Gang Fang's Blog

Link to paper: https://arxiv.org/pdf/2302.06403

My interest in this paper originally came from my study of GFlowNet, which is a new deep learning framework proposed by Mila, and is said to be useful in constructing compositional objects. Consciousness can be considered as a compositional object because it appears to be sequential when ideas and thoughts build, one after another.

As the title of the paper suggests, the paper discusses two prominent properties of phenomenal, or in a more layman term, subjective conscious states, and these two properties are richness and ineffability. The most important contribution of this paper is a new framework that the authors proposed to explain where these two properties come from. Though this new framework builds on top of existing work, which is fairly established. This paper reads more like an integration of multiple theories, rather than an introduction to a whole new idea. Mind you, this is not a complaint because as someone who has near-zero exposure to literature in brain science and consciousness, I enjoyed very much the introduction of various theories as I made progress in my reading towards its conclusion. Finally, I was disappointed a bit about the absence of GFlowNet in the paper but nevertheless, I am satisfied to see the Global Workspace Theory of Consciousness is referenced and discussed under the context of the proposed framework.

Before moving on to the next chapter discussing ideas presented in the paper, I wanted to highlight at the high level this paper attempts to tackle the so-called hard problem of consciousness involving subjective experience, or at least the prominent properties of it. The hard problem of consciousness by Chalmers is the problem of showing phenomenal consciousness can be explained in terms of or reduced to underlying physical processes. The author’s answer is the information dynamical systems perspective. (In contrast, the easy problem of consciousness is all functional. It asks questions about features of the mind that can be explained computationally or neuroscientifically without touching on the subjective aspect.)

Concepts: neural dynamics

Here are several important concepts necessary for author’s framework: Shannon’s Information Theory, Kolmogorov Complexity Theory, Neural Activation State, Neurodynamics, State’s Attractors, Working Memory, and Global Workspace Theory.

The paper started with the introduction to Neural Dynamics, which is a computational view of the brain. It explains the state space of neural activation, and neural activation can be numerically quantified in several different ways. For example, firing of neurons, their firing rate, membrane voltage, and so on. With the billions of neurons together forming a vector, a state can be specified, and the entire space of combinations of these vectors compose the state space.

Once the concept of state-space is established, the natural follow-up question is how our brain moves through this space and the mechanism of it. This question is answered by Neural Dynamics, which describes the trajectory of the state change through time. And can be depicted using a vector field as below.

In the vector field of Neural Dynamics, sinks can be found with an accompanying basin. These sinks are called State Attractors. Neural Activity Trajectories, once reach the basin of an attractor, progress towards the attractor state and remain there. Note that this typically happens in the absence of intrinsic noise in neural activity or changes in external input. This can be related to the subjective experience of attention. When we focus attention on a specific thing, it takes a sufficiently strong disruption to pull us away from that focus, similar to the neural state being pulled away from the attractor by a strong external disturbance.

One more interesting idea about attractors is they are mutually exclusive.
From the state space perspective, this is a discretization of the space. because the neural state eventually reaches the fixed point of an attractor and the attractors are not continuous, but discrete. They and their basins occupy different areas of the state space. This explains the subjective experience of attention, where we can focus on one particular thing at a time, but not multiple. Also, the transition of attention from one thing to the next feels swifter than continuous.

Framework: an information dynamical systems perspective on conscious experience

The last section discusses Neural Dynamics, the foundational building block for the framework proposed in the paper. We will now look at the framework in this section.

The first discussion happens around working memory and its properties. Working memory is central to the Global Workspace Theory of Consciousness. The claim is that we are consciously aware of the contents in our working memory, which is this global workspace used by other brain regions to communicate in a broadcasting fashion. The attractor model postulates that working memory emerges from recurrently connected cortical neural networks that allow representations to be maintained in the short term, on the order of seconds, by self-generated positive feedback.

Properties of conscious states/working memory are stability and robustness. As described in the last section, discrete attractor dynamics predict that our experience consists of a sequence of relatively stable states that transition shiftly from one to another. An interesting example the authors provided is the Necker Cube. There are multiple (usually two) interpretations of the structure of a Necker Cube and we can only perceive one single interpretation at a time rather than a mixture of both. Occasionally, this interpretation will change to the alternative one, but that happens rapidly and abruptly.

Next, the authors dive into the central discussion of the paper, which is richness and ineffability of consciousness. The two properties of consciousness are, to me, two sides of the same coin in that only rich content or experience is ineffable. The definition provided in the paper of richness in the context of mental states is the large amount of specificity: details, texture, nuance, or informational content contained by a mental state. And the definition of ineffability is that experience is too great for words, where the conscious informational content exceeds what we can remember or report.

To move one step further, the mathematical or information-theoretical definition of richness of a random variable X is given by its entropy H(X). When the entropy of X is high, we know there are large number of possible values for X, and the probability distribution of X is relatively flat, and therefore, its state is more unpredictable. Similarly, the mathematical or information-theoretical definition of ineffability is information loss (when trying to express a conscious state in words) measurable by the conditional entropy H(X|Y), X represents the rich consciousness and Y represents verbal report or recall. It can be understood as how well Y describes X, how much uncertainty remains about the value of X once the value of Y is given.

The alternative theoretical foundation to information theory for describing richness and ineffability is Kolmogorov Complexity. The benefit of Kolmogorov Complexity is that it is defined on individual states of consciousness without assuming a given probability distribution because knowledge of the distribution is generally a non-trivial assumption. With Kolmogorov Complexity, ineffability corresponds to conditional Kolmogorov Complexity of an input x given an output y, K(x|y), the length of the shortest program needed to produce x if y is given. Or intuitively, the complexity of x minus the number of bits that can be saved from knowing y.

Intra-personal ineffability

The diagram above is the central model proposed by the author describing the relationship among neuro-dynamical trajectories, attractor states, conscious experience and verbal reporting.

Conscious Experience S is a function of the subject’s cognitive parameters θ and working memory trajectories x and encodes the experience meaning.

The dynamical systems model of working memory distinguishes between two kinds of working memory states, attractor states and transient states, where the latter includes all time-varying states occupied by the system and the former corresponds to the system output, or the accessible contents of working memory.

The snapshot belows shows my understanding of the relationships among GWT, the neural dynamical system, consciousness, working memory and attention.

Here are three aspects that are left out in the picture:

• relationship between the global workspace in GWT and working memory: it has never been stated that they were the same thing, but “it is easy to see the connection between the concepts of a global workspace and working memory and there is little distinction between them in the Global Workspace Theory”.
• relationship between Global Workspace Theory and reporting/recall, GWT predicts that only representations with sufficient amplification and temporal duration (i.e., attractor states) can be broadcast to the rest of the brain for downstream verbal-behavioral reporting. These representations are by definition attended to.
• how Global Workspace Theory explains consciousness: information becomes conscious by gaining entry into a limited workspace that serves as a bottleneck for the distributed activity present across the brain.

The last thing in this section is the hierarchical attractor dynamics. Attractor dynamics appear to be ubiquitous across organizational levels and cortical regions of the brain. tAnatomically, the inferior temporal cortex is an example of a sensory processing area that responses discriminatively to novel stimuli, whereas the prefrontal cortex is implicated in maintaining attention-modulated projections of such representations in working memory. Neural activity in both regions maintains persistence over time and exhibits attractor dynamics. The ability of prefrontal attractor to stabilize in its high firing rate attractor state is attributable to positive feedback from strong internal recurrent connections that suppress incoming stimuli.