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Randall Beer on dynamical systems and information theory

Episode 1 15.03.2015

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Season 2015

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Is the brain a dynamical system, an information processor, or a prediction machine , and does it even matter which label we choose? Computational scientist Randall Beer argues that these are not competing theories but complementary mathematical lenses, and that real progress requires building theory around carefully analyzed toy models rather than debating metaphors. Subscribe for more from the Convergent Science Network podcast series. Randall Beer joins Paul Verschure and Tony Prescott at the BCBT summer school to present his approach to understanding brain, body, and environment as coupled dynamical systems. Beer makes a sharp epistemological argument: statements like “the brain is a dynamical system” or “the brain is an information processor” are not testable theories but pre-theoretical intuitions, each backed by a body of mathematics that serves as a lens for examining neural systems. No experiment could definitively prove or disprove any of them. What matters is the utility of each lens for generating insight, and Beer advocates maintaining a toolkit of multiple mathematical languages rather than committing to any single framework. The discussion centers on Beer’s detailed analysis of a minimal agent performing relational categorization , distinguishing the relative size of two falling objects. Using both dynamical systems theory and information theory applied to the same evolved neural controller, Beer demonstrates that each lens reveals complementary features invisible to the other. Dynamical analysis highlights bifurcations, transient manifolds, and the role of sensor discontinuities, while information-theoretic analysis reveals which combinations of system elements carry the most relevant information at each moment. The invariant pattern across many evolved solutions is a transient manifold that gets spread into a sheet and then sliced by a bifurcation into a decision. Key topics include why brain-body-environment should be the unit of analysis rather than the brain alone, how toy models in the tradition of Galileo’s frictionless planes can build fundamental theory, what the difference is between ontological and epistemological claims about neural computation, why dynamical systems theory and information theory are complementary rather than competing, and how Beer plans to extend these analytical tools to the biological nervous system of C. elegans. Part of the Convergent Science Network podcast series from the BCBT Summer School.

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Brain Dynamical dynamical systems Dynamical Theory Information Processor information theory Rather

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Both the triumphs of humanity and its most evil deeds have resulted from collaboration. In a time where humanity is required to aspire to the former and minimize the latter, the question arises of how collaboration arises and why it fails. Surprisingly, this phenomenon, so central to who we are, is not well understood. Hence, a collaborative effort is required to understand collaboration in its full biological, psychological, sociological, cultural, and economic complexity and to translate this understanding into operational impact. This series of podcasts is one step toward achieving these complementary goals. The Collaboration Podcast presents interviews with people who are central orchestrators of collaboration in various domains including business, government, science, art, health, sustainability, and the military. The discussions were conducted by Prof. Dr. Paul F.M.J. Verschure and members of the Program Advisory Committee of the Ernst Strungmann Forum on Collaboration (https://www.esforum.de/forums/ESF32_Collaboration.html) during 2021 and had the goal to sketch a map of opportunities, challenges, and obstacles in human collaboration. The forum took place in May 2022, and now we would like to share this series of interviews with a broader audience. The full report of the Forum will be published in 2023 by MIT Press. The podcast was produced by the Convergent Science Network (https://www.convergentsciencenetwork.org/). Context: The stability of social systems depends critically on realizing sustainable methods of “collaboration,” yet how and by which means collaboration is achieved is not clearly understood; neither are the conditions or processes that lead to its breakdown or failure. Collaboration can be understood as cooperation between agents toward mutually constructed goals. Part of the reason for our lack of understanding is that the phenomenon of collaboration is, by nature, a highly multidisciplinary problem, and effective research into its complexities has been difficult to achieve across the broad range of scientific and technical disciplines involved. The need for a fundamental understanding of collaboration, however, has become increasingly important. Not only does humankind demand answers as it attempts to address critical challenges at multiple scales (e.g., climate change, migration, enhanced automation, social and economic inequality), but ever-increasing technological and economic means of interconnecting people and societies are disrupting long-established, familiar patterns of how we interact. Radical technological changes that are ongoing have the potential to reshape collaboration in ways that are currently hard to predict or influence (e.g., by altering configurations in interaction, information creation, and modes of communication). On one hand, such changes could disrupt hitherto stable forms of collaboration by affecting critical communication channels and traditional roles, as can be observed in the rapidly changing patterns in governance, commerce, and social interaction. Conversely, technology could lead to the emergence of novel, successful forms of collaboration that deviate from traditional “hierarchical” architectures. Evidence of this can be seen in areas as diverse as highly automated manufacturing plants, the open science movement, collaborative software repositories, user-centered services, and the sharing of economy-based modes of organization. Without a fundamental understanding of the mechanisms, processes, and boundary conditions of collaboration, it is not possible to evaluate or predict which of these possible scenarios are sustainable or even plausible. The Forum “How Collaboration Arises and Why it Fails” (May 8–13, 2022, Location: Frankfurt am Main, Germany) Chairs: Andreas Roepstorff and Paul Verschure Program Advisory Committee: Jenna Bednar, Julia R. Lupp, Bhavani R. Rao , Andreas Roepstorff, Ferdinand von Siemens, and Paul Verschure

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00:00:03 - This is the Convergent Science Network podcast. Leading researchers in the domain
00:00:10 - of neuroscience, brain theory and technology are interviewed by Paul Verschure and Tony Prescott.
