EDIT (Oct 1, 2022): I now think a) I'm overextending some of these theories of consciousness, and so am mistaken about some of them in practice (e.g. GWT is not meant to be a general theory of consciousness or explain what makes something conscious, and is better thought of describing neural correlates of consciousness in humans in practice, although this also counts against the theories) and b) perhaps sometimes misinterpreting theories (possibly most of the "(Other) Higher-order processes" section).

Summary: The necessary features for consciousness in prominent physical theories of consciousness that are actually described in terms of physical processes do not exclude panpsychism, the possibility that consciousness is ubiquitous in nature, including in things which aren't typically considered alive. I’m not claiming panpsychism is true, although this significantly increases my credence in it, and those other theories could still be useful as approximations to judge degrees of consciousness. Overall, I'm skeptical that further progress in theories of consciousness will give us plausible descriptions of physical processes necessary for consciousness that don't arbitrarily exclude panpsychism, whether or not panpsychism is true.

The proposed necessary features I will look at are information integration, attention, recurrent processes, and some higher-order processes. These are the main features I've come across, but this list may not be exhaustive.

I conclude with a short section on processes that matter morally.

Some good discussion prompted by this post ended up on Facebook here.

Disclaimer and level of confidence: I am not an expert in neuroscience, consciousness or philosophy of mind, and have done approximately no formal study on these topics. This article was written based on 1-2 weeks of research. I'm fairly confident in the claim that theories of consciousness can't justifiably rule out panpsychism (there are other experts claiming this, too; see the quotes in the Related work section), but not confident in my characterizations of these theories, which I understand mostly only at a high level.

Related work

Similar points are made by Brian Tomasik here. For more of Brian's writings on consciousness and panpsychism, see his section of articles here, especially also:

• https://longtermrisk.org/the-eliminativist-approach-to-consciousness/
• https://reducing-suffering.org/is-there-suffering-in-fundamental-physics/

In this paper, it's argued that each of several proposed precise requirements for consciousness can be met by a neural network with just a handful of neurons. The authors call this the "small network argument". (Thanks also to Brian for sharing this.) I quote:

For example, two neurons, mutually interconnected, make up a recurrent system. Hence, these two neurons must create consciousness if recurrence is sufficient for consciousness (e.g. Lamme, 2006). Minimal models of winnertake-all computations require only three “competing” neurons which are fully connected to three presynaptic input neurons, plus potentially a single neuron controlling vigilance (Grossberg, 1999). Hence, such a network of seven neurons is sufficient to develop resonant states allowing learning (Grossberg, 1999) and working memory (Taylor, 1998). Analogously, if neural oscillations or synchrony are the main characteristics of consciousness, then, a group of three interconnected neurons firing in synchrony is conscious. Similarly, a thermostat, typically modelled as a single control loop between a temperature sensor (‘perception’) and an on-off switch for a heater (‘action’), is a classical example of a perception-action device. It can be formulated as a two-neuron feedforward network with a sensory neuron connecting onto an output neuron controlling the heater switch.

(...)

Still, attention can be integrated within a small network just by adding one extra input arising from a second group of neurons (e.g. Hamker, 2004)- containing potentially a very small number of cells.

In this paper, the same point is made, and it's further concluded that popular theories like IIT, RPT and GNWT "endorse panpsychism" under a slightly limited form "where all animals and possibly even plants would be conscious, or at least express the unconscious/conscious dichotomy." The author writes:

Current models of consciousness all suffer from the same problem: at their core, they are fairly simple, too simple maybe. The distinction between feedforward and recurrent processing already exists between two reciprocally connected neurons. Add a third and we can distinguish between ‘local’ and ‘global’ recurrent processing. From a functional perspective, processes like integration, feature binding, global access, attention, report, working memory, metacognition and many others can be modelled with a limited set of mechanisms (or lines of Matlab code). More importantly, it is getting increasingly clear that versions of these functions exist throughout the animal kingdom, and maybe even in plants.

In my view, these don't go far enough in their conclusions. Why shouldn't an electron and its position count as a neuron and its activity? With that, we get a fuller panpsychism.

For descriptions of and discussion about specific physical theories of consciousness, see:

• https://plato.stanford.edu/entries/consciousness-neuroscience/#NeurTheoCons
• http://www.scholarpedia.org/article/Models_of_consciousness
• https://plato.stanford.edu/entries/consciousness/#SpeTheCon
• https://www.openphilanthropy.org/2017-report-consciousness-and-moral-patienthood#AppendixB

Information integration

1. Anytime what happens at one location depends causally separately on each of at least two other different locations (regardless of the dependence of those two locations with each other), this is a kind of information integration, in my view. This is widespread. For example, an electron's position depends causally on multiple things.

