copied parameters to break replica symmetry (its
  ablation: removing the noise slows pretraining) and a function-recovering
  warmup on replayed data after each expansion; its depth growth departs
  from stack-the-whole-model in favor of adjacent layer duplication.

## Links

variant-of:: [[net2net]] (extends Net2Net's function-preserving neuron splitting from vision CNNs to Transformer PLMs — head-wise MHA expansion, coupled FFN/embedding mappings, residual-connection constraints)
combines:: [[progressive-stacking]] (depth-wise expansion iteratively stacks the widened model on itself, Gong et al. 2019's move, after the width expansion)
uses:: [[function-preserving-width-expansion]] (FPI: source neurons duplicated by uniform sampling and rescaled by multiplicity so the widened matrices compute the original function; the same trick ELLE later imports)
uses:: [[upper-layer-parameter-mixing]] (AKI: each layer's expanded matrix stacks the widened current-layer weights with sampled rows of the widened upper layer's — breaking FPI's replica symmetry and importing adjacent-layer knowledge at the cost of exact function preservation)

## Papers engaging this method

```dataview
LIST FROM [[]] AND ("papers" OR "influences")
```