Does giving two policies the same seed in a digital twin actually pair them?

What it found

Common random numbers pair two policies only while their read pointers into the random stream stay aligned. If one policy consumes an extra draw with probability q per step, the paired correlation is exactly ρ = ∑_t∑_d Bin(t,q)(d) w_tw_t+d/∑w_t² (matched to simulation within 0.012). A flat 20-step score keeps ρ=0.95/0.77 at q=0.05/0.3, but a terminal-only score has ρ=(1−q)^T (0.36/0.001). Sizing a comparison as if seeds stayed synchronised (n=12) gives power 0.85 to 0.11 against a nominal 0.90; keying each draw by (episode, step) restores ρ=1. Stylised: Gaussian per-step noise, policies differing only in draw consumption, no robot data.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

More in Digital twins & sim-to-real

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Proper scoring & elicitation28Effort & peer prediction9Verification games & slashing19Detection & tolerances14Markets as routers13Prediction-market design9Paying contributors8Decentralised training systems23Digital twins & sim-to-real164LLM chip design loops40Robot manufacturing loops53Ambient AI assistant46Self-replicating manufacturing34Simulation-first design64Engineered clothing45Task-specific AI accelerators40Algorithmic chip-design loops42Open-source purpose-built robots44The software-engineering loop43Adversarial human imitation41Open-source residential construction41Autonomous multi-angle capture34Sensing, imaging and 3D31Energy supply and dense energy storage39Robot societies among people31Agentic co-design of low-cost robots27Laundry-hanging robots25Machine learning on qualitative data23Robots on the building site27Civilizations & group psychology1History & human sciences1

Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.