00:00:19 - It's Paul Verschure with the Convergent Science Network podcast together with
00:00:23 - my colleague Tony Prescott.
00:00:25 - And we're here today with Randy Beer, here, one of the speakers of our BCBT summer school.
00:00:30 - And Randy, you have been now for quite a while pushing a very specific view
00:00:37 - on how we should understand brain behavior and environment.
00:00:41 - So what's that specific perspective you bring to bear on that?
00:00:45 - Well, I mean, part of it is just that we should look at brain,
00:00:49 - body, and environment as the unit of analysis, that we shouldn't just focus on neural activity.
00:00:55 - It shouldn't just focus on anatomical sort of connectivity of brains and so
00:01:00 - on, that we need to think of them in context. Mm-hmm.
00:01:03 - Beyond that, I guess I've primarily until very recently, which I'll talk about,
00:01:09 - pushed the idea that we need to think about this brain-body-environment system as coupled dynamics,
00:01:17 - as coupled dynamical systems, and we need to use tools from dynamical systems
00:01:21 - theory to try and understand the behavior that such things produce.
00:01:27 - But lately, what we've been doing and what I mentioned in my talk was I also
00:01:31 - think we We can bring other bodies of mathematics to bear on these systems.
00:01:36 - In particular, we've been exploring the use of information theory and then the
00:01:41 - relationship between dynamics and information.
00:01:43 - Right. But before we get down and dirty on that, I think you also,
00:01:49 - you could now argue if you say, well, the unit to analyze is actually brain, body, and environment.
00:01:55 - I could say, well, that's nice. Now you have just complexified the problem and
00:01:59 - you will still be forced to sort of decompose that or split it up in some way,
00:02:04 - right? So how does that not get you in trouble?
00:02:07 - Well, I mean, I guess that presupposes that splitting things up is a bad thing. Yeah.
00:02:15 - I think you always have to make some splits. When you talk about brain-body-environment
00:02:18 - system, you've taken a physical universe and you've carved it up into what's
00:02:24 - the brain and what's the body and what's the environment.
00:02:26 - So I don't necessarily have an opposition to making splits.
00:02:31 - But I think the focus when you're studying, say, the brain-body-environment
00:02:36 - system from a dynamical point of view is on the interaction between the components
00:02:40 - rather than thinking about each of the components in isolation and imagining
00:02:45 - that the total behavior is just some kind of a sum of the individual behaviors.
00:02:50 - Right. But then on top of that, you also made a pretty strong point,
00:02:54 - I thought, by saying, well, I don't necessarily want to advocate a single view
00:02:59 - on how we should understand these systems,
00:03:02 - and I certainly don't want to make any ontological commitments to any of these views.
00:03:06 - So why are you saying that? Why are you so strong? Well, I think there's been
00:03:11 - a lot of debate about, say, let's just focus on the brain because that's often
00:03:17 - what this debate involves.
00:03:18 - The brain is a computer.
00:03:21 - The brain is an information processing system. The brain is a dynamical system.
00:03:25 - The brain is a prediction machine. The brain is a complex network, and so on and so forth.
00:03:30 - What I tried to do in my talk was suggest that it might be more fruitful to
00:03:35 - reformulate that a little bit.
00:03:38 - So that's sort of an ontological claim into more of an epistemological claim,
00:03:43 - which is simply that underlying each of those positions, there's some body of
00:03:48 - mathematics, information theory, dynamical systems theory, Bayesian theory,
00:03:53 - formal language, formal theory of computation,
00:03:56 - which isn't intrinsically right or wrong.
00:03:59 - It's kind of a lens through which we can look at the operation of a system.
00:04:03 - And I think the focus should be on the utility of using these various lenses
00:04:08 - as a way to understand, to make predictions about, to get interesting insights
00:04:15 - into the systems that we look at.
00:04:17 - In that sense, dynamical systems theory isn't right or wrong as compared to
00:04:21 - information theory or Bayesian whatever. whatever, it's a matter of under what
00:04:25 - conditions are these different things useful. Now that's not to say that I don't want...
00:04:30 - A general theory. It's just to say that I don't think any of the things that
00:04:34 - have been put on the table are really formulated in a way that they are.
00:04:38 - They're offering such theories. Part of the thing, I was talking with Tony earlier,
00:04:41 - it's not clear how you would ever definitively test one of these things.
00:04:46 - What experiment would you do to disprove the statement that the brain is a dynamical system?
00:04:52 - What test would you do to disprove the idea that the brain makes predictions?
00:04:57 - But you could also argue that this is partially just comparing apples and oranges,
00:05:03 - because the examples you give, dynamical systems, information theory, are methods, right?
00:05:07 - And methods, you could say, are by definition neutral towards… That's the point.
00:05:12 - …unnatural status, right? That's the point. I mean, they're not theories.
00:05:16 - But I don't think these other things are really theories either.
00:05:18 - If anything, I think they're pre-theoretical sort of intuitions about how things
00:05:24 - must be in order to accomplish the behavior that the systems produce.
