Models of Consciousness

One in a series of talks from the 2019 Models of Consciousness conference. Jonathan Mason

Mathematical Institute, University of Oxford

Over recent decades several complementary mathematical theories of consciousness have been put forward including Karl Friston’s Free Energy Principle and Giulio Tononi’s Integrated Information Theory. In contrast to these, in this talk I present the theory of Expected Float Entropy minimisation (EFE minimisation) which is an attempt to explain how the brain defines the

content of consciousness up to relationship isomorphism and has been around since 2012. EFE involves a version of conditional Shannon Entropy parameterised by relationships. For systems with bias due to learning, such as various cortical regions, certain choices for the relationship parameters are isolated since giving much lower EFE values than others and, hence, the system defines relationships. It is proposed that, in the context of all these relationships, a brain state acquires meaning in the form of the relational content of the associated experience.

In its simplest form involving only “primary relationships” EFE minimisation can also be considered as a generalisation of the initial topology (i.e. weak topology). For us the family of functions involved are the typical (probable) system states, the common domain of these functions is the set of system nodes (e.g. neurons, tuples of neurons or larger structures) and the common codomain is the set of node states. In the case of the initial topology a topology is already assumed on the common codomain and the initial topology is then the coarsest topology on the common domain for which the functions are continuous. In our case no structure is assumed on either the domain or codomain. Instead EFE minimisation simultaneously finds structures (for us weighted graphs, but topologies could in principle be used) on both the domain and codomain such that the functions are close (in some suitable sense) to being continuous whilst avoiding trivial solutions (such as the two element trivial topology) for which arbitrary improbable functions (system states) would also be continuous. Thus we find the primary relational structures that the system itself defines. In this context objects (visual and auditory) are present and EFE then extends to secondary relationships between such objects by involving correlation for example. To aid application of the theory, computationally cheaper surrogates for EFE are being developed.

Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Aaron Sloman

School of Computer Science, University of Birmingham, UK

Most recent discussions of consciousness focus on a tiny subset of loosely characterized examples of human consciousness, ignoring evolutionary origins and transitions, the diversity of human and non-human phenomena, the variety of functions of consciousness, including consciousness of: possibilities for change, constraints on those possibilities, and implications of the possibilities and constraints -- together enabling extraordinary spatial competences in many species (e.g. portia spiders, squirrels, crows, apes) and, in humans, mathematical consciousness of spatial possibilities/impossibilities/necessities, discussed by Immanuel Kant (1781). (James Gibson missed important details.)

These are products of evolution's repeated discovery and use, in evolved construction-kits, of increasingly complex types of mathematical structure with constrained possibilities, used to specify new species with increasingly complex needs and behaviours, using lower-level impossibilities (constraints) to support higher level possibilities and necessities, employing new biological mechanisms that require more sophisticated information-based control. Such transitions produce new layers of control requirements: including acquisition and use of nutrients and other resources, reproductive processes, physical and informational development in individual organisms, and recognition and use of possibilities for action and their consequences by individuals, using layered mixtures of possibilities and constraints in the environment, over varying spatial and temporal scales (e.g. sand-castles to cranes and cathedrals).

I'll try to show how all this relates to aspects of mathematical consciousness noticed by Kant, essential for creative science and engineering as well as everyday actions, and also involved in spatial cognition used in ancient mathematical discoveries. In contrast, mechanisms using statistical evidence to derive probabilities cannot explain these achievements, and modern logic (unavailable to ancient mathematicians, and non-human species) lacks powerful heuristic features of spatial mathematical reasoning. New models of computation may be required, e.g. sub-neural chemistry-based computation with its mixture of discreteness and continuity (see recent work by Seth Grant).

Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Pedro Resende

Técnico Lisboa

I present a mathematical definition of qualia from which a toy model of consciousness is derived, partly as an attempt to provide a mathematical formulation of the theory of qualia and concepts put forward by C.I. Lewis in 1929. This formulation is guided by the identification of basic principles that convey abstract aspects of the behavior of physical devices that “detect” qualia, such as brains of animals seem to do. The ensuing notion of space of qualia consists of a topological space Q equipped with additional algebraic structure that yields a notion of subjective time and makes Q a so-called stably Gelfand quantale. This leads to interesting conceptual consequences. For instance, “stable observers” emerge naturally and relate closely to the perception of space, which here, contrary to time, is not a primitive notion; and logical versions of quantum superposition and complementarity are obtained. Indeed a mathematical relation exists to quantum theory via operator algebras, due to which a space of qualia can also be regarded as an algebraic and topological model of quantum measurements.

Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Peter Grindrod (joint research with Christopher Lester)

Mathematical Institute, University of Oxford

We seek to model the human cortex with 1B to 10B neurones arranged in a directed and highly modular network (a network of networks); with the tightly coupled modules (each containing 10,000 neurones or so) representing the cortical “columns”. Each neurone has an excitable and refectory dynamic and the neurone-to-neurone connections incur individual time delays. Thus the whole is a massive set of modular delay-differential equations (expensive to solve on a binary computer, but easily implemented within 1.5kg of neural wet- ware). Our early work has shown why evolution has resulted in such a design to ensure optimal use of the limited space and energy available. Indeed we can show that if the time delays were all integers rather than reals then much of the potential behaviour (dynamical degrees of freedom) would be lost.

Simulating a 1B neurone directed graph produces its own big data challenge. We focus on the inner life of these complex dynamical system, and show that the dynamical responses to external stimuli result in distinct, latent (internal), dynamic “states" or modes. These inner subjective and private states govern the immediate dynamical responses to further incoming stimuli. Hence they are candidates for internal “feelings”. So, what is it like to be a human? A human brain must also possess such inertial dynamical states, and a human brain can experience being within them: they are natural and necessary byproducts of the system's architecture and dynamics, and they suggest that the "hard problem of consciousness” is mainly explicable, and can be anticipated, in terms of network science and dynamical systems theory.

The numerical simulation at such large scales requires a special computing platform, such as SpiNNaker (at the University of Manchester). We will set out

the methodology to be deployed in (i) defining such complex systems; (ii) in simulating the spiking behaviour being passed around when such a system is subject to various stimuli; and (iii) the post processing - reverse engineering - of the whole system performance, to demonstrate that internal states/modes exist. We cannot reverse engineer a real human brain at the neurone-to- neurone level, but we can do so for such ambitious simulations.

Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Camilo Miguel Signorelli

Department of Computer Science, University of Oxford

Empirical evidence regarding neural studies of consciousness and conscious perception is mainly unknown in fields such as physics and mathematics, or sometimes even misunderstood by many scientists inside the own field of consciousness research. A critical survey of these experiments reveals different aspects and dynamical features among distinct processes related to the conscious phenomenon. These features and distinctions need to be incorporated in any attempt of modelling consciousness and the study of mathematical structures of consciousness.

Therefore, part of that evidence is first reviewed to later generate a preliminary multi-layer model called Consciousness interaction, suitable for further mathematical generalization. In this “prototype” of theory, biological and cellular principles together with mathematical structures are fundamental ingredients and important complement for current physical descriptions such as dynamical systems, emergent, and sub-emergent properties. One advantage of the mentioned approach is the potential of reducing the apparent number of theories of consciousness to a few models, without the need for a single experiment. Moreover, new insights and empirical predictions are expected after this theoretical exercise, eventually producing a list of few experimental tests to verify or falsify current and future models of consciousness.

Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Sean Tull

Department of Computer Science, University of Oxford

Integrated Information Theory (IIT), developed by Giulio Tononi and collaborators, has emerged as one of the leading scientific theories of consciousness. At the heart of IIT is an algorithm which, based on the level of integration of the internal causal relationships of a physical system in a given state, claims to determine the intensity and quality of its conscious experience. However, IIT is known to possess several technical problems, and is only applicable to simple classical physical systems. To be treated as fundamental, it should ideally be extended to more general physical theories.

In this work, we investigate the formal structure of IIT, and define a notion of generalised integrated information theory in order to address these problems. Formally such a theory specifies a mapping from a given theory of physics to one of conscious experience, each satisfying minimal conditions needed for the IIT algorithm.

In particular we show how a generalisation of IIT may be constructed from any suitable physical process theory, as described mathematically by a symmetric monoidal category. Specialising to classical processes yields IIT as usually defined, while restricting to quantum processes yields the recently proposed Quantum IIT of Zanardi et al. as a special case.

Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Stuart Hameroff

Center for Consciousness Studies, University of Arizona, Tucson, Arizona

The Penrose-Hameroff ‘Orchestrated objective reduction’ (‘Orch OR’) theory suggests consciousness arises from ‘orchestrated’ quantum superpositioned oscillations in microtubules inside brain neurons. These evolve to reach threshold for Penrose ‘objective reduction’ (‘OR’) by E=h/t (E is the gravitational self-energy of the superposition/separation, h is the Planck-Dirac constant, and at the time at which Orch OR occurs) to give moments of conscious experience. Sequences, interference and resonance of entangled moments govern neurophysiology and provide our ‘stream’ of consciousness. Anesthetic gases selectively block consciousness, sparing non-conscious brain activities, binding by quantum coupling with aromatic amino acid rings inside brain proteins. Genomic, proteomic and optogenetic evidence indicate the microtubule protein tubulin as the site of anesthetic action. We (Craddock et al, Scientific Reports 7,9877, 2017) modelled couplings among all 86 aromatic amino acid rings in tubulin, and found a spectrum of terahertz (‘THz’) quantum oscillations including a common mode peak at 613 THz. Simulated presence of 8 different anesthetics each abolished the peak, and dampened the spectrum proportional to anesthetic potency. Non-anesthetic gases which bind in the same regions, but do not cause anesthesia, did not abolish or dampen the THz activity. Orch OR is better supported experimentally than any other theory of consciousness.

Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Sir Roger Penrose

Mathematical Institute, University of Oxford

A common scientific view is that the actions of a human brain could, in principle, be simulated by appropriate computation, and even that it may not be too far into the future before computers become so powerful that they will be able to exceed the mental capabilities of any human being. However, by using examples from chess and mathematics, I argue, that the quality of conscious understanding is something essentially distinct from computation. Nevertheless, I maintain that the action of a conscious brain is the product of physical laws, whence consciousness itself must result from physical processes of some kind. Yet physical actions, over a huge range, can be simulated very precisely by computational techniques, as is exemplified by the LIGO gravitational wave detectors confirming precise calculations, within Einstein’s general relativity theory, of signals from black-hole encounters in distant galaxies.

Despite this, I argue that there is a profound gap in our understanding of how Einstein’s theory affects quantum systems, and that there is reason to believe that the events termed “collapse of the wave-function” take place objectively (gravitational OR), in a way that defies computation, yet should be observable in certain experiments. It is argued that each such event is accompanied by a moment of “proto-consciousness”, and that actual consciousness is the result of vast numbers of such events, orchestrated in an appropriate way so as to provide an actual conscious experience (Orch-OR).

Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Xerxes Arsiwalla

Institute for Bioengineering of Catalonia Barcelona, Spain

Theories of consciousness such as Integrated Information Theory (IIT) and its various approximations are grounded on intrinsic information and causal dynamics. However, what seems to be missing or at least is not explicitly addressed in this framework is the role of meaning. One could argue that conscious experience not only generates information, but also meaning. We postulate that meaning associated to experience is intrinsically generated, is compositional, specific and integrated. How can this be formalized within the context of IIT? Here we propose a framework for computing the compositional meaning of the maximally irreducible conceptual structure or Q-shape in IIT.

A Q-shape is a set of concepts and their relations. To compute the meaning of a Q-shape we apply the category theoretic formulation of Distributional Semantics, used in natural language processing. This assigns to every concept in the Q-shape, a distributional meaning and a grammatical type. By consistency, concepts with very high phi (core concepts) will be the most pertinent for the experience at that specific instance. The distributional meaning of each core concept depends on its relations to all other concepts in the Q- shape and can be computed using a vector space spanned by a basis of concepts as is done in Distributional Semantics.

The grammatical types associated to core concepts are constrained by their relations to other core concepts. Furthermore, a pre-group algebra imposes ordering of grammatical types. We then show how the sub-network of core concepts in the Q-shape can be identified with a category theoretic process diagram. The compositional meaning of this process diagram is computed within a monoidal category and yields the meaning associated to the experience. We demonstrate this computation with a simple toy model. Finally, we comment on how meaning imposes phenomenologically relevant constraints to any information-based theory of consciousness.

Filmed at the Models of Consciousness conference, University of Oxford, September 2019.

One in a series of talks from the 2019 Models of Consciousness conference. Adam Barrett

Sackler Centre for Consciousness Science, University of Sussex, UK

Integrated Information Theory (IIT) has gained a lot of attention for potentially explaining, fundamentally, what is the physical substrate of consciousness. The foundational concepts behind IIT were extremely innovative, and it has been very exciting to see certain predictions being upheld in experiments. However, many problems have been uncovered with the mathematical formulae that IIT proposes for measuring consciousness exactly. This has led to fragmentation amongst consciousness researchers, between those who accept IIT, and those who reject IIT.

In this talk, I make the case for a `weak’ form of IIT as a pillar of a future theory of consciousness, and summarise some of the problems with `strong’ IIT. Weak IIT maintains that neural correlates of consciousness must reflect two key aspects of phenomenology.

First, that each conscious moment is extremely informative (it is one of a vast repertoire of possible experiences). Second, that each conscious experience is integrated (it is experienced as a coherent whole). I review some of the empirical evidence for this, in the form of greater diversity and connectivity in observed neural dynamics from conscious versus unconscious humans. I then discuss how the Phi measure of integrated information is not well-defined, and not unique given the axioms of IIT, and hence that the current version of strong IIT should be rejected. I conclude with some discussion on possible ways forward.

Filmed at the Models of Consciousness conference, University of Oxford, September 2019.