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Foundation Lab

Iterated Amplification

Concrete proposal for scalable oversight when AI exceeds human capability

Concept 87 of 100Scaling & AlignmentPhase 12
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#87IDAScaling & Alignment
key equation
A′=arg⁡min⁡πKL(Amp(H,A)∥π)A' = \arg\min_\pi \mathrm{KL}(\text{Amp}(H,A) \| \pi)
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Selected Foundation Object

Keep the equation fixed; move through the evidence.

Concept 87 of 100IDAScaling & Alignment / Phase 12: Advanced alignment & safety research
Current question

Like teaching: break hard problems into pieces students can help with

A′=arg⁡min⁡πKL(Amp(H,A)∥π)A' = \arg\min_\pi \mathrm{KL}(\text{Amp}(H,A) \| \pi)
PredictionCommit before tracing the equation.

Ask what should change under a concrete input, then trace that expectation through the equation.

EvidenceCompare the equation and source.

Use the key equation and canonical papers as the available witnesses, without implying that a runnable panel exists.

InvariantName what survives notation changes.

The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.

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Why It Matters for Modern Models

  • Concrete proposal for scalable oversight when AI exceeds human capability
  • Human decomposes task, assistants solve subtasks, distill back
  • Foundational to modern AI safety research

What Tutorials Skip

What is still poorly explained in textbooks and papers:

  • Like teaching: break hard problems into pieces students can help with
  • Distillation compresses the amplified procedure into single model
  • Each iteration enables supervision of harder tasks

Visualization Status

Core Math (Optional Deep Dive)

If you want intuition first, start with the key equation and cited sources. Come back here for the full walkthrough.

Key Equation
A′=arg⁡min⁡πKL(Amp(H,A)∥π)A' = \arg\min_\pi \mathrm{KL}(\text{Amp}(H,A) \| \pi)

Amplify human HH with assistants AA, then distill:

A′≈arg⁡min⁡πEx[KL(Amp(H,A)(⋅∣x)∥π(⋅∣x))]A' \approx \arg\min_\pi \mathbb{E}_x\left[\mathrm{KL}\big(\text{Amp}(H,A)(\cdot|x) \| \pi(\cdot|x)\big)\right]

Then iterate: A←A′A \leftarrow A'.

Recursion: as AA improves, Amp(H,A)\text{Amp}(H,A) becomes more capable.

Canonical Papers

Supervising strong learners by amplifying weak experts

Christiano et al.2018arXiv
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Connections

Prerequisites

🧪Distillation⚖RLHF

Enables

🥪Sandwich

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