00:05:29 - But I think that begs the question, though, if these aren't general theories,
00:05:33 - what would a general theory look like in your view?
00:05:36 - I mean, how would you go about starting to build some parsimonious general description
00:05:42 - of, for instance, the brain? Yeah, so, I mean, I don't have one to offer.
00:05:46 - What I'm arguing for is a methodology to get there. And the methodology is not
00:05:52 - this discussion we've just had about different mathematical languages.
00:05:57 - The methodology is this sort of toy models approach, okay, that we need to start
00:06:02 - with simple enough models that raise these issues that we're trying to understand
00:06:06 - and build a theory for that.
00:06:08 - And then tried to incrementally extend it. Now, I'm not saying that's the only
00:06:12 - way to go, but if you look in science, I think historically fundamental theories
00:06:15 - have generally been built around toy models, which were then subsequently extended.
00:06:20 - I'm not saying you can't build sort of empirical theories in other ways,
00:06:24 - but fundamental theories in science have typically been built that way.
00:06:27 - So you're saying it's too early to say what a general theory might look like.
00:06:32 - Yes, I think that's a fair statement. Well, I'm not sure if I would agree with
00:06:34 - that. I mean, I mean, if you look at theories also in physics,
00:06:37 - people would basically be trying to explain natural phenomena that they would
00:06:42 - be confronted with, and they would find validity of the explanations in making
00:06:47 - predictions you can test, right?
00:06:48 - So it's not necessarily similar kind of toy systems as you study.
00:06:52 - What I'm talking about is, so for example, take motion.
00:06:56 - Okay, if you look at the world 350 years ago, motion is a really complicated thing.
00:07:02 - Birds fly, waves crash on the beach, rocks slide down the sides of mountains,
00:07:08 - lights move across the sky.
00:07:10 - What possible principles could underlie all of that?
00:07:15 - And the fact is that people didn't even recognize those as being the same things 350, 400 years ago.
00:07:22 - So if you started out trying to build a theory of these things like that,
00:07:27 - you would be in trouble. And of course, that's not how it developed.
00:07:30 - Galileo, for example, just to pick a starting point, looked,
00:07:34 - considered the motion of balls...
00:07:37 - Across frictionless planes. And he argued that if you thought about that,
00:07:42 - which by the way is quite different from what you actually see if you roll a
00:07:45 - ball across the floor, in particular, friction brings it to a stop.
00:07:49 - But what he realized was that that's a surface appearance, which is actually
00:07:54 - not what you would expect in this highly idealized case of an object moving
00:08:00 - frictionlessly across a plane.
00:08:02 - Ising models are an example of that, where you took a really simple model trying
00:08:07 - to get a handle on what phase transitions were fundamentally about.
00:08:11 - I mentioned in my talk there's a lot of interesting models in quantum gravity
00:08:15 - now which are in principle incapable of accounting for our actual universe,
00:08:22 - and yet they're designed as conceptual tools to kind of play with issues like
00:08:25 - what does it mean to quantize time, which is an issue that comes up a lot.
00:08:29 - This is a really important point because it really means, okay,
00:08:33 - what is the ontological status is in the end of the models that we try to study.
00:08:37 - And you're following a very, I think, a well-defined route where you're saying,
00:08:42 - well, let's not be over-enthusiastic about what we can really achieve today.
00:08:47 - Let's be systematic and focus first on our methods and sharpen these methods
00:08:52 - on test cases that we can sort of control and understand.
00:08:55 - And maybe out of that will come sufficient insight to start to think about theory.
00:09:00 - This is how I hear. Well, again, you keep using methods, but I don't think of
00:09:05 - them as methods. I think of them as mathematical languages.
00:09:09 - Evolutionary algorithms is a method. Dynamical systems theory is not a method.
00:09:13 - It's a mathematical language that you can apply to any system that fits a certain
00:09:17 - form, namely that you can have a state space, a time set, and an evolution operator.
00:09:21 - If you can describe those things, then you've got it. I don't think it's a contradiction, though.
00:09:25 - You described it as a lens, so it's something that you use on the outside.
00:09:30 - Yeah, it's a language. It's a language that you use to talk about something.
00:09:35 - I'm not saying that all modeling takes that form.
00:09:40 - It's one of the reasons why I emphasize this term toy models,
00:09:43 - which is what they're typically called in physics.
00:09:45 - Because I think it's a particular kind of model that in the behavioral and brain
00:09:49 - sciences most people don't realize.
00:09:51 - Typically what modeling means in the behavioral and brain sciences, biology in general.
00:09:55 - Wait, I really tried to characterize what you're doing in those terms.
00:09:58 - So how I read or how I listen to what you're saying, how I understand it is
00:10:03 - to say, well, let's first sharpen these languages that give me this lens to
00:10:08 - look at, if you want, nature.
00:10:11 - Once I've done that sufficiently and I've sharpened these languages,
00:10:14 - then we can start to worry about theory.
00:10:16 - But theory is not right now our highest priority.
00:10:20 - No, I don't think that's accurate.
00:10:23 - What I'm trying to put forward, for example, in the talk, I basically laid out
00:10:27 - what you might call, I didn't use the word, but we've used it elsewhere,
00:10:30 - kind of the information flow architecture of this relational categorization agent.
