∇Continuous Function
FoundationsChecking saved investigationReading browser-local route memory before showing a continuation.

Foundation Lab

Model Collapse & Synthetic Data

Synthetic data is essential AND dangerous

Concept 99 of 100TheoryPhase 13
Open DemoAll Foundations
#99CollapseTheory
key equationp_{t+1} = (1-\alpha)p_* + \alpha p_{\theta_t} \rightarrow \text{collapse}

Selected Foundation Object

Keep the equation fixed; move through the evidence.

Concept 99 of 100CollapseTheory / Phase 13: Cutting-edge 2024-2025 research
Current question

Like photocopying a photocopy: quality degrades

p_{t+1} = (1-\alpha)p_* + \alpha p_{\theta_t} \rightarrow \text{collapse}
PredictionCommit before the demo.

Ask what should change when the equation is manipulated, then let the visualization test that expectation.

EvidenceCompare local witness and source.

Use the runnable panel, the key equation, and canonical papers as separate forms of evidence for the same object.

InvariantName what survives notation changes.

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

Next moveContinue through the atlas.

Use prerequisites, dependents, and semantic links to repair the next gap without leaving the object behind.

Open demoInspect equationBrowse atlasNext foundation

Why It Matters for Modern Models

  • Synthetic data is essential AND dangerous
  • Web is increasingly AI-generated: training data pollution
  • Dataset provenance becomes critical for safety

What Tutorials Skip

What is still poorly explained in textbooks and papers:

  • Like photocopying a photocopy: quality degrades
  • Mode collapse: diversity shrinks, tails disappear
  • Solution: always anchor training with real data

Interactive Visualization

Core Math (Optional Deep Dive)

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

Key Equation
pt+1=(1−α)p∗+αpθt→collapsep_{t+1} = (1-\alpha)p_* + \alpha p_{\theta_t} \rightarrow \text{collapse}

Recursive training on synthetic data causes collapse:

pt=(1−α)p∗+αpθtp_t = (1 - \alpha)p_* + \alpha p_{\theta_t}
θt+1=F(pt)\theta_{t+1} = F(p_t)

Repeated application drives pθtp_{\theta_t} away from real p∗p_* (degeneration).

Mitigation: anchor with real data, filter synthetic outputs, track provenance.

Canonical Papers

AI models collapse when trained on recursively generated data

Shumailov et al.2024Nature
Read paper →

Connections

Prerequisites

ℒML/CE/KL↗Scaling

Next Moves

Choose the next question to carry this object forward.