Integrated Information Theory: A Way To Measure Consciousness in AI?

The notion of conscious AI has been widely explored throughout science fiction, from Isaac Asimov’s I Robot series to modern-day films such as Ex Machina, Bladerunner 2049, and the Matrix Trilogy. In some cases in the mainstream, the possibility of conscious AI has even been linked to the development of generalist agents and chatbots. While the media envisions a world where what it means to be human, in the face of synthetic/artificial consciousness, is fundamentally altered, it does not give much thought to the very elements that give rise to conscious experience.

Humans value their existence because it is meaningful to them; each experience we have throughout our lives contributes to our essence as individuals. Experiences allow us to resonate or disagree with others, formulate belief structures and personal ideologies, and decide how we want to shape the course of our lives; they influence how we think, learn, and grow over time. Our capacity to act on the world and be acted upon is what gives life structure, and it is within this structure that we can derive meaning. 

Yet, most of us take the fact that we are conscious as a given, precisely because of our capacity to attribute meaning to things through experience. Our understanding of our consciousness is self-referential and undeniable. The 17th-century existential philosopher, Rene Descartes, embodied this idea in his famous quote, “I think therefore I am.”

However, in the case of AI, we encounter a problem: how can we know what it is like to think as an AI would think? And, what logical and physical mechanisms of an AI’s thought structure would give rise to conscious experience? Even if we were able to phenomenologically reduce an AI’s conscious experience to its essential properties or qualia, would we be able to relate or make sense of these properties as they relate to consciousness? 

Integrate Information Theory (IIT), pioneered by neuroscientist Giulio Tononi, aims to address these very questions in a way that is both universal and uniquely mathematically quantifiable. But, before we turn to ITT, let us briefly discuss the ‘Hard’ problem. 

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The ‘Hard’ Problem

Science is a descriptive and investigative field whose primary objective is to explain the properties and laws that govern our physical reality by referencing empirical evidence and observation – the purpose of observation in the scientific method is to refine, refute, or adapt existing theoretical frameworks. For instance, Newtonian mechanics are premised on the idea that gravity is a force that is directly proportional to an object’s mass, yet it was not until Einstein developed his Theory of Relativity that we realized this was not exactly the case – gravity, rather, is the curvature of space-time, a concept that has since been verified by numerous astronomical observations such as the principle of gravitational lensing

Gravity is observable and quantifiable; it is one of the fundamental properties that govern our existence in the natural world – it can be explained and justified by reference to physical phenomena alone. Consciousness, however, is a metaphysical property of human existence that manifests itself through subjective experience. While there must necessarily be physical systems that give rise to it, attempting to root our conception of consciousness in these systems presents us with an intractable problem: how can we know what it is like to experience the world as something else? For instance, if I show you the color red, the area known as the ‘color center’ in your ventral occipital lobe will activate, revealing the physical system that is responsible for your capacity to perceive color. However, my subjective experience of the color red will intrinsically differ from yours – I might find that it inspires feelings of anger while you find it to be relaxing. 

The Hard Problem of consciousness can thus be summarized in the following way: while we are capable of understanding the physical systems that underlie the basic elements of our cognition, we cannot, by reference to these systems and the capacities they give rise to adequately explain why it is that something is having a conscious experience, to begin with. This would necessitate an additional first-person qualitative and functional understanding of what it is like to experience the world from the perspective of the entity in question. 

IIT thus aims to develop a theory of consciousness that is empirically and quantitatively grounded but retains the ability for qualitative assessment. 

Essential Properties of Experience or ‘Axioms’

IIT considers an unusual approach to the characterization of consciousness by adopting a top-down theoretical framework. Instead of trying to identify various neural correlates and functionally explain how it is that they give rise to conscious experiences, IIT assumes that the essential properties of consciousness are self-evident. In other words, the theory seeks to first characterize the nature of consciousness and then define its origins. 