EDIT: It seems Integrated Information Theory depends on more than just information integration as I describe it above, although the theory is considered panpsychist. Rather, integration is a kind of mutual dependence, so that causal cycles are necessary, and IIT focuses on irreducible systems, in which each part affects each other part; see here. See the next section on recurrent processes.

Attention and recurrent processes

0. Bottom-up attention is just information integration, which is feedforward, i.e. no directed loops, so no neuron can feed into itself, including through other neurons. A causal relationship like $A\to B\to \cdots \to A$ is recurrent, where $X\to Y$ indicates $X$ causes $Y$ or $Y$ depends causally on $X$.

1. Top-down/selective attention is “global” recurrent processing and reduces to local recurrent processing, because “global” is meaningless without qualification to what system it is global to. See the reduction from GWT to RPT here. See the description of GWT (GNWT) in the abstract here.

2. Recurrent processing reduces to feedforward processing over time, because the causal graph is feedforward, with nodes labelled by "neuron, time" pairs. Think unfolded/unrolled recurrent neural networks in AI. For example, "Neuron $A$ fires, causing $B$ to fire, causing $A$ to fire again, causing $B$ to fire again" is the same as "$A_0$ fires, causing $B_0$ to fire, causing $A_1$ to fire, causing $B_1$ to fire", which is feedforward and not recurrent.

All recurrent processing necessary for consciousness has finite depth in practice or else you're not conscious, and the difference between depth 3 (enough for a cycle) and any higher depth is a matter of degree, not kind. Unbounded in principle shouldn’t matter if it’s always finite, because that would mean events that never happen determine whether or not a process is conscious.

• Maybe the “same” neuron should be used in the cycle, but this is an important metaphysical claim, and requires identity to be preserved in some way over time in a way that matters, and it's also unfalsifiable, since we could approximate recurrent behaviour arbitrarily closely with purely feedforward processes. This seems pretty unlikely to me, but perhaps not extremely unlikely to me. Indeed, feedforward networks are universal approximators, so any function a network with recurrence can implement, a feedforward network can approximate, at least in terms of inputs and outputs. This is the "unfolding argument" in this paper. To me, the stronger argument is that every network is metaphysically a feedforward one, including all of its inner workings and intermediate processes and states, assuming identity doesn't matter in a strict sense.
• Maybe the feedforward processing should work in a certain way to suitably simulate recurrent processing. This seems like a matter of degree, not kind, and feedforward processing with depth at least 3 should basically always simulate some recurrent process with nonzero accuracy, i.e. $A\to B\to C$ simulates some $D\to E\to D$ to some degree. EDIT: Maybe $D\to E\to D$ shouldn't be called recurrent, since it only has one instance of each of $D\to E$ and $E\to D$, so we should look at $D\to E\to D\to E$ or $D\to E\to D\to E\to D$; the latter has two of each arrow.

3. Recurrent processing is ubiquitous anyway. An electron influences other particles, which in turn influence the electron. (Credit to Brian Tomasik)

(Other) Higher-order processes

See also Brian's writing here, from which some of these arguments are taken.

1. Requiring higher-order of degree > 2 is arbitrary and should be reduced to 2, if the kind of required higher-order relationship is the same.

2. The line between brain and outside is arbitrary, so second-order theories reduce to particular first-order ones. For a mental state (brain process) $X$ to be experienced consciously, higher-order theories require some $Y$, which takes output from $X$ as input, with certain relationships between $X$ and $Y$. But why should $X$ be in the brain itself? If neurons relate to changes in the outside world with the same kind relationship, then the outside world is experienced consciously. So second-order reduces to a kind of first-order. Relatedly, see the generic objection to higher-order theories here which roughly states that Y being "aware" of a rock X doesn't make X a conscious rock.

3. If $X$ causes $Y$, then $Y$ predicts $X$ to nonzero degree. Under one characterization of higher-order processes (e.g. see here), we require $Y$ to predict future “brain” state/processes $X$ with input from $X$ for $X$ to be experienced consciously (if we also require attention for some kind of reflectivity, see the first section). How accurately does $Y$ have to predict $X$ and how should we measure this? If it were perfectly, we wouldn’t be conscious. The line seems to be arbitrary, so this is a matter of degree, not kind, and basically any $Y$ connected to $X$ should predict $X$ to nonzero degree.

