Physics model reveals fundamental trade-off between prediction and energy efficiency in intelligent systems

Artificial intelligence is increasingly becoming part of our everyday lives, from digital assistants to robots that respond to their surroundings. Each of these capabilities is based on physical computational processes that consume energy. An international research team led by Hans Briegel from the Department of Theoretical Physics at the University of Innsbruck, Austria, has investigated the physical limits on the efficiency with which intelligent systems process information. Their findings are published in Physical Review X.

Physics of information processing

An agent is a system that gathers information from its environment and responds to that feedback, much like a robot moving through a room while constantly making new observations. "Through his actions, the agent changes the world he himself is trying to predict. We wanted to understand what that changes about the physics of information processing," explains Lukas Fiderer, the study's lead author.

In 1961, physicist Rolf Landauer identified a fundamental physical cost of erasing information. However, the relationship also works in reverse: Under suitable conditions, an agent can use information about a physical system to extract energy from it. The new study investigates the greatest average amount of useful energy an ideal agent can extract per interaction through repeated exchanges with its environment. It thus provides a precise thermodynamic benchmark for comparing different ways of organizing the agent's memory and actions.

Thermodynamically optimal performance

Previous research showed that an agent that passively processes information can only achieve thermodynamically optimal performance when it consistently focuses its memory on prediction, remembering information from past interactions that helps it anticipate future observations. The new study develops a model for agents whose actions influence their observations, which more closely reflects real-world applications.

The authors mathematically prove that, in some environments, agents who retain all the information necessary for optimal prediction cannot, in fact, achieve the best possible energy efficiency. To achieve this, they must forget parts of their own action history—including information that would actually have improved their predictions.

A simple example illustrates what forgetting means here: A robot that opens a door could remember precisely how hard it pushed to predict how the door will move. If it forgets how hard it pushed, it loses information that would improve its prediction of the door's movement. The study shows that, in some environments, agents must give up such useful information to maximize the energy they extract through their interactions.

"The surprising part is that an agent can benefit energetically from forgetting information that would actually improve its predictions," says Fiderer. The effect persists even if the agent is given more storage capacity, and it is independent of the practical storage costs of today's hardware: "The trade-off between prediction and forgetting persists even if we disregard the practical costs of building and maintaining memory. This, then, is a conflict arising from the fundamental laws of physics," says Fiderer.

Foundation for efficient agents of the future

"Today's computers are still far from these fundamental limits. Our work gives us a way to explore what efficient agents could look like as the technology moves closer to them," says Fiderer, who believes a proof-of-principle demonstration of the result should be possible with modern experimental setups.

The results also raise more fundamental questions: "Prediction and forgetting are familiar features of intelligent behavior. Finding a connection between them in a fundamental thermodynamic objective may provide insights for the research and development of more sustainable AI systems," says Fiderer.