IIT posits five ‘axioms’ or essential properties of conscious experience:

  1. Axiom of existence
  2. Axiom of composition
  3. Axiom of information
  4. Axiom of integration
  5. Axiom of exclusion

The axiom of existence stems from the initial cartesian assumption, which is encapsulated in the Descartes quote mentioned earlier, that the existence and experience of consciousness are undeniable. When an entity is conscious, it perceives its existence from its perspective, its experiences are immediate and actual – the reality of these experiences cannot be denied by external observers. 

The axiom of composition posits that all conscious experience is in some way structured, and this structure is what allows us to distinguish between various elements in our physical reality. For instance, my capacity to perceive physical pain or pleasure will in turn structure my physical experience and behavior, namely the extent to which I seek out objects or experiences that relate to these phenomena. 

The axiom of information goes one step further, purporting the idea that experience is not universal, but rather specific and targeted. My experience of kicking a ball is non-transferable; it is distinct from my experience driving a car, watching a movie, or cooking a meal. 

The axiom of integration, which is at the heart of IIT, states that the characteristics of conscious experience are not mutually exclusive, but rather interdependentconsciousness is holistic and unified by nature. For instance, if I see a red fire hydrant, I cannot separate my experience of the color red from my identification of the object as a fire hydrant. The experience is unified; what I see before me is precisely a red fire hydrant. 

Finally, the axiom of exclusion states that conscious experience is definite both in terms of content and the speed at which it occurs. My experience of an empty dark room, while it is distinguishable from my experience of my bedroom, is not actually any more or less potent; consciousness is specified, and as an effect of this specificity it is also exclusive, meaning that each conscious experience is equally potent. Moreover, the rate at which conscious experience occurs is consistent – the temporal flow of conscious experience remains constant across experiential domains. 

From Axioms to Postulates 

Postulates within IIT are what justify and describe axioms or the essential features of conscious experience in terms of their physical properties. Importantly, physical systems must be composed of elements in a state whereby each element must possess at least two internal states. When an input is provided it affects the internal states of an element in a specific fashion, such that the output produced is a function of the change in internal states. Neurons and logic gates represent some common examples in this context. Understanding what is meant by elements in a state is vital to the notion of cause and effect, which functionally underpins all the physical properties of axioms. 

The axiom of existence claims that the experience of consciousness is intrinsic; the substrates of the system that gives rise to conscious experience must then be composed of elements in a state that are themselves intrinsic to the system. For such a system to exist it must be actionable, effectively possessing cause-effect power; a thing cannot exist if it cannot act or be acted upon. The axiom of existence does not merely necessitate that consciousness retains the function of causal power, but also that it can exercise cause and effect upon itself, precisely because it is self-referential and subjective. 

The axiom of composition claims that conscious experience is structured; this implies that any subsets of elements in the physical substrate must be able to come together to form a meaningful composition or representation of conscious phenomena. Thus, the compositions formed between various physical elements of a conscious system must also possess cause-effect power; if this is the case, then elemental compositions allow for the development of higher order mechanisms, which contribute to and uphold the complex structure of conscious experience. 

The axiom of information claims the specificity of conscious experiences. If an experience is distinct, then the systematic structure that gives rise to it must itself possess mechanistic properties that constitute what IIT refers to as a cause-effect repertoire; this repertoire is what allows for the differentiation of specific experiences, effectively constituting a system’s cause-effect structure. At any point in time, this structure is in a given state – the cause-effect repertoire defines and constitutes the cause-effect power of any mechanism in a given state, while the cause-effect structure defines and constitutes the cause-effect power of every mechanism and its corresponding system of elements.

The axiom of integration claims that consciousness is holistic and unified. This implies that the mechanical and functional elements composing the system must be interdependent; every mechanistic element must retain the power to exercise cause over other elements and be affected by individual elements as well as the system as a whole. In other words, if a system can be structurally reduced such that individual elements are removed incrementally without manipulating or changing the overall cause-effect structure, then the system in question does not satisfy this postulate. 

The axiom of exclusion claims that conscious experience is definite and temporally consistent. This implies that the subsets or supersets of mechanistic elements in a system have differential cause-effect structures, but of these subsets or supersets, only one is a maximally irreducible conceptual structure, or as IIT refers to it, MCIS. In other words, a conglomeration of intertwined cause-effect structures would make no difference to the system; if a mechanism is in a given state such that it specifies a specific cause-effect repertoire concerning one system, it should additionally specify another cause-effect repertoire for another system. This would be redundant

These postulates, taken in conjunction with their respective axioms, posit that consciousness is a system whose functional properties can be defined by the aforementioned postulates while its phenomenology can be characterized by reference to its axioms. 

The Phi Metric and the Application of IIT to Evaluate Consciousness in AI 

The ultimate goal of IIT is to evaluate and mathematically quantify the degree of conscious experience any system has. This is achieved by calculating the maximum amount of integrated information in a system, which is quantified using the phi metric. For instance, a computer’s hardware is composed of logic circuits, which define the connections between respective logic gates or elements in a state. Suppose we were to systematically partition the various mechanistic elements in a system, and find that no connections are lost. In that case, we can conclude the system cannot exercise cause-effect power upon itself, thereby having no phi value. 

Similarly, a system where partitioning leads to the severing of some connections but not others would have a comparatively low phi value. In simpler terms, if we find that the removal or activation of certain elements does not affect others, we can assume the system has a low degree of connectivity, and subsequently, information integration. The more holistic a system is, the higher its phi value; if the elements composing a system are non-redundant, interdependent, and universally connected, then we can expect to record a high phi value. Importantly, phi does not evaluate the quality of conscious experience, but rather, its quantity, whereas the axioms are what provide phenomenological and qualitative insight. 

While IIT is, quite frankly, a beautifully succinct and versatile theory of consciousness that can be applied in both synthetic and biological systems, it is nonetheless limited in cases where dimensionality and complexity increase exponentially, under the principle of Bell’s number. In a relatively simplistic system with a limited number of elements, the number of possible partitions can still be obtained pragmatically. However, as systems become more complex, effectively increasing the number of elements that constitute respective mechanisms, the number of connections between elements will increase exponentially. This makes the calculation of the phi metric, while still possible in principle, extremely difficult. Consider the human brain, which has over 86 billion neurons; how could one possibly begin partitioning the various systems in such a complex structure? The same issue applies to large neural network and NLP models, some of which currently have over 10 million nodes and up to 176 billion parameters. 

Fortunately, the pragmatic limits of calculating phi could theoretically be resolved by implementing computational models whose primary function is the partitioning of various elements within a system. With the aid of computer processing power, it may be possible to calculate a phi value within highly complex systems. If a high phi value is obtained, and the relevant phenomenological axioms specified by IIT are also identified within a system, then it is likely that the system possesses some degree of consciousness. However, as with most theories of consciousness, caution should be taken, especially when attempting to classify synthetic or artificial systems as the functionality and methodology of their cognition differs from our own. 

Nonetheless, IIT predicts consciousness in systems with a sufficiently high level of information integration – the question we should be considering, in this case, is whether phi should have a threshold value; if certain systems possess mechanistic elements that correspond with the relevant axioms and cause-effect structure but lack a unified composition, we need to be able to evaluate whether a minimum level of connectivity is sufficient for conscious experience. It would be wise, in our attempts to qualitatively and quantitively assess consciousness in AI systems, to generate a comparative model that we can use to assess the degree of consciousness in AI. I would intuitively assume that such a model would be based on the human brain since it is currently the only system we know for sure is capable of conscious experience. 

Contributor

Sasha is currently pursuing an MSc in Bioethics at King’s College, London. Prior to engaging in his current studies, Sasha was a Division 1 Ski Racer at Bates College, where he graduated with a Bachelor’s in Cognitive Psychology and Classical Philosophy. He is deeply interested in applied ethics, specifically with respect to AI-driven exponential technologies and how they might one day affect humanity

About Sasha Cadariu

Sasha is currently pursuing an MSc in Bioethics at King’s College, London. Prior to engaging in his current studies, Sasha was a Division 1 Ski Racer at Bates College, where he graduated with a Bachelor’s in Cognitive Psychology and Classical Philosophy. He is deeply interested in applied ethics, specifically with respect to AI-driven exponential technologies and how they might one day affect humanity

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