Simulating Proto-Consciousness
By: Antonio Hidalgo-Landa
Tags: Consciousness Research, Entropy, Consciousness, Simulation, Proto Consciousness

Introduction

The aim of this work is to explore the simulation of the most fundamental phenomena of consciousness from an algorithmic standpoint. Our focus is purely functional, leaving philosophical questions aside. Nevertheless, we provide broad context by including perspectives from other authors, such as David Chalmers’s hard problem and the global workspace theory of Baars and Stanislas Dehaene.

The main source for our model is information theory. We can easily imagine that a conscious being exists in a mental plane where everything is reduced to information. This plane is inhabited by information sources. In our world, our brains process vast amounts of information. Some of this information is produced as a consequence of our actions, and other information is not. When the information is generated by our actions, we can say that we are acting as an information source. When the information is not a consequence of our actions, we can say that the information source is not us but something else.

In summary, we explore consciousness in the realms of information theory and conclude that a conscious entity is expressed as an information source that prioritises its own entropy. After formalising our models, we implement a representative simulation for a basic form of consciousness (proto-consciousness). In conclusion, our simulation demonstrates the essential features identified by contemporaneous theories such as the global workspace theory and minimal selfhood.

Limitations of the Study

Consciousness remains an overly broad area where we can still find many unknowns. Therefore, many different approaches are appropriate to explore the various aspects of consciousness.

David Chalmers proposed that while there are many problems related to consciousness, there is one fundamental hard problem: the subjectivity of the experiences of conscious beings. One example is the redness in the colour red. Do we all perceive the same red, or is it different in each other’s minds?

For Chalmers, easy problems of consciousness include the reportability of mental states, the integration of information by a cognitive system and the difference between wakefulness and sleep. However, he questions the role of subjective experiences. In order to illustrate the problem, we can imagine a philosophical zombie as an automaton (Chalmers, 1996). These zombies might be able to mimic all the behaviour of a conscious being but without a real consciousness of their previous experiences.

Rupert Glasgow explores the most intrinsic and fundamental roots of consciousness from a biological standpoint. Glasgow denotes this primitive form of consciousness as ‘minimal selfhood’ (Glasgow, 2018). While Chalmers questions the boundaries of consciousness from an existential point of view, Glasgow explores them from a biological perspective. Glasgow observation is that while, it is plausible that greater apes and pets have consciousness or at least some kind of proto-consciousness, the idea of consciousness in lesser animals, like invertebrates, looks less attractive. Lastly, he explores a very different and archaic proto-consciousness, if any, when he considers more simplistic life forms, like echinoderms (starfish), porifera (sea sponges), plants and prokaryotes.

The proponents of global workspace theory (Bernard Baars) see the mind as an orchestration of conscious and unconscious processes (Baars, 1997). In this framework, we can assume that any subconscious process can be automated, placing them outside of the hard problem’s boundaries. The model focuses on resolving the question, ‘What is it that moves a sentient being?’ If we have the ability of problem-solving, how do we know that a problem is a problem?

As we limit the scope of our study to the most minimum and fundamental phenomena, we exclude any well-known mechanism that we can currently automate. For example, there are cleaning and vacuum machines that perceive and internally model the floor and their surroundings, autonomous vehicles that explore and survey vast areas of other planets and semi-autonomous vehicles that predict traffic behaviour to drive us to our destinations safely. No one would claim that a semi-autonomous vehicle or a robotic vacuum cleaner is conscious, although we can recognise that they effectively carry out tasks such as perceiving and modelling their surroundings, decision-making or planning. Therefore, we do not include them in our study.

Methodology

This study focuses on simulating proto-consciousness. We use contemporary perspectives on consciousness as the foundation of our formulations, formalising our definition of proto-consciousness using information theory. Lastly, we implement a simulation using Python, Pandas and Scikit-learn.

After formalising the definition of proto-consciousness, we explore the metrics and the measurements associated with the formal model. Information theory offers a formal way to measure information by measuring entropy. These metrics allow us to measure the potential impact that an information source has on its surroundings as well as the amount of information of which the information source is aware. With the definition of a simple goal such as maximising its own entropy, we ensure that the information system is working in its own interest. The definition of our goal might be simpler than the validation, which might be challenging from a computability perspective. Our model must validate that a function is returning a local maximum, as the maximum depends subjectively on the information contained as a reference. We can imagine that in a game of chess, sacrificing the queen might look like a bad move, but it can be a local optimum if the player thinks that the sacrifice will lead him or her to checkmate. It is hard to determine if the move was a local maximum or just luck unless we know the evaluation that the player performed for each of his or her options.

