∇Continuous Function
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Foundation Lab

Self-Improvement & Distillation Loops

Makes data generation and model improvement a closed loop

Concept 98 of 100Scaling & AlignmentPhase 13
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#98Self-ImproveScaling & Alignment
key equation\theta_{k+1} = \arg\min_\theta \mathcal{L}(\theta; D_k \cup \text{self-gen})

Selected Foundation Object

Keep the equation fixed; move through the evidence.

Concept 98 of 100Self-ImproveScaling & Alignment / Phase 13: Cutting-edge 2024-2025 research
Current question

Model bootstraps on its own outputs (filtered by verifier)

\theta_{k+1} = \arg\min_\theta \mathcal{L}(\theta; D_k \cup \text{self-gen})
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

  • Makes data generation and model improvement a closed loop
  • DeepSeek-R1: RL → reasoning → distill to smaller models
  • Reduces reliance on scarce human labels

What Tutorials Skip

What is still poorly explained in textbooks and papers:

  • Model bootstraps on its own outputs (filtered by verifier)
  • Teacher-student paradigm: large model → small model
  • Risk: distribution shift, mode collapse

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
θk+1=arg⁡min⁡θL(θ;Dk∪self-gen)\theta_{k+1} = \arg\min_\theta \mathcal{L}(\theta; D_k \cup \text{self-gen})

Iterative self-training loop:

Dk+1=Dk∪{(x,y^):y^∼πθk(⋅∣x)}D_{k+1} = D_k \cup \{(x, \hat{y}) : \hat{y} \sim \pi_{\theta_k}(\cdot|x)\}
θk+1=arg⁡min⁡θE(x,y)∼Dk+1[−log⁡πθ(y∣x)]\theta_{k+1} = \arg\min_\theta \mathbb{E}_{(x,y) \sim D_{k+1}}[-\log \pi_\theta(y|x)]

Distillation: min⁡θsEx[KL(πθt(⋅∣x)∥πθs(⋅∣x))]\min_{\theta_s} \mathbb{E}_x[\mathrm{KL}(\pi_{\theta_t}(\cdot|x) \| \pi_{\theta_s}(\cdot|x))]

Canonical Papers

Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models

Chen et al.2024ICML
Read paper →

Connections

Prerequisites

🧪Distillation⚖RLHF

Next Moves

Choose the next question to carry this object forward.