R² (Recursion Squared) Scaling Law
AI systems that implement recursive self-reflection (R²) will show quadratic capability gains compared to linear scaling in non-recursive architectures.
85% confidence
Shareable summaryThe ARC Principle predicted recursive AI would scale quadratically. o3's 87.5% ARC-AGI score (vs o1's 32%) supports this claim.
Falsification criteria
- If recursive architectures (like o1, o3, DeepSeek R1) show only linear scaling, this prediction is falsified
- If non-recursive architectures consistently outperform recursive ones on reasoning tasks, this prediction is falsified
- Threshold: R² systems must show at least 1.5x better scaling efficiency to be considered supported
Supporting evidence
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OpenAI o3 achieves 87.5% on ARC-AGI (vs o1's 32%)
2024-12-20
Demonstrates ~2.7x improvement through recursive reasoning
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DeepSeek R1 matches o1 with open-source recursive architecture
2025-01-20
Independent replication of recursive scaling benefits
Timeline
- Made public
- Expected resolution
Checkpoints
- 2025-06-01 Q2 2025 model releases comparison
- 2025-12-01 Full year 2025 analysis