Information theory shows the use of entropy for measuring information. We advocate for the use of entropy to measure the level of awareness of these proto-conscious entities. We propose using entropy in the following ways:

Entropy of the perception system

Entropy of the model of the projected selves

Difference between the entropies of the projected selves

Entropy of the perception system

We can measure awareness at different levels. The first is the perception level. We understand the perceived world as an information source, and hence we can measure its entropy. We use the historical data of the information source (perception) for calculating the entropy:

Η(W) = — Ww p (w) log2 (p (w))

where w refers to the perception in a single instant and p(w) is the number of occurrences of each perception in the historical data.

p (w) = |w|W

Entropy of the model and the projected selves

Our algorithm categorises the data into different statuses that form the basis for further analysis. These statuses can be seen as a second layer of awareness of the perceived data. The entity models a projection for each action that it considers. Each projection is another information source with a measurable entropy. Thus, we measure the awareness of the world being considered by the entity. As we measure projections rather than historical data, we also measure the accuracy of the predictions through the following metrics:

Entropy of the projections

Entropy of the actions

Accuracy of the projections

The process of reading involves perceiving letters, which form words, which form phrases, and so on. The entropy of the information source may differ depending on the events that we measure (e.g. letters, words, phrases, etc.). Similarly, the entropy of our projections will vary depending on whether we consider each isolated event or we contextualise them. As we could only run a finite number of tests and experiments, we have kept our experiments simple. We measured several simulations of simple scenarios, where the perceived world was limited to an array of four elements with a memory of three, and a slightly more complex scenario, with an array of eight elements and a memory of four. Furthermore, we have compared our results to the same algorithm using a random action selector. The model uses clustering to identify representative statuses within these events.

Η(Self’) = — Self’w3 p (w3) log2 (p (w3))

where w3references a set of a few contiguous instants and p(w3) is the number of occurrences of this set in the projection Self’.

p (w3) = |w3|W

The self is also modelled as an information source. Hence, we can use entropy to measure the amount of information within the self. This will be the entropy of the number of different effects that the entity can achieve with its actions:

Η(X) = — Aa p (Self’ (a)) log2 (p (Self’ (a)))

where

p (Self’ (a)) = |Self’ (a)|Actions

Difference of entropies between the projected selves

We validated our theories by comparing the entropies generated by a simple proto-conscious entity in different scenarios and by random selection. The proposed entity relies on learning algorithms to build its models of the surrounding world. Therefore, the models generated by the entity will be more accurate in a scenario favourable to learning. Consequently, we expect that the projections in a world where the main component of change is a single entity will be more accurate than the ones in a rapidly changing world, or the ones in a world where the entropy has little influence.

Our expectation is that entities that are better aware of their surroundings and can prioritise their actions will produce a higher entropy.

Note that the capacity of the entity to understand and influence its surroundings is limited. Hence, we expect a lower capacity of influence in rapidly changing environments, where the entity will struggle to make sense of its surroundings.

We can sum up the following two metrics:

Projection accuracy against rapidly changing and converged surroundings

Entropy of the perception system on good learning surroundings against a random selection

Background, Formal Models for Consciousness

Intuitively, consciousness involves the awareness of the self and the world surrounding it. In other words, to be conscious is to have a model of the self and a model of the world. Consciousness can also be understood as the capability to pursue one’s own interests. Let us examine a few different interpretations of the concept.

The first challenge that we come across is the definition of consciousness. Similarly to intelligence, there is no consensus about a formal definition, though both concepts are intuitive. Therefore, there are no standardised qualitative or quantitative metrics to measure consciousness. Traditionally, the extensive literature on consciousness has lacked empirical facts, according to Endel Tulving of the Canadian Psychological Association (Tulving, 1985).

Minimal selfhood explores proto-consciousness in different biological forms. Glasgow explores features, which alone may not be sufficient to form a proto-consciousness, but together provide a foundation for minimal selfhood. For example, whirlpools and forest fires can exhibit some of these features such as self-organisation and self-propagation. Minimal selfhood implies intrinsic reflexivity, which requires both reflexibility and continuity in time.

