Recently I was referred to a paper titled Causal Entropic Forces published in Physical Review Letters that attempts to link intelligence and entropy maximization. You can find reviews of this paper here and here. The paper starts with

Recent advances in fields ranging from cosmology to computer science have hinted at a possible deep connection between intelligence and entropy maximization….In this Letter, we explicitly propose a first step toward such a relationship in the form of a causal generalization of entropic forces that we show can spontaneously induce remarkably sophisticated behaviors associated with the human ‘‘cognitive niche,’’ including tool use and social cooperation, in simple physical systems.

The authors then go on to define a causal path version of entropy. Briefly, this is a generalization from standard entropy, a measure of how many states a system can be in at a specific point in time, to causal path entropy, a measure of how many paths that system can follow during a given time horizon. In technical language, microstates are mapped to paths in configuration space, and macrostates are mapped to configuration space volumes:

In particular, we can promote microstates from instantaneous configurations to fixed-duration paths through configuration space while still partitioning such microstates into macrostates according to the initial coordinate of each path

In other words, an initial coordinate establishes a volume in configuration space which represents possible future histories starting at that point. This is the macrostate (depicted as a cone in the image above)

Having defined this version of entropy, the authors then add the condition of entropy maximization to their model; this is what they call causal entropic forcing. For this to have a net effect, some macrostates have volumes which are partially blocked off for physical reasons. Consequently these macrostates have less available future paths, and less causal path entropy. The result is that different macrostates with different entropies can be differentially favored by condition of causal entropy maximization:

there is an environmentally imposed excluded path-space volume that breaks translational symmetry, resulting in a causal entropic force F directed away from the excluded volume.

Note that, contrary to actual thermodynamical systems that naturally exhibit entropy maximization for statistical reasons, causal entropic forcing is not physical, it is a thermodynamics inspired premise the authors add to their model as a “what if” condition, to see what behaviour results. So, what happens when systems are subject to causal entropic forcing?

 we simulated its effect on the evolution of the causal macrostates of a variety of simple mechanical systems: (i) a particle in a box, (ii) a cart and pole system, (iii) a tool use puzzle, and (iv) a social cooperation puzzle…The latter two systems were selected because they isolate major behavioral capabilities associated with the human ‘‘cognitive niche’’

Before you get excited, the “tool use puzzle” and “social cooperation puzzle” are not what one would imagine. They are simple “toy simulations” that can be interpreted as tool use and social cooperation. In any case, the result was surprising. When running these simulation the authors observed adaptive behaviour that was remarkably sophisticated given the simplicity of the physics model it emerged from. What’s more, not only was the behaviour adaptive, but it exhibited a degree of generality; the same basic model was applied to both examples without specific tuning.

The remarkable spontaneous emergence of these sophisticated behaviors from such a simple physical process suggests that causal entropic forces might be used as the basis for a general—and potentially universal—thermodynamic model for adaptive behavior.

How does this fit in with intelligence?

I see two different ways one can think about this new approach. One, as an independent definition of intelligence from very simple physical principles. Two, in terms of existing definitions of intelligence, seeing where it fits in and if it can be shown to be equivalent or recovered partially.

Defining intelligence as causal entropy maximization (CEM) is a very appealing as it only requires a few very basic physical principles to work. In this sense it is a very powerful concept. But as all definitions it is neither right nor wrong, its merit rests on how useful it is. The question is thus how well does this version of intelligence capture our intutions about the concept, and how well it fits with existing phenomena that we currently classify as intelligent[1]. Ill consider a simple example to suggest that intelligence defined this way cannot be the entire picture.

That example is unsurprisingly life, the cradle of intelligence. The concept that directly collides with intelligence defined as CEM is negentropy. Organisms behave adaptively to keep their biological systems within the narrow space of parameters that is compatible with life. We would call this adaptive behaviour intelligent, and yet its effect is precisely that of reducing entropy. Indeed, maximizing causal entropy for a living being means one thing, death.

One could argue that the system is not just the living organism, but the living organism plus its environment, and that in that case the entropy perhaps would be maximized[2]. This could resolve the apparent incompatibility, but CEM still seems unsatisfying. How can a good definition of intelligence leave out an essential aspect of intelligent life: the entropy minimization that all living beings must carry out. Is this local entropy minimization implicit in the overall causal entropy maximization?

CEM, intelligence and goals

Although there is no single correct existing definition of intelligence, it can be said that current working definitions share certain common features. Citing [3]

If we scan through the definitions pulling out commonly occurring features we find that intelligence is:

• A property that an individual agent has as it interacts with its environment or environments.

• Is related to the agent’s ability to succeed or profit with respect to some goal or objective.

• Depends on how able to agent is to adapt to different objectives and environments.

In particular, intelligence is related to the ability to achieve goals. One of the appealing characteristics of CEM as defining intelligence is that it does not need to define goals explicitly. In the simulations carried out by the authors the resulting behaviour seemed to be directed at achieving some goal that was not specified by the experimenters. It could be said that the goals emerged spontaneously from CEM.  But it remains to be seen whether this goal directed behaviour results automatically in real complex environments. For the example of life I mentioned above, it looks to be just the opposite.

So in general, how does CEM fit in with existing frameworks where intelligence is the ability to achieve goals in a wide range of environments[3]? Again, I see two possibilities:

• CEM is a very general heuristic[4] that aligns with standard intelligence when there is uncertainty in the utility of different courses of action
• CEM can be shown to be equivalent if there exists an encoding that represents specific goals via blocked off regions in configuration space (macrostates)

The idea behind the first possibility is very simple. If an agent is faced with many possibilities where it is unclear which one will lead to achieving its goals, then maximizing expected utility would seek to follow courses of action that allow it to react adaptively and flexibly when more information becomes available. This heuristic is just a version of keep your options open.

The second idea is just a matter of realizing that CEM’s resulting behaviour depends on how you count possible paths to determine the causal entropy of a macrostate. If one were to rule out paths that result in low utility given certain goals, then CEM could turn out to be equivalent to existing approaches to intelligence. Is it possible to recover intelligent goal directed behaviour as an instance of CEM given the right configuration space restrictions?

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References

[1] Our intuitions about intelligence exist prior to any technical definition. For example, we would agree that a monkey is more intelligent than a rock, and that a person is more intelligent than a fly. A definition that does not fit these basic notions would be unsatisfactory.

[2] http://prd.aps.org/abstract/PRD/v76/i4/e043513

[3] http://www.vetta.org/documents/A-Collection-of-Definitions-of-Intelligence.pdf

[4] This seems related to the idea of basic AI drives identified by Omohundro in his paper http://selfawaresystems.files.wordpress.com/2008/01/ai_drives_final.pdf. In particular 6. AIs will want to acquire resources and use them efficiently. Availability of resources translates to the ability to follow more paths in configuration space, paths that would be unavailable otherwise.