Why do we need to care category theory and quantum cognition?

In my latest Consciousness Dialogue with Alex Maier [Link], @alexvmaier we chatted a bit about this issue.

Why am I motivated to learn and apply category theory on the data in consciousness research? Why am I interested in quantum cognition by Busemeyer, Bruza, Trueblood, @EmmanuelPothos , ….?

In our discussion, I pointed out an empirical need for a theory that can explain enigmatic findings in similarity experiments. In most similarity experiments, we (implicitly) assume that inverse of similarity (=dissimilarity) is like a distance. A metric (or distance) needs to satisfy the following three axioms. https://en.wikipedia.org/wiki/Metric_(mathematics)

1. Minimality: d(a,b) = 0 <=> a = b
2. Symmetry: d(a,b) = d(b,a)
3. Triangle inequality: d(a,b) <= d(a,c) + d(c,b)

In the video, we chatted a bit on the violation of “2. symmetry”. We are preparing several drafts on this. If you are interested, please see Tversky 1977, Pothos et al 2013 Psych Review.

There is one thing that I couldn’t mention in the video. And in fact, this may be more important. We need a “theory” that is “independent” of the data. This is most eloquently described Steve Phillips’s paper in 2010 (PLoS Comp)

“The Ptolemean (geocentric) theory’s additional assumption (called “epicycles”) is ad hoc. It is unconnected with the rest of the theory and motivated only by the need to fit the data—the assumption could not be confirmed independently of confirming the theory.”

Category theory is a mathematical theory constructed to study “structures”.

Quantum cognition is a mathematical theory that is based on noncommutative probability theory.

These theories are built independent of the data that we want to explain (e.g., the properties of consciousness / qualia). We don’t know if it’s applicable to the data or not.

This is different from testing “theories” that were constructed from the data to be explained. Such “theories” is unfortunately immune to “ad hoc” explanation. Even the theorists themselves do not notice how the theory has changed over the time “to fit” it with the data….

On the process theory and qualia

On Picturing Quantum Processes by Coecke & Kissinger

David Bohm and David Peat wrote in 1987 “We haven’t actually paid much attention to thought as a process. We have engaged in thoughts, but we have only paid attention to the content, not to the process”

I’m guessing that the same may be true for qualia / consciousness.

Here “process” means what is discussed in “process theory”. Process is anything that has zero or more inputs and zero or more outputs. Process theories seem quite useful in the context of quantum theory (and it has a link to category theory).

A function takes one or more inputs and outputs one. Functions are just one example of processes.

A more general notion is a relation. A relation links many inputs to many outputs. It can be considered as a stochastic output. Relations are much closer to what neurons are and more likely to be useful to understand how the brain works. (But most neuroscientists including myself probably don’t know much about relations…)

Ch3 of the Picturing Quantum Processes explains it very well “3.3 Functions and Relations as Processes”.

And processes are even more general. It allows even NO inputs or NO outputs. And this is the reason I think processes are much better concepts than functions or relations when we think about qualia and consciousness.

Thinking about consciousness as something that is defined / induced / evoked by stimulus is misleading. Something that causes motor output is also misleading. Consciousness exists in dreaming and hallucination. Consciousness exists in locked-in or even more severe brain damaged patients. Phenomenal consciousness may or may not be reportable. But if phenomenal consciousness is considered as a process, it doesn’t matter.

死ぬまであと４５年＝５４０ヶ月＝３０００週。何ができるか、何がしたいかを考え直してみた。

Die With Zero という本は、死ぬときに貯金を０にするように、貯めて貯めて、アリのように生きるのはこれからの時代にはあわないという本だ。寿命が伸びること、伸びた分の年老いたときにお金を使っても、対して楽しめないこと、人生の目的は思い出づくりだ！ など、読んで考えられさせられるところが色々あった。

Die with zero を読んでいるうちに気になって、自分の寿命予測をしてみた。https://www.arealme.com/when-will-i-die/ja/ というサイトを使用。多分生年月日・性別などで予測してるんだろう。運動・食事・睡眠についても聞かれたが、どれだけ精度が高いのかは不明。
そして、出た私の寿命予測はあと４５年！

最近やっているライフハックを続けて、更に健康を高めるような生活すれば、楽に１４０歳くらいまでは生きれるかなぁと思っていた。なので、突如、予定より５０年くらい私の人生の残り時間が短くなる宣告を受けた。（なので、今週から食事も改善することに着手。Eat To Live という本がおもしろい）