Two contemporary theories seek to provide a formal foundation for consciousness. On the one hand, global workspace theory (GWT) describes the mind as a theatre where many conscious and unconscious processes take place. The proponents of GWT seek evidence with ‘contrastive analysis.’ The large body of evidence from GWT provides paired comparisons between similar conscious and unconscious processes (Baars, 1997).

On the other hand, the neuroscientist Giulio Tononi has led integrated information theory (IIT). IIT formalises a phenomenological description for consciousness (Tononi et al., 2014). Thus, Tononi provides a mathematical framework to work with consciousness from qualitative and quantitative standpoints.

GWT identifies the following nine functions within consciousness: adaptation and learning function, definitional and contextualising function, access to a self-system, prioritising and access to the control function, recruitment and control function, decision-making and executive function, error-detecting and editing function, reflective and self-monitoring function and optimising the trade-off between organisation and flexibility. IIT finds that the maximally irreducible conceptual structure (MICS) generated by a complex of elements is identical to its experience. On the other hand, minimal selfhood requires intrinsic reflexivity as self-maintenance, self-reproduction and self-containment.

Table 1: Features identified in three formal consciousness theories

We can find some common ground between the three theories’ approaches to modelling the consciousness. The three theories reference entities that are not only delimited from an outer world but also possess a model of themselves within a model of the outer world. They may use this model for auto-regulation, self-maintenance or simply as a conceptual structure. Minimal selfhood and the GWT coincide in a second quality: the conscious entity can pursue its own interests.

We understand that there may be other levels or characterisations of consciousness. In our study, we have focused on entities that can represent the world and themselves and can pursue their own interests.

Discussion

Let us begin by contextualising David Chalmers’s hard problem with a thought experiment. In this thought experiment, conscious entities have mental models of themselves and the world and the ability to pursue their own interests. These conscious entities inhabit a virtual world like those in open-world first-person massively multiplayer online games. The perceptions of one of the players are fed to an AI. This AI can create a model of the surrounding virtual world from these perceptions, similarly to how smart cleaning robots create floor maps of their surroundings. The AI builds an ontology of the world based on its play-time.

Given the state of AI technology today, we can attribute advanced capabilities to our AI. AI used in social networks like Facebook can identify people in photos and make suggestions for tagging them. Moreover, semi-autonomous vehicles can identify signals, traffic and bystanders. Finally, there are several examples of algorithms that employ reinforcement learning to beat world champions in different games, including chess, Go, Atari video games and even contemporaneous games such as Star Wars 2 (Vinyals et al., 2019).

Although there may be many technical challenges to actually building a machine like this, most of the technology is already within reach. We can find an analogy with Chalmers’s hard problem. If we consider the various functions that we have identified in this self-governed AI independently, it becomes clear that current technology is not far from solving them. Nevertheless, one more pivotal challenge must be overcome before this AI is able to look after itself. Reinforcement learning allows algorithms to learn by themselves, but the technique relies on a reward function. In the case of a competitive game, the reward function is generally defined based on whether the algorithm wins or loses the match. In our case, we wish to make the primal motor that moves our entity driven by its own interests. For the sake of the thought experiment, we can suspend our disbelief and stipulate that the entity pursues its own interests. In this case, we encounter David Chalmers’s hard question. Would this entity be conscious, or would it be a philosophical zombie?

However, before entering the suspension of disbelief, there are other questions that must be addressed. If an entity can recognise the world surrounding it as well as itself, how can this entity pursue its own interests? How does the entity define its own interest in the first place?

In the context of GWT, a mind is like a theatre populated with conscious and subconscious processes. When we perform an action, like dancing, playing sports or working, our subconscious learns to do it automatically. We can picture the same analogy for mental phenomena. Thoughts and memories are intertwined in our mind. Unconscious processes may be triggered by the presence of other thoughts and external impulses. These subconscious processes can bring thoughts into conscious thinking. The processes can be easily defined as deterministic or stochastic functions based on a reward function, e.g. homeostasis. In general, we will bring thoughts to our mind of experiences that have been useful so that we can avoid danger and pursue our own good.

However, having a thought and making a voluntary decision are two very different things. One possible view is that decisions, like thoughts, emerge from our subconscious. When we think that we are making a conscious decision, we are actually consolidating in our memories the rationale behind the subconscious decision. Nevertheless, our minds spend considerable effort on problem-solving. Whether problem-solving is conscious or unconscious, minds have the ability to resolve problems, and more notoriously, to identify them. In order to identify that something is a problem, it is necessary to have a reference framework. How do you know that good is good and bad is bad?

One common view is that we rely on our internal homeostasis (Glasgow, 2018). When we feel good and our body is balanced, we make positive mental associations. When we feel bad or endangered, we associate our thoughts negatively. Simple animals need no more than these capabilities, but humans can extrapolate the concept of good to others and think of a greater good.

Homeostasis favours survival, and conscious life has evolved in strongly homeostatic organisms. However, the question remains, what is the basis of homeostasis? We argue that maximising entropy is the key to this problem. We suggest that any living form seeks to maximise its potential footprint in the world, either by living longer or increasing the amount of choice in its surroundings. This is not limited to lifeforms but extends to the cosmos. Galactic dust clusters together to form planets and stars, atoms fuse in supernovas creating more complex forms and streams of water carve their course in the ground and rock.

This implies that to simulate proto-consciousness, we should build a model of the surrounding world, a model of the self, a model of the attention of the present self and a prioritisation mechanism for decisions. Moreover, this prioritisation mechanism must be driven by the entropy of the entity.

Theoretical Model

In this section, we formalise the concepts that we have discussed. In summary, we seek to define an entropic entity that prioritises its own entropy and includes the following elements:

A mechanism to perceive the world

A mechanism to influence the world

An internal model of the external world

An internal model of the self

A prioritisation method for the entropy of the self

A mechanism to perceive the world

Imagine yourself in the middle of the void. Imagine that you cannot see, hear or feel anything. There is not much that you can do. Now, imagine that you also have no memories. What kind of thoughts would you be able to think? The scenario could be very challenging. Without any other entity present, developing or learning a language would be futile. Wittgenstein argues in his Philosophical Investigations that our language is limited to what the speaker can know (Wittgenstein & Anscombe, 1997). What kind of concepts would you be able to form if you had never perceived anything? Would you form an awareness of time? Therefore, we see that the perception of a surrounding world plays a fundamental part in consciousness.

Modern technology can easily capture audio and video recordings. In fact, image and sound are merely waves propagating at different frequencies. Moreover, modern technology provides many more sensor types. These sensors can transform their input into digital signals over a time spectrum. Therefore, a perception of the world can be reduced to a time series of bits, where the bits may represent one or many channels with digital signals from the surrounding world. We can express the perceived world as an information source:

W(t) =Xt1, Xt2, … Xtn where {t1, t2, … tn} represent the time instants where the signal was sampled and {Xt1, Xt2, … Xtn} represent the samples. Each Xn can be represented as a finite array of bits containing the digital signals perceived.

A mechanism to influence the world

Consciousness can be studied from a behavioural standpoint. Analysing what a subject does may help us determine whether or not the subject is conscious of its surroundings. GWT points out that consciousness requires a function for accessing the self-system. Within this self-system, we have some influence over the rest of the world. Minimal selfhood ascribes the property of self-maintenance to conscious beings. From the perspective of the information theory, we can consider that there is an entropy within the self that is different from the entropy of the rest of the world. For example, animals influence the world surrounding them with their behaviours. In fact, any self-contained being influences the world by keeping its own self-balance. Hence, we can see that conscious entities can influence the world both actively and passively. Humans have evolved further, and we use our intellect to influence the world. In modern societies, exchanging information has more impact than any direct human action. Our world is currently populated by machines and large societies that depend more on communication and information exchange than on direct human physical efforts. Therefore, both physical actions and information can be used to influence the world. Consequently, the self can be manifested as its own information source within the perceived world.

Thus, we can define the mechanisms of influencing the world as an information source with an alphabet composed of the different actions (or inaction) that the entity can perform.

A(t) =At1, At2, … Atn where {t1, t2, … tn} represent the time instants, and {At1, At2, … Atn} the action or inaction performed by the conscious being.

An internal model of the external world

The next step is processing the external signals into a model of the world. This can be seen as an analogue to the maximally irreducible conceptual structure (MICS) described in the IIT. Within the context of GWT, the evidence shows that consciousness requires an adaptation and learning function and a definitional and contextualising function, Table 1. The internal representations of the external world must adapt and learn from the surrounding world, which is subject to constant change (entropy). We can view the world as an empty void populated with subatomic particles moving around. However, what appears to be chaos at first glance is part of a harmonious orchestration of more complex forms. Subatomic particles coordinate to form atoms or photons, these merge into molecules and waves, and so on. Each of these concepts can be contextualised in its current form and traced back through its known history. Richer conceptual contextualisation will produce more accurate prediction models. Hence, we wish to find a balance between model accuracy and prediction speed. These predictions and classifications can then be used for decision-making and prioritisation. Therefore, these models will perform better when they build more accurate relationships between the concepts that they create from the input signals.

From a formal perspective, we have a function that takes the input of the external signals and forms a model. The model outputs will then be used for decision-making. The overall idea is to use reinforcement learning based on maximaising the entropy of the self, which is an information source. The model plays an important role in this learning. On the one hand, it is the classifier engine that will ultimately be responsible for differentiating the boundaries of its own entropy, and hence the self. On the other hand, decision-making relies on it directly. Hence, we prefer models with a rich and accurate representation of the world.

Entropy can measure the information contained by the model, including how many different concepts it is modelling, the dimension of each concept is and how accurate these models are when compared to the actual input from the world. This also brings us to another fundamental function of consciousness described in GWT: error detection and editing.

Consequently, we can formally define a training function for creating the model and another for predictions and classifications.

We consider W as the current perception of the world and A as the action to be predicted. Note that the model contains an internal state. For example, we may want to consider not only the current perception of the world but the immediate time sequence, or any other relevant information.

The model also contains a prediction function. The outputs from the prediction function will be used as input for decision-making and prioritisation. Note that the prediction is effective when it correctly predicts how an action impacts the conscious entity. This may be reflected through multiple paths. For example, some decisions might be poor in the short term but worthy in the long run, like pension schemes. Another example is when we have a dichotomy, such as choosing between siding with one friend or another in a confrontation. Consequently, we will also have times when there is nothing impactful in the forecast.

Model.predict(W, A)

An internal model of the self

One characteristic of these models is the differentiation of concepts, especially of the self. Following our discussion, the world can be perceived as entropy. However, not all the perceived entropy comes from the same source. It is possible to identify different information sources within the perceived entropy. For example, we can identify a vehicle moving and associate the vehicle and all its contents with the same information source. The most noteworthy of these information sources is the self, which we denote as Self.

We can consider several levels when modelling the self as an information source. At the first level, the self is identified through the information most directly intertwined with the perceived world, such as a model of the self’s body. The second level models the self as an extension of its actions. Lastly, the third level adds a time component. This includes a model of the history of the self, a model of its narrative line and a model for trends, trajectories and projections.

We can illustrate this from our thought experiment. Imagine a conscious entity, the player, connected to an open-world first-person video game, where the game is the only thing that this entity perceives. The first level of the model considers the body of the player’s avatar. There are a set of components inherent to the avatar. The body moves wherever the player moves and falls wherever the player falls. In this first level of modelling, we also include the modelling of goals and internal states subjacent to the self. The game provides the player with a representation of homeostasis, e.g. the player’s health points. This can be used towards the reward function of the player’s prioritisation algorithm. Any feedback from the prioritisation algorithm can be modelled, as well as part of this level of modeling. The second level of modelling takes into account the actions of the avatar. Finally, the third level of modelling incorporates the current narrative of the self, or its history. The player can recall its past experiences to find similarities in new scenarios, and also project itself on alternative options to decide which one is best.

A prioritisation method for the entropy of the self

The GW theory offers evidence for decision-making and executive functions as well as functions involved in prioritising and access to the control. Such functions take the perception of the world and its internal models as input. The output of the function will be the action that the entity will take to maximise its entropy. Note that this function is not an absolute maximum, as it only considers the information from its model and may be constrained by other factors, such as the homeostasis function.

Prioritisation: ({A}, W, Model) → {A} | Η(Self’) = max (Η(Self*))

The input of this function is the current priority list for the actions, the perception from the model (W) and the model (Model). We denote the list for the actions as {A}, and it can be empty. The result of the function will be another list of actions with new priorities. The function must maximise the entropy of the self within the scope of the information available. We denote the projection of the information source of the self as Self’ and the selected prioritised actions as {A}. Moreover, Self* denotes all the possible projections for the information source of the self, taking into account the existing perception (W) and the model. Note that the projection and the quality of the function will be limited by the quality of the projections of the Self.

Complex organisms can carry out more than one task at the same time, and therefore they can consider several prioritisation mechanisms simultaneously. From an information theory perspective, we have several information sources, one for each prioritisation mechanism. However, the self can interpret all the intertwined prioritisation mechanisms as a whole, single self. The continuity of the model is maintained by consolidating all the prioritisations in a single narrative. Therefore, the model of the self can keep a single narrative, but the self may prioritise several actions following different mechanisms. Daniel Kahneman illustrates this in his work Thinking, Fast and Slow. Kahneman argues that we operate in two ways: a logical self and a self that operates in auto-pilot. Additionally, he claims that although we have a self that lives our experiences, we pay more attention to the self described in the narrative of our memories. This remembering self relies on distorted reflections of our actual experience (Kahneman, 2011).

Software Design

For simplicity, we built a representative but illustrative example, thus reducing the complexity of the world and the model. The simulation contains the following elements:

A simulation of an oversimplified entropic world

An entity that could take actions that affect the world

A perception system

An internal model of the world, adaptively constructed by the entity

An internal model of the self, adaptively constructed by the entity

A prioritisation mechanism to select the next action

A simulation of an oversimplified entropic world

In this initial work, we considered a very basic representation of an entropic world. For the purpose of this study, a world is identified as an information source. The primary function of this world is to represent an entropic environment where we can distinguish changes. We leave for further work the modelling of more complex worlds, like a world made of concepts, an open-world first-person video game or even the real world.

We used an evolutionary algorithm to define this information source. We designed the world for the simulation as a basic array of elements, and we enabled mutations and crossovers. The crossover function copies the status of one of the neighbours, and the mutations change an element to a random state. These two functions maintain a world of constant change. While the crossover tries to align the status of the world, the mutations introduce noise and change.

The world is defined as a set of elements that can change states. We represent it as an array of integers. We have used a turn-based approach to introduce changes in the world. Each turn, there is a chance for a mutation or a crossover among the elements of the world.

An entity that can take actions that impact the world

We introduced entities into this world. These are defined in a very simplistic form, as they do not even possess a body. In the simulation, these entities are considered pure information sources that can perform the same operations defined previously: mutations and crossovers. Therefore, the set of actions that an entity can perform, A, includes mutations or crossovers over any element of the world, plus inaction.

Perception system

The current status of the world can be seen as the status of the world in a snapshot, but also can be seen as the sum of all its previous statuses. The perception of the world in a snapshot, X, is represented as an array of integers, representing each element of the world.

X =x0, x1, … xm-1

In our simulation, the perception of the world is not limited to a single snapshot, We implemented a finite number collection of statuses captured over time. We advocate for a finite number collection in a queue format (FIFO) for simplicity and to facilitate computation.

W(t) =Xt1, Xt2, … Xtn

An internal model of the world built by itself adaptively

Conscious entities create a model of the world within themselves. Nevertheless, this model of the world does not represent only its most immediate perception but also all the events that surround it. We used adaptive models to capture and represent the world and the forces that affect it.

Model.predict(W, A)

Machine learning can be implemented with case-based reasoning (CBR). CBR uses previous instances similar to a situation to produce a prediction. We used CBR to predict an action’s effects on the world given the current status and the actions available to the entity. Given a state of the world (W(t)), we can predict what will happen, taking into account similar cases from the past. However, even when two snapshots of the world look the same, the circumstances surrounding them might be different. Hence, we also modelled these circumstances. Clustering is a common technique in unsupervised machine learning where the machine learns to segregate data. We used a clustering algorithm to map the perceptions to a set of finite states so that we could group them and find similarities dynamically.

In summary, the model of the world comprises the following elements:

The clustering model for the status

The CBR for modelling the effects of the actions and inactions

The queue with the last snapshots

The last status

An adaptive internal model of the self

The entities in our model are very simplistic, as they do not even possess a body. These entities are pure information sources that can affect their surroundings. For modelling the self, we focused on building the projection of the self (Self’) for each of the options that the entity could choose (Self*) . We used the CBR model to compute both.

The projection of the self (Self’) following an action (a) is obtained as the prediction of the CBR for that action with the current internal state.

Self’(a) = CBR.predict(W,a)

In this study, the projection is for one single instance, but we would like to implement several stacked strategies in future work, such as the prediction for the next instance in the short and long term.

A prioritisation mechanism to select the next action

The prioritisation function enables the entity to decide its next action. For simplicity, we considered only the projection of the future self on the next instant of time. However, in future work, we would like to add other strategies to this process, such as the use of goals and beliefs that emerge from the models of the world and the self.

Prioritisation: ({A}, W, Model) → {A} | Η(Self’) = max (Η(Self*))

The entropy rate of an information source is, informally, the time density of the average information in a stochastic process. For stochastic processes with a countable index, the entropy rate Η(X), is the limit of the joint entropy of n members of the process Xk divided by n, as n tends to infinity.

Η(X) = n →∞( XxYyP(x,y)log2(P(x,y)n)

Consider that any given state has N+1 actions (counting inaction). We defined the entropy of the self as the amount of influence that the entity has over the current and subsequent states. For example, if all the elements in the world have the same state, crossovers would be futile, and so the number of available effective actions would be fewer. The entropy is higher when the entity can effectively do more things (i.e. each action produces a different status). Lower entropy represents statuses that give the entity fewer options to make an impact.

Η(X) = — Aa p (Self’ (a)) log2 (p (Self’ (a)))

where

p (Self’ (a)) = |Self’ (a)|Actions

Note that we are only taking into account the gains in entropy for the next immediate instant of time.

Simulation Results

Our goal was to measure the entropy of the perceived input and the entropy of the model to determine the awareness of the model and its action capacity. We focused on the following two metrics:

projection accuracy in rapidly changing vs converged surroundings

entropy of the perception system in good learning surroundings vs random selection

We measured the entropy perceived by the system, the entropy of the projection and the error of the projection in different scenarios. On the one hand, we compared the metrics with a random selection algorithm. On the other hand, we evaluated the system in a rapidly changing environment, in a slowly changing environment and in an environment converging to low entropy (no actions possible).

Projection entropy and accuracy

Entities that are aware of their surroundings can produce more accurate projections of them. Therefore, we measured the awareness of an entity and its surroundings. We measured the behaviour of the entity in a rapidly changing environment, where a high amount of change will limit its capacity to learn the impact of its actions. Then, we compared this scenario to the behaviour of the entity in a low-paced environment, where the actions of the entity had little effect.

In total, we modelled three environments: a rapidly changing environment with many external changes (i.e. changes not triggered by the entity); a converging environment with few external changes that tends toward low entropy (thus, the entities’ actions have little impact); and a balanced environment, where external changes happen slowly, but frequently enough to enable change.

Figure 1: Prediction accuracy (error). The figure shows the mean absolute error between the prediction and the actual status. Note that the algorithm used a scalar representation after abstracting the perception using clustering.

An examination of the accuracy between the projection and the perception shows that a balanced environment led to more errors, and the errors were more severe. Committing more errors provides more chances to learn and adapt. The orange line, representing the accuracy error in the converging environment, has been the best performer. When there is little to do, there is little to learn.

The ability to focus is a fundamental function for perception. The perceived data shows that only certain information is meaningful and this is determined by an abstraction process. When the world is rapidly changing, it is harder to identify which portion of the perceived data is meaningful and which is mere noise. In our experiment, perceiving the rapidly changing world usually produced noise with little to learn. This highlights the significance of the function that Baars describes as ‘definitional and contextualising.’ Without this contextualisation, perceived data cannot be transformed into meaningful information.

Entropy of the surroundings

The line representing the error accuracy in the balanced environment had the highest accuracy error. However, Figure 2 shows that in the long run, the proto-consciousness performed better in the balanced environment. In this environment, the proto-consciousness can maximises entropy in the surrounding world better than a random selection algorithm. Therefore, it can adapt better.

It is worth noting that while the entropy is very high in the rapidly changing world, the model is not very useful. Because we found no significant difference between the proto-consciousness’s choices and random choices in this world, there is no evidence of the model assimilating the perceived information. However, in the balanced world, the proto-consciousness adapts better to the environment than random choice. Note here that adaptation and learning is the first function for consciousness identified by Baars.

Figure 2: Entropy of the perceived world

Conclusion and Future Work

There is no clear consensus on the formal definition of consciousness and its measurement. Therefore, as the discussion of metrics for measuring consciousness is still open from a formal standpoint, we have applied state-of-the-art views like global workspace theory (GWT) and integrated information theory (IIT) to the problem. From these theories and the studies of Rupert Glasgow on the boundaries of minimal selfhood, we have developed a model for simplified consciousness, a ‘proto-consciousness.’

We have focused on formalising consciousness and its measurement, given the lack of consensus in this area. Therefore, we have narrowed the scope of our study to simulations and proto-consciousness. Our model may not be real, but a simulation.

The model is based on information theory and the measurement of information as entropy. It describes proto-consciousness as an information source’s ability to prioritise its own entropy over any other information source. We have discussed the relationship between this definition and the characteristics ascribed to consciousness by the GWT, IIT and minimal selfhood. Although all three theories offer formal definitions, IIT describes a more passive form of consciousness focused on environmental awareness, while GWT and minimal selfhood each include an active component of consciousness.

We built and measured a simplistic representative implementation of our model, including a non-deterministic world with an entity that uses its perception of the world to maximise its own entropy. We measured the entropy of the world and compared it in different scenarios. On the one hand, we focused on worlds where the entropy decreases over time. On the other hand, we compared the entropy of our proto-conscious entity (which prioritises its own entropy) and an entity driven by random choice. The results were that the proto-conscious entity adapted better to the non-deterministic world and prioritised its own benefit. The proto-conscious entities ended in a world where they had more actions available.

Our simulations were representative and highly simplistic to facilitate experimentation and measurements. One of the aspects that we simplified the most is the representation of a non-deterministic world. Ideally, we would like to employ more complex environments, like the three-dimensional worlds of open-world first-person multiplayer video games. Additionally, we would like to use more advanced machine learning algorithms to improve the predictions and adaptability over time. In addition to a sequence with the most recent snapshots of the world, we would like to consider more sequences with different lengths and time frames. We would also like to consider sequences measured in seconds, minutes, hours, days, months or years.

The world is perceived in data, images, sounds and feelings. However, from all this data, conscious entities extract and contextualise a small portion of meaningful information. In future work, we want to find better ways to integrate this input data into the models of the world that we build in the system. In our simplistic implementation, we considered a simple prediction of the world in the next instant. However, for future work, we would like to explore more complex models. We could add different prediction systems and stack them together, including short-term, mid-term and long-term systems. In addition, these models could use inference rules, pattern matching and ontologies to detect relevant features and improve predictions. Additionally, we can use rule systems and pattern matching to build heuristics. Ultimately, the main purpose of the entity is to prioritise its own entropy. Hence, we wish to explore more complex prioritisation algorithms such as minmax and game theory. We considered these elements pivotal for making analogies and deductive reasoning but excluded them from the initial scope as we did not consider them essential for building a model of minimal selfhood or proto-consciousness.

Information theory provides a solid ground for measuring information flows. However, inside the model, we accumulate data that we use to improve our predictions and prioritisation. We measured the entropy of the whole simulation in these simplistic simulations. In the future, we will explore the measurement of the current information inside the model.

In summary, we proposed a formal definition for proto-consciousness considering previous state-of-the-art work like GWT, IIT and minimal selfhood. We used information theory to provide the grounds for measuring awareness. We demonstrated with an implementation of the proposed model that a proto-conscious simulated entity can act for its own benefit, prioritising its number of available actions. In future work, we will explore more complex simulations in more complex environments, more complex models to represent the surrounding environment and alternatives to measure awareness inside the model.

Bibliography

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Glasgow, R. (2018). Minimal Selfhood and the Origins of Consciousness.

Tononi, G., Albantakis, L., & Oizumi, M. (2014, May 8). From the Phenomenology to the Mechanisms of Consciousness: Integrated Information Theory 3.0. PLoS Comput Biol, 10(5). https://doi.org/10.1371/journal.pcbi.1003588

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Vinyals, O., Babuschkin, I., & Silver, D. (2019, October 30). Grandmaster level in StarCraft II using multi-agent reinforcement learning. Nature, (575), 350–354. https://doi.org/10.1038/s41586-019-1724-z

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Appendix A: Python workbook

Appendix B: Work in docx