Infinitely large, randomly wired sensors cannot predict their input unless they are close to deterministic

Area of Science:

• Complex systems
• Information theory
• Sensor technology

Background:

• Predictive sensors are crucial for scientific advancement.
• The relationship between sensor size, wiring randomness, and predictive capability is not well understood.

Purpose of the Study:

• To investigate if increasing the size of randomly wired sensors improves their predictive ability.
• To determine the conditions under which random sensor networks can predict their input.

Main Methods:

• Theoretical analysis of infinitely large, randomly wired sensor networks.
• Information-theoretic measures to quantify predictive information.

Main Results:

• Infinitely large, random sensors are generally nonspecific and nonpredictive.
• Predictivity emerges only when random sensors approach deterministic behavior.
• Nearly deterministic random sensors can capture approximately 10% of input information in typical environments.

Conclusions:

• Sensor size alone does not guarantee predictive power in random networks.
• A high degree of determinism is necessary for randomly wired sensors to be predictive.
• The findings have implications for designing effective predictive sensing systems.