Life Shift や Life Span でも言われているように、今後確実に寿命は、全人口を通じてさらに伸びるだろう。問題なのは「健康寿命」がみんな一様に伸びるのかということ。私の世代だと、どうやら女の人で平均１３年、男で平均９年、最後の人生を「不健康」に生きる確率が高い。

私は、９年間も不健康に生きる気が、無い。なので、死ぬ直前まで、やりたいことができる頭と体をキープしたい。意識と脳の関係性についてどこまで明らかになるのかを見届けたい。

寿命予測は、他の人に対してやってみても色々考えさせられた。私の両親の寿命予測をすると、あと１３−１７年くらいだ。週で言うと７００−９００週。２週に一回のズームやったとして会うのはあと３５０回くらい。後悔しないように色々思い出づくりができたらと思う。

親以外の人間関係についても考え直すきっかけになった。新しい人間関係を作るのは若い時は重要だった。が、私にとってはこれからは、コアな関係（２週に一回はどう？といえる感じの仲）と、ゆるい関係（メールすれば返事がくる？）の区別が大事だなと。各人と何がしたいか、何ができるか考えよう。

最終的には意識の研究をしたいが…

たまに、学生（とくに大学生）から、「最終的には意識の研究をしたいが、今はとりあえず分子生物学、とか、機械学習を博士課程ではやりたいと考えているがどう思うか？」的な質問を受ける（日本でもオーストラリアでも）。（こういうのはなぜかシンクロして数人から同時に聞かれる）

分子とか機械学習の研究やるのは良いが、自分のゴールを見失わないようにした方がいい。私の知り合いに、学生の頃から意識をやりたくて研究者になったが、それ以外の研究で成果を出して、その後はそのフォローアップに研究人生を費やした人がいる。

で、引退直前にある学会で、「ああ、俺はこういうのがやりたかったんだ！」と思い出した。このままじゃ死にきれない、とそこから舵を取り直し、ラボの方向性を完全に変更して意識研究。今は幸せそう。

死ぬ前の５大後悔にも通じる話。https://theguardian.com/lifeandstyle/2012/feb/01/top-five-regrets-of-the-dying…　本当に自分がやりたいこと、そしてそれが自分の強み・得意なことなのか、真剣に考えぬいてから始めた方がいい。当たり前の話しで外でもよく言われていることだけど。

というTweetをしたらある程度反響があったのでブログに載せてみた。

後に、「とりあえず」でやっているわけではない、色々と考えがあってやってます、というリプライをもらった。考えがあってやってんだったら、なんで私の意見を聞きたいのかよくわからない。。。

ただ、このリプライした後で、「科学的な適職」By 鈴木祐 に出会い、まだちゃんと読んでないが、上のアドバイスは今後良くない部分も含んでイそうだなぁと思う部分もあるので、また後日Tweetなり、ブログなどで考えを書きます。

Eventually, I want to do research on consciousness, but …

Sometimes students (both undergrads and PhD students) ask me questions like, “Eventually, I want to do research on consciousness, but for now, I am thinking of doing molecular biology or machine learning for my doctoral degree. What do you think?”

[Usually, they don’t state why they are studying molecular biology or machine learning now. My guess is that they are hedging the risk. Currently popular topics seem to give more job opportunities, perhaps?]

Fine to start with any field. But make sure not lose your original goal. I know a guy who wanted to be a researcher because of his interests in consciousness from young. Upon publication of a great paper in other field, he spent all his research career to follow it up.

Just before his retirement at a conference, he realized, “Oh, this [=consciousness] is exactly what I wanted to do!” He thought he can’t die without doing consciousness research and changed the direction of the lab completely, starting consciousness research. He seems to be happy now.

This story sounds consistent with the five biggest regrets before dying. https://theguardian.com/lifeandstyle/2012/feb/01/top-five-regrets-of-the-dying….

I tend to suggest students to seriously think about what you really want to do and whether it is something you are good at. It’s an obvious thing, but hope it helps for some.

At some point, I might want to write something about scientifically proven ways to find the best job for you.

Our latest paper finally came out! The Yoneda lemma paper!

Naotsugu Tsuchiya, Hayato Saigo, A relational approach to consciousness: categories of level and contents of consciousness, Neuroscience of Consciousness, Volume 2021, Issue 2, 2021, niab034, https://doi.org/10.1093/nc/niab034

Finally, our paper is out! In this paper, we introduce one of the most important consequence in category theory, the Yoneda Lemma, to consciousness research! @FQXi

The Yoneda perspective, applied to consciousness research, implies that we can characterize any quale through characterizing a massive relationships between a quale and other qualia! In math terms, hA~=hB <-> A~=B.

