New 'Curse of Precision' scaling law reveals exponential data cost for robotics
The number of demonstrations needed grows super-exponentially as precision approaches a hard limit c.
A new paper from Cuijie Xu and 7 co-authors introduces "The Curse of Precision: A Data Scaling Law for High-Precision Robotic Manipulation," accepted at ICRA 2026. The researchers systematically investigate the relationship between demonstration data and precision in closed-world tasks like robotic assembly. They find that to maintain a fixed success rate, the required number of demonstrations grows super-exponentially as target precision approaches a limit c. This relationship follows the model log(N) ∝ 1/(P-c), meaning that near the precision ceiling, even tiny improvements demand exponentially more data.
Crucially, the paper reveals that limit c is not a static physical constant of the task but an emergent property of the whole agent system—including its sensors, actuators, and expert policy. Experiments on canonical manipulation tasks validate the law and show that system improvements (e.g., adding a wrist camera or using a more effective expert) measurably lower c, thereby expanding the achievable precision. This provides a quantitative metric for system capability and a practical methodology for debugging high-precision manipulation systems.
- Demonstration data scales super-exponentially with required precision: log(N) ∝ 1/(P-c).
- The precision limit c is not fixed; it emerges from sensor, policy, and hardware choices.
- Adding a wrist camera or better expert policy measurably lowers c, expanding precision.
Why It Matters
Provides a quantitative framework to guide data collection and system design for high-precision robotic tasks like assembly.