00:10:38 - That's something that one might imagine being the basis of an information processing
00:10:43 - theory that you could imagine building for lots of other agents.
00:10:48 - What is the pattern of flow of information over time across all the elements of the system?
00:10:56 - Okay, so I don't think, I understand why you're saying this,
00:11:01 - but I don't view myself as basically saying we should postpone theory and just focus on methods.
00:11:07 - I rather see myself as saying we should try to build theory around these toy
00:11:12 - models first and then try to extend it.
00:11:15 - But I guess what other people are saying, which is different from you,
00:11:20 - is, for instance, Gary Marcus was here earlier this week, and he was saying
00:11:24 - in quite a strong way that symbol processing, he was using the example of list processing,
00:11:30 - is a fundamental mechanism that the brain must use.
00:11:33 - So he's taking something that we've learned from symbolic AI,
00:11:38 - and he's saying this isn't just a tool for thinking about how the brain does computation.
00:11:43 - The brain really does computation in this kind of way, or the brain really does
00:11:48 - solve the problems it has in this sort of way.
00:11:50 - And I think in the past, I mean, you may have had a stronger position,
00:11:54 - for instance, in terms of dynamical systems.
00:11:57 - But are you saying now that all of these approaches which are using these tools
00:12:03 - or methods or lenses, whatever,
00:12:05 - not just to study the brain, but as metaphors for understanding the brain,
00:12:10 - you're saying that that's no longer a good way?
00:12:13 - I think the metaphors can be very misleading at this point.
00:12:18 - Like I said, the way I would say it is, how would you empirically,
00:12:21 - so I didn't hear the talk, I can't comment directly, but how would you empirically
00:12:25 - resolve the hypothesis that the brain is a dynamical system?
00:12:30 - It's just not. It's not. And the same thing is true with information processing
00:12:34 - or symbol processing or so on. I'm not sure.
00:12:37 - I don't see what experimental program would resolve that question.
00:12:40 - I guess you'd have to be more specific in terms of what kind of dynamic system
00:12:45 - it was. We can answer this, right?
00:12:46 - Because you could argue that people like Zhao Jingwang and,
00:12:50 - Gustavo Deco here, who actually are applying the dynamical systems view of,
00:12:55 - let's say, attractor landscapes to complex brain dynamics, trying to explain
00:13:00 - the properties of prefrontal cortex in particular,
00:13:04 - trying to explain behavior phenomena like attentional selection and so on.
00:13:09 - So I could argue that there's actually a pretty prominent movement in computational
00:13:14 - neuroscience doing that directly.
00:13:16 - But that sounds like exactly what I meant by using the lens of of dynamical systems theory, okay?
00:13:23 - I don't see how any of that is an ontological claim.
00:13:26 - It's saying the utility of the dynamical systems language is quite high for
00:13:31 - at least some subset of brain processing.
00:13:34 - Well, actually, that's been just the debate very much in the hippocampal literature.
00:13:39 - On whether you might find a memory shaped like in a tractor landscape in CA3
00:13:46 - of the hippocampus, right?
00:13:47 - And then people observe that if you smoothly change environments,
00:13:51 - you actually don't have very stable responses in that system.
00:13:56 - And then they would say, well, here, you see, these cannot be attractors,
00:13:58 - because if it's an attractor, you should jump into that same state if the environment
00:14:02 - is the same, right? Yeah.
00:14:05 - However, then it was shown that under continuous plasticity,
00:14:09 - actually, you might have attractor landscapes that also are reshaping themselves.
00:14:12 - So you don't necessarily always follow the same attractor. So I think in that
00:14:16 - domain, people really have been trying to be pretty literal in saying,
00:14:20 - well, this dynamic systems picture of memory is literally captured in that structure.
00:14:27 - And I hear you saying like, well, this might be a mistake. This might be an over-interpretation.
00:14:33 - I mean, whenever you look through a mathematical lens, it focuses you on certain kinds of questions.
00:14:39 - Looking through the lens of information theory does not lend itself to,
00:14:43 - for example, bifurcations.
00:14:45 - So if you look through the lens of dynamical systems theory,
00:14:47 - of course, the vocabulary that you're going to be bringing to bear are going
00:14:50 - to be things like attractors and bifurcations, but not just those.
00:14:53 - That was part of the point I made in my talk. Transient dynamics,
00:14:56 - which is sort of what you're referring to, is also to be expected.
00:15:01 - All the focus on attractors, I think, in dynamical systems theory over the years
00:15:06 - has been a bit of a special case because we know that when you take dynamical
00:15:11 - systems and drive them with lots of signals from an external environment,
00:15:14 - you're almost never going to be in true attractors.
00:15:16 - You're almost always going to be in transient structures.
00:15:19 - So again, I don't see anything inconsistent there. Using a particular language
00:15:23 - suggests or makes it more natural or gives you the tools to answer certain kinds
00:15:29 - of questions and not other ones.
00:15:30 - So it's not at all surprising that the language of dynamical systems applied
00:15:35 - to the system you're describing would suggest those kinds of avenues.
00:15:41 - But what I'm saying is the statement that the brain is a dynamical system is
00:15:48 - not a very theoretically interesting statement.