Along the way to get to the Yoneda lemma, we gently introduce various useful concepts in category theory (e.g., category, functor, natural transformations, hom functors, equivalence). This paper can serve as an entry point to category theory for consciousness researchers!

This paper will be the first part of our trilogy. The second one (under revision) will extend this approach to “enriched category theory”. With that, we can deal with the graded levels of relations between qualia (e.g., similarity ratings).

This will allow many important theoretical tools in category theory to connect with empirical psychophysics, neuroscience (e.g., representational similarity) and theoretical research (e.g., maximally irreducible conceptual structure in the integrated information theory).

(The last one (which we haven’t started writing…) is supposed to close any loose end through sheaf theory.) Anyways, I didn’t know that this paper was already published already last week…

Our lab’s Research Statement

Overview:

The goal of our research is to understand the physical substrate of consciousness. How is our conscious experience supported by our brain? To address this question, we need to make various breakthroughs. We strive to establish new paradigms and techniques based on our creative ideas. We will develop new and clever experimental or analytical developments. They will allow us to observe and manipulate consciousness for rigorous scientific investigation.

We have contributed to this in several domains (See Research focus so far). We are also building novel empirical methodologies (See Future and ongoing research).

Building on our basic research, we also work on research translation. In particular, into clinical and industry domains. These researches aim to improve the accuracy in measurement of consciousness. It also aims to improve conscious creativity while reducing mind wandering. It also aims to improve (collective) intelligence research informed by consciousness research.

Research focus so far

We have used various techniques. The range of techniques include but not limited to: psychophysics, neuroimaging, and modeling. We collaborate with researchers who work on the brains of humans and animals. Interdisciplinary collaboration has involved philosophers, clinicians, engineers, neurophysiologists, mathematicians and physicists.

1) Understanding the boundary between conscious and nonconscious processing.

One of the most effective ways to study consciousness is to contrast

conscious and unconscious states of the brain. When conscious, people or animals are awake. Unconscious states can result from brain injury, general anesthesia, or deep sleep.

Another most effective method is to contrast conscious and nonconscious processing. When we are conscious, we perceive certain things but not others at a moment. That is the contrast in contents of consciousness, or qulia for short.

We invented a technique, known as Continuous Flash Suppression (CFS; Tsuchiya & Koch 2005).

CFS is a technique in visual psychophysics. With CFS, researchers can suppress a salient visual stimulus. CFS can suppress almost any image for a long duration in a controlled manner. CFS helps uncover the neural processing that does not give rise to consciousness. We used CFS to study nonconscious emotional processing in the lesion patients (Tsuchiya et al 2007). Cognitive neuroscientists worldwide use CFS in combination with neuroimaging. Our work continues to clarify the boundary between the conscious and the nonconscious.

2) Clarifying the relationships between consciousness and associated psychological processes

What is the relationship between consciousness and other psychological processes? Attention, memory, access and report are all important parts of our life. How are they related to consciousness?

Philosophers and psychologists have long discussed the relationship between attention and consciousness. And this discussion is now extending to AI and other fields.

Based on empirical evidence, we have been proposing to distinguish the two (Koch & Tsuchiya 2007). The two can work together but often dissociate. Sometimes working towards the opposite directions. We demonstrated it using psychophysics (van Boxtel, Tsuchiya, Koch 2010) and EEG (Davidson et al 2020). Key is to independently manipulate consciousness and attention. We have various paradigms at hands to do this (Matthews et al 2018).

No-report paradigms are also necessary to truly understand the neural basis of consciousness (Tsuchiya et al 2015). They allow us to distinguish the effects of the act or intention to report on the contents of consciousness.

3) Testing the quantitative theories of consciousness

We have been working on Integrated Information Theory (IIT) of consciousness. IIT is currently one of the most promising quantitative theories of consciousness. Its explanatory and predictive power on consciousness is quite attractive. Yet, IIT has been criticized as being impossible to be tested.

Our aim is to test IIT in its prediction. Towards this aim, we developed accurate proxies of integrated information (Oizumi et al 2016 x2, Cohen et al 2019). Our tools are available on the web. We have characterized integrated information in relation to other known measures. Based on these developments, we have started testing IIT’s claims with real neural recordings (Haun et al 2017, Leung et al 2021). Our measures of integrated information can be applied to other fields of network science. Physicists, social neuroscientists and others have started using them for their research objectives.