• We could say $Y$ predicts $X$ if $X$ does not receive input from $Y$, and the correlation between $Y$ at $t_1$ and $X$ at $t_2>t_1$ is nonzero, or $Y$ at $t_1$ and X at $t_2$ are not statistically independent. However, this too seems pretty ubiquitous: if neuron $X$ fires because it receives some sensory input, and neuron $Y$ fires because $X$ does, there's a better chance than average that $X$ will continue to receive similar input and fire again, so $Y$ firing predicts $X$ firing again, and often does so reasonably well.
• (More plausible than the stipulation that $X$ does not receive input from $Y$ is that there's a dependence or correlation between $Y$ at $t_1$ and X at $t_2>t_1$ even if we hold constant the information flowing from $Y$ to $X$.)
• Maybe instead, with times $t_0<t_1<t_2$, $X$ acts at $t_0$, $Y$ receives input from $X$ and reacts at $t_1$, $X$ acts again at $t_2$, and Y at $t_1$ should correlate with some measure of difference between $X$ at $t_0$ and $X$ at $t_1$, so that $Y$ predicts changes in $X$. But even this can often happen by coincidence, and I don't see a non-arbitrary and principled way to distinguish coincidence from non-coincidence. I assign probability ~0 to the claim that $Y$ does not predict changes in $X$ if $X$'s behaviour causes $Y$'s, since this would require a perfect probabilistic balancing of events. Furthermore, there are multiple ways to measure change in $X$, it's unlikely any particular one is "the right way", and it's extremely unlikely this perfect balance would be achieved for multiple nonequivalent measures at the same time.

4. Even if we require higher orders, these will happen ubiquitously by chance, because these higher order relationships are everywhere, like in 3. One particle affects another, which affects another, which affects another, etc.. (Credits to Brian Tomasik again.)

5. Learning isn't necessary. Maybe we require $Y$ to be trainable to get better at predicting $X$ (or to improve the degree of their higher-order relationship). However, it doesn’t seem like we should require it to continuously be trained, so if we disconnect the system to update $Y$ (e.g. by anterograde amnesia or disconnecting the reinforcement learning system), why would $X$ no longer be consciously experienced? See “Do non-RL agents matter?” here.

Remark: If $Y$=brain relates to $X$=environment in a higher-order way and to no other systems, and we require higher-order relationships, then any suffering isn’t happening in $Y$ alone, but in $X$ and $Y$ together. If there’s suffering in $X$ and $Y$, it’s more like $Y$, the brain, is conscious of pain in $X$, the environment, according to higher-order theories. This is still compatible with panpsychism, but seems like a morally important difference without the higher-order requirement, if only as a matter of degree. Also very weird.

What about specific combinations of these processes?

For example, sensory inputs feeding into top-down and bottom-up attention feeding into working memory, a self-model and output. Essentially, this is a graph embedding problem: how well does this abstract organization of processes, this "pattern", apply to this specific physical process? I think if each of the processes in the pattern can be found ubiquitously in nature, the pattern will have to be very complex, perhaps intractably and unjustifiably complex, to not be found ubiquitously in nature as well. It seems unlikely we'll be able to require specific numbers of neurons in subnetworks implementing one feature, e.g. in an attention subnetwork. Sure, we could say, the smallest number ever used for introspective report so far, but we won't be able to prove that it can't be done with fewer, and this number will continue to decrease over time. It is not enough to knock out neurons in an existing brain to rule our the possibility that it couldn't be done with fewer; you'd have to test different organizations of these neurons. I doubt that this will ever be feasible in a way that gives us reliable observations, e.g. reports we'll trust.

Still, this seems like it might be a more promising route for progress, if we don't think specific individual kinds of low-level processes are enough. Looking into more global or holistic features like brain waves might also be promising.

A major concern is overfitting our theory to our observations in humans. We want a general theory of consciousness, not a theory of consciousness in human brains.

Processes that matter morally

1. As far as I know, there’s no (plausible) account of what suffering, pleasure, preference and preference satisfaction, etc. are in terms of basic physical processes, to distinguish them from other conscious processes. I expect any such account to face objections and reductions similar to those above.

2. I don’t think morally relevant processes depend in principle on learning, since you could remove the learning/updates. See “Do non-RL agents matter?” here.

3. However, systems that were tuned by learning or are more similar to systems tuned by learning, in my view, matter more in expectation.