00:15:51 - It's kind of like saying that.
00:15:55 - Gravitation is a differential system, right?
00:15:59 - That's not the sort of theory, quote-unquote, that's put forward in physics.
00:16:04 - But that's the analogous statement, I think. Rather, the statement that you
00:16:09 - see in physics is something like gravitation involves an inward-verse-square
00:16:15 - law of attraction, say, for Newton.
00:16:17 - Or gravitation is a curvature of space-time, whose particular form I can describe
00:16:25 - using differential equations.
00:16:26 - That's the analogy I'm trying to make. It's sort of at the wrong level to make
00:16:30 - these grand sweeping statements.
00:16:34 - Take, for instance, the statement that the brain is a dynamical system.
00:16:37 - So, people have made that statement in order to point out what it's not.
00:16:43 - And for people like Esther Tellem, for instance, she would make that statement
00:16:46 - very strongly because she was trying to.
00:16:49 - Counteract a view, for instance, that knowledge is iconic, that there are representations
00:16:54 - that are maybe pre-specified in some way and that come to life when you do cognition. And she would.
00:17:01 - Presented a very powerful argument i think to say that
00:17:03 - look these representations don't have to pre-exist that
00:17:07 - if you take a dynamic systems perspective then in
00:17:11 - the uh when you engage in the
00:17:13 - behavior that the mind generates these representations in an emergent way even
00:17:18 - you might not even use the word representation many people would object to that
00:17:21 - so really it's a very strong position about what the brain is not perhaps as
00:17:26 - much as about what the brain is and And powerful explanations can follow, for instance,
00:17:32 - about the development of behavior, how we come from a system that can do very
00:17:36 - little to a system that is capable of this behavioral complexity.
00:17:40 - So within psychology, certainly, I think that's been a powerful approach.
00:17:46 - Maybe we shouldn't call it a theory, but a powerful approach for refining our
00:17:50 - ideas to think about what cognition is.
00:17:53 - Yeah, and again, I'm just repeating myself, but the fact is when you apply different
00:17:57 - lenses is to a system, they're going to suggest different things because they
00:18:01 - bring different vocabularies to bear, they bring different perspectives to bear.
00:18:05 - And if you take something like the lens of dynamical systems theory,
00:18:08 - which is this is exactly what Esther did and applied it to a kind of problem
00:18:12 - that people had never thought of in those terms before, it's going to be very
00:18:15 - productive, which is not, again,
00:18:18 - addressing the question of testing or what it means to say the brain is a dynamical system.
00:18:23 - But there's sort of an intermediate issue then before we start to look at the
00:18:28 - specific test case that you analyzed.
00:18:31 - You cannot completely disconnect the lens you take and your ontological commitments
00:18:36 - because that lens, like if you take the lens of dynamical systems,
00:18:39 - it will bias the kind of data you will consider and what properties you consider.
00:18:44 - And in that sense, it will bias your interpretation of what these things really
00:18:47 - mean. That's all true except, I think, the statement about ontological commitments.
00:18:50 - Because if you take a lens provisionally, the way I'm suggesting,
00:18:56 - then you're not making ontological commitments, or at least you're not making
00:18:59 - absolute ontological commitments.
00:19:00 - You're basically saying, I think it might be useful to look at this system through
00:19:05 - the lens of dynamical systems theory.
00:19:06 - So for the purposes of doing that, I'm going to think of it as having this state
00:19:10 - space and so on and so forth. Right.
00:19:13 - If I'm doing that provisionally, if I'm just as likely to later pick up another
00:19:16 - lens, then I'm not making any fundamental commitment.
00:19:19 - Whereas some of these other things that you're suggesting are really fundamental commitments. Sure.
00:19:24 - But we cannot deny that there might be biases. Absolutely. Every lens has a
00:19:29 - bias. Every lens. This was the point.
00:19:31 - Which is why I think it's useful to emphasize that one should have a set of
00:19:34 - lenses in one's toolkit.
00:19:36 - Okay. And the second thing is, of course, you now say, look,
00:19:38 - I propose an approach where we in detail analyze toy systems,
00:19:44 - and this is the way forward because the toy systems are sort of more controllable.
00:19:49 - But of course, there's then this risk that if you choose your toy system incorrectly,
00:19:54 - that you're going to sort of dig the tunnel in the wrong direction, right?
00:19:57 - So how do you make sure that your toy systems has the constraints that help
00:20:02 - you to generalize towards a phenomenon you really want to capture?
00:20:04 - So basically any methodology has pluses and minuses.
00:20:08 - And in general, that is certainly a concern with the methodology that we're talking about.
00:20:13 - The way I'm trying to address it is, as I mentioned at the very end of my talk,
00:20:17 - I think we've honed some of these tools to the point where they're worth trying
00:20:21 - on a biological system, which is a very different sort of model that we're doing
00:20:26 - there. It's not a toy model.
00:20:28 - It's intended to be an empirically testable model. And so you have to engage
00:20:32 - in the prediction, experimental test, refinement kind of loop,
00:20:35 - which is not something that makes any sense for the toy models because they're
00:20:38 - not intended to making any predictions.
00:20:39 - And so, this is a big reason why I've been shifting to applying evolutionary
00:20:45 - algorithms and these dynamical and information theoretic analysis techniques to C.