Future and ongoing research

4) Big data analysis on loss of consciousness

We have been trying to distinguish states of wakefulness from loss of consciousness. We try to develop better classification between wake and anesthesia-induced loss of consciousness (Cohen et al 2017, 2018, Leung et al 2021). We are also interested in distinguishing dreamful vs. dreamless NREM sleep (Wong et al 2020). We are extending this direction into conscious vs. unconscious brain injured patients.

Our focus so far has been on electroencephalography (EEG) data. EEG has high temporal resolution. making it easy to test some theoretical measures of consciousness. EEG is available in many hospitals and much cheaper than other devices. Thus any methods to detect consciousness based on EEG is easier to translate to clinics.

To develop novel methods, we have collaborated with physicists to apply complexity measures (Munos et al 2020). We are also applying >7700 analysis methods at the same time on the same data to search for the best . This method is called highly comparative time series analysis (Fulcher 2017). For this end, we are quite keen to collaborate with many scientists to construct a large EEG dataset.

5) Massive report paradigms to characterise the structure of conscious experience.

Traditional psychophysics on consciousness has focused on binary categorical responses. For example, seen vs. unseen responses through button presses. While easy to analyze, they are poor in capturing richness of consciousness. We need a better way to characterize the structure of human conscious experience.

We have been developing various ways to extend reporting methods. We call these as “massive report paradigms” to distinguish it from simpler alternatives. To collect a big enough dataset, we develop various web-based psychophysics experiments.

The challenge of these new experiments is the complexity of the analysis. We have been exploring automatizing the scoring procedure. Here, we see a huge opportunity for collaborating with researchers in other fields. AI, math, linguistic and topological data analysis.

6) Discovering a structural mapping between consciousness and information

What do we need to understand the relationship between the brain and consciousness? We have proposed a three-step approach  (Tsuchiya et al 2016). It starts with revealing the structures of consciousness. In parallel, it tries to reveal the structures of information. This information structure has to be relevant to consciousness. Then, it eventually reveals the structural mapping between consciousness and information.

The last step of the project requires collaboration with theoreticians. We are using various concepts from category theory and tools from applied mathematics. It benefits from interdisciplinary collaboration with mathematicians, physicists and artificial intelligence.

Our policy of recruiting new members

New (updated on Oct 20, 2021) 

Our policy of recruiting new members (prospective PhD candidates and postdocs) 

We believe that it’s important to have a “get-to-know” period (like an internship period) before we make decision on whether to work with you. 

During the friends period, we ask you to work with us on one project. This can be a summer/winter intern project. It can be a research unit in your university, where I serve as a co-supervisor. Or a new collaborative project with your current supervisor. It may be with / without contract and would last for a couple of months or up to one year, depending on the cases. 

From our end, we want to see several aspects in you that we think are critical. We want to see if you fit with us.

TIPS

Techniques: This includes various knowledge and skills. These are the things difficult to glance from your CV. For example, we want to see if you can program in the way that everyone can understand. We want codes that are easy to debug. We don’t need any complex and clever codes for our projects.

Intelligence: We care your intelligence in various domains. This includes communications skills and mindsets. Can you communicate effectively with others using various tools? Can you plan projects taking into account of rest and failure? Can you manage yourself? Do you strive to beat yourself yesterday? 

Personality: We want to make sure if your personality fits with the existing members. We want to become friends before collaborators! 

Speed: We want to see if you can adapt and grow speedily. When you receive feedback and suggestions, do you react quickly? Can you improve the projects and yourselves? 

— 

During the friends period, you can also test us, and in particular, see if you like with working with me. I know that this is quite unusual kind of laboratory. But I hope this makes sense to both of us. We are striving to make our lab happier and more productive lab! 

Procedure:

We are not urgently and actively recruiting postdocs or PhD candidates at the moment. But, if you are interested in working with us in the future, please send your CV.  Depending on the project and availability of the lab members, we may offer you the friends period.

Projects: 

Please see this page on our Research Statement. 

As described , we are interested in people who share the goal with us. To address the problem of consciousness. Any background is welcomed. In particular,  mathematics (especially category theory), physics (especially quantum physics, quantum information), and linguistics (especially cognitive linguistic – how much of what we experience is influenced by our language?).  But these are neither necessary nor sufficient. 

Most projects in the friends periods are either online psychophysics or data analysis. But it can be a theoretical project. Data analysis projects require substantial programming skills. We tend to work with Python, Matlab, R or other language.