00:20:51 - Elegans because I think it might be the kind of actual biological system where
00:20:58 - we can try these things out.
00:20:59 - Right. And it may fail in various ways.
00:21:02 - And so, that is ultimately the epistemological test, right? Are these useful or not?
00:21:08 - Exactly. But now, so the test case that you discussed was a population,
00:21:14 - if you want, of very simple agents.
00:21:17 - That might be static or active, and that we're supposed to detect a looming object.
00:21:28 - And you define this as a categorization task.
00:21:31 - Yeah, you can call it classification if you want to, but the point is it's not
00:21:34 - just detecting, it's actually making some discrimination about the relationship
00:21:38 - between the two objects it sees in sequence. Okay.
00:21:42 - So what's important here, there's, let's say, a simple environment that has
00:21:46 - certain properties, that's the looming stimulus, right?
00:21:49 - There's a simple embodied agent because it can move in space.
00:21:53 - And then there is a control system that, if you want, transforms properties
00:22:00 - of that stimulus into a reaction, if you want.
00:22:04 - And then the control system, this neural-like control system that you were in
00:22:09 - the end studying with either dynamical systems approaches or an information
00:22:12 - theoretic approach, you generated many, many, many exemplars of that using a
00:22:17 - genetic algorithm. Yes. Okay.
00:22:21 - So, then you compared, let's say, the static case versus the active case.
00:22:24 - And you also showed us in this analysis that if you analyzed,
00:22:28 - in particular, this neural controller of this agent, using either a dynamical
00:22:32 - systems perspective or an information theoretic perspective,
00:22:35 - you would have a very complementary dissection, if you want,
00:22:38 - of the functional properties of this agent.
00:22:42 - So, what does the dynamical systems lens on that system now exactly tell us? What do we learn from it?
00:22:52 - Well, so for example, one of the things that doesn't come up at all in the information
00:22:57 - theoretic analysis is how important the bifurcation idea is,
00:23:02 - that there's this discontinuous change in the system's response properties.
00:23:05 - That's just not a notion in information theory.
00:23:08 - Another one has to do with the role of the discontinuities that the sensors introduce.
00:23:12 - I mean, these again are not notions in information theory. You're just seeing
00:23:15 - these generalized correlations being developed and distributed around over time.
00:23:20 - On the other hand, one thing that's not so obvious from the dynamical systems
00:23:27 - analysis alone, because it deals with sort of the full state space of dynamics,
00:23:31 - is which particular combinations of elements are the most appropriate ones to
00:23:36 - be focusing on at any given point in time, which is something that the information
00:23:39 - theoretic analysis, I think, brought out much more cleanly than the dynamical
00:23:43 - analysis does. But as you say, they're complementary.
00:23:45 - So it's not like either is inconsistent with what the other one says,
00:23:52 - but they bring out different features of the system.
00:23:54 - And that's why I think it's really interesting to look for bridges between these
00:23:58 - different stories, which was the final part I wasn't able to get to in the talk. Okay.
00:24:02 - But now the variation across these populations that you analyzed,
00:24:06 - because in the end you actually analyzed one exemplar, I think,
00:24:10 - from this whole population.
00:24:11 - Yeah, we actually looked at about 10 of each, but only one in this great detail. Right. Okay.
00:24:17 - You generate these with genetic algorithms. Is that a key ingredient of this
00:24:22 - experiment, or it could have been any way in which you can generate a variable
00:24:25 - population? I think the latter, yeah.
00:24:27 - I think any stochastic optimization technique would have been fine,
00:24:30 - the way I'm using genetic algorithms.
00:24:32 - But I do think the stochastic feature is important, because otherwise you end up biasing things.
00:24:38 - So you tend to fall into the same architecture each time, and you're not really
00:24:43 - exploring the space of the possibilities in the same way. That's,
00:24:46 - I think, the important feature. Right.
00:24:47 - But then the fixed feature was the number of sensors that you had at the surface
00:24:52 - of this agent to detect the looming stimulus.
00:24:56 - Then you had three hidden units that would sort of transform the sensor state
00:25:01 - into a motor state, which was encoded by two units that could,
00:25:05 - for the active case, drive you to the left or to the right.
00:25:08 - Well, even in the passive case, they drive you. That's why I don't really like
00:25:11 - the static versus... Okay. In both cases, in the end, they have to move to express their decision.
00:25:17 - The difference is just whether or not they move only when the second object
00:25:21 - is falling or whether they move during the time that both objects are falling.
00:25:25 - Anyway, just a minor correction. No, no, this is good.
00:25:27 - So then the task itself was indeed, if you want, you had a training case and a test case, right?
00:25:34 - There was a probe trial second, and then there was an exposure trial.
00:25:38 - Yeah, so there's a cue and then a probe. Right. And then between those,
00:25:42 - the system could, in this network structure, maintain some sort of memory if
00:25:47 - its dynamics would allow that. Yes.
00:25:49 - Now, how many different network templates did you find that would give rise
00:25:56 - to the same kind of dynamical landscape?
00:25:59 - Well, so it depends what you mean by the same.
00:26:01 - You're going to tell me. Every single run comes up with different parameters.
00:26:07 - So the problem is interestingly rich enough that it's not like there's just
00:26:10 - a unique solution. And that's, I think, very, very typical.
00:26:18 - So the details of every, say, dynamical analysis or every informational analysis would be different.
00:26:23 - But the general idea of having some transient manifold evolving through the
00:26:29 - state space of the entire system, not just the inner neurons,
00:26:33 - but that's what I focused on for the passive agent, applies across the board.
00:26:38 - The geometry of that particular manifold at the end of the Q stage is very interesting.
00:26:44 - And also which dimensions of the state space that manifold actually transits.
00:26:53 - So if you think about it, in the passive agent, it's basically the interneuronal
00:26:59 - state space that's important.
00:27:00 - And as you pointed out, some of them are more important than others for that particular agent.
00:27:05 - In the active agents, one way of thinking about it is, I didn't show a dynamical
00:27:09 - analysis of an active agent, but you could do it.
00:27:11 - But it's not the extent of that manifold in the internal state space,
00:27:16 - it's actually its extent in the body position part of the state space,
00:27:21 - which after all is just part of the total state space of the system.
00:27:24 - So those kinds of considerations and these issues about how does the pattern
00:27:29 - of information, how does the information flow through the system and so on.
00:27:34 - What I was after, Randy, is to say, look, you generate let's say a thousand exemplars. Right.
00:27:40 - I don't know how big the pool really was. Was it 1,000? No, it's smaller than that. Okay, whatever.
00:27:44 - Dozens. Okay. But then I would expect, but maybe I'm wrong here,
00:27:48 - that at least if you would analyze from a dynamical systems perspective,
00:27:56 - the whole population of exemplars you have, you would expect some prototypical
00:28:02 - forms of dynamics to emerge.
00:28:05 - And you characterized some of that, let's say the manifolds, but that to me.
00:28:11 - Would more suggest, okay, where do we look for these invariants?
00:28:15 - So can you be more specific about the invariant patterns you might see?
00:28:19 - Like for instance, in the example, you showed that we indeed saw one neuron
00:28:21 - doing most of the job. I mean, it's my characterization.
00:28:24 - Was that like a pattern emerging in, let's say, 30% of your exemplars?
00:28:30 - I don't have the statistics for it. But I mean, in general, there's no reason
00:28:35 - that it would be one neuron over the other.
00:28:37 - There's no reason in general why it couldn't be multiple neurons.
00:28:39 - And you do see examples of all of that.
00:28:41 - Why I'm asking you this and why this is important to me is that if we want to
00:28:46 - understand biological systems or brains or what have you, should we focus on
00:28:52 - the invariant patterns across exemplars?
00:28:54 - This is now a guiding principle like the retina projects to the thalamus.
00:28:59 - Okay. And we see that in all of them.
00:29:01 - So this is, of course, it's a completely different kind of description.
00:29:05 - So the question is, in this dynamical picture, if we start to complexify and
00:29:11 - say, oh no, every individual is very individual, there are no general features.
00:29:15 - Then it might not give us a lot of leverage to understand how these things work.
00:29:18 - I understand exactly what you're saying.
00:29:20 - And that's why I'm saying that if you're looking for generalities in these agents,
00:29:24 - you need to look at the level of these transient manifolds and the way in which they're transformed.
00:29:29 - You need to look at the way they're split.
00:29:31 - That's an important feature that you show up over and over again.
00:29:34 - When you drop the second agent, this curve of states, when you drop the second object,
00:29:40 - the curve of states gets spread into a sheet of states and then bifurcation
00:29:45 - slice that sheet into a decision.
00:29:47 - That is true across the board. Okay.
00:29:50 - So one thing that I'm not clear about is that you seem to be doing two things
00:29:54 - here with these toy systems.
00:29:56 - One is to, first of all, refine and sharpen your lenses and say,
00:30:02 - how are these lenses useful for understanding these model systems?
00:30:05 - And the second thing is maybe going towards a,
00:30:11 - a set of theories about these kinds of systems, and ones that you might build
00:30:15 - out of these, where perhaps you might start to develop a kind of taxonomy of
00:30:20 - simple machines, or machines with these kinds of simple neural circuits.
00:30:26 - I mean, is that right? Is that a goal?
00:30:29 - I don't know about taxonomy specifically, but… Well, a theory about these kinds
00:30:33 - of machines… Yes, that's what I'm trying to get at.
00:30:35 - And again, the point is that we're going to be testing these same ideas in the
00:30:40 - C. elegans models that we're building now.
00:30:42 - So I mean, the idea we didn't, so you're right, part of it has to do with tool development.
00:30:46 - Some of the information theoretic tools we're using didn't exist before we started
00:30:49 - trying to do an information theoretic analysis of these agents.
00:30:52 - Some of them did, some of them were developed specifically to do that.
00:30:55 - Now that we have the tools, we can apply them to other systems like the C. elegans system.
00:31:01 - So part of it is tool development, but also part of it is that as you look through
00:31:04 - these different lenses lenses and start to formulate explanations of what you see through that lens,
00:31:12 - those become tentative at least frameworks for trying to actually build theories.
00:31:17 - So the thing I mentioned, if the information theory is there's now,
00:31:20 - we now have this notion of sort of an information flow architecture.
00:31:23 - Okay, which transcends the detailed
00:31:26 - elements and the actual quantitative information about there's .37,
00:31:32 - you know, general mutual information between these two elements,
00:31:36 - but it leads us to focus on certain kinds of what's the overall pattern of flow through the system?
00:31:40 - What are the appropriate variables
00:31:42 - to look at? What are the appropriate informational quantities and so on?
00:31:46 - That's something we can apply to other systems like the C. elegans system.
00:31:49 - Is that something that's going towards a reduced description of the machine? Possibly.
00:31:54 - I think it's an idea at this point. I mean, and we're going to be testing it,
00:31:59 - as I said, in the C. elegans system.
00:32:02 - But now there's something interesting about the C. elegans example,
00:32:04 - that C. elegans, as you also pointed out yourself, we have 302 identified neurons.
00:32:10 - They are connected in a rather heterogeneous way.
00:32:14 - As are most nervous systems, actually, when you look at them.
00:32:17 - No, but I mean, what I mean with that is that they don't really implement any
00:32:20 - kind of parallelism, really.
00:32:22 - It's more… I have no idea what you mean by that.
00:32:24 - It's actually a highly recurrent network. No, but what I mean with that is not
00:32:29 - that we have, let's say, basic circuit templates that are replicated in a parallel fashion, right?
00:32:35 - It's a very complicated thing. Yeah, there are no cortices in C.
00:32:38 - Elegans. For instance, right?
00:32:40 - But neither is there a cerebellum or basal ganglia and so on, right?
00:32:43 - So you have a bunch of cells that are complex in themselves and that have,
00:32:48 - let's say, heterogeneous asymmetric kinds of interactions that we don't fully
00:32:51 - understand, that we want to understand. Yeah, I mean, there's a lot of symmetry too.
00:32:54 - There's bilateral symmetry, for example. Sure, absolutely.
00:32:57 - But what I'm driving at is to say that already at this sort of topological nature.
00:33:05 - The C. elegans nervous system might be rather different from the agent you have been using.
00:33:09 - And it sort of illustrates this point I made earlier. Like if you go for a toy
00:33:13 - system, it should, of course, be a segue into this natural system you want to understand.
00:33:17 - That and now i could say well the agent you studied definitely
00:33:21 - has a parallelism in this in its organization
00:33:24 - that you have a bunch of of uniform receptors that only vary in their placement
00:33:29 - on the periphery the same holds for the internet three interneurons they're
00:33:32 - in some sense identical but they vary in how they're interconnected whatever
00:33:36 - but there's a symmetry there again and the same for these output units so this
00:33:39 - kind of parallelism and symmetry you will not find in the C. Elegans brain.
00:33:43 - So has it then made it right? So why would I therefore believe that the lens
00:33:48 - you have sort of sharpened on this artificial agent would help you to get access to the C.
00:33:55 - Elegans system? You don't need to believe it because we're trying it. Sure, I know.
00:33:59 - The result of that will either support or not the idea.
00:34:07 - I mean, it's not something one has a belief in, except maybe in whether or not
00:34:11 - one spends time pursuing this direction.
00:34:14 - But in the end, we're going to find out whether some of the things I just described
00:34:17 - to you in our dynamical and information
00:34:19 - analysis of the relational categorization agent carries over to C.
00:34:24 - Elegans. So what have you found so far?
00:34:32 - The only thing I can say right now is we've done an information theoretic analysis,
00:34:38 - which isn't published yet, on the C.
00:34:41 - Elegans circuits and the tools that we developed and the ideas and especially
00:34:46 - this notion of information flow architecture turned out to be extremely powerful
00:34:49 - in characterizing what's going on.
00:34:52 - Because even in C. elegans, so
00:34:54 - even in biological systems, you have a tremendous amount of variability.
00:34:58 - There are a number of famous examples of this which I could get into,
00:35:01 - but I'm not sure we want to spend the time.
00:35:03 - There's every reason to expect that the variability that you see in these toy
00:35:08 - models using evolutionary algorithms is in fact a desirable feature of them
00:35:13 - because it's actually more reflective of what you see in biology than this idea
00:35:17 - that there's the one true brain or the one true whatever.
00:35:20 - But it's interesting, right? Because traditionally, I think initially you worked
00:35:25 - a lot on a dynamical systems perspective.
00:35:26 - Yes, I did. And I think the information theoretic one is a bit more recent as
00:35:29 - far as I understand. Yes, oh, absolutely it is, yeah.
00:35:31 - But it's interesting now with C. elegans, your first success,
00:35:35 - if you want, has been with the information theoretic measure.
00:35:37 - Well, that's not entirely true. I mean, so we published about a year and a half
00:35:40 - ago our first paper on this model, and that was basically much more dynamical than it is now.
00:35:46 - On the C. elegans model? On the C. elegans model, yeah. Yeah,
00:35:48 - it's the more recent work that we're doing that's looked at the information
00:35:51 - flow architecture idea in the context of C-elegance.
00:35:54 - What's interesting with the C-elegance is that we do know the full connectivity of the circuit.
00:35:59 - Yes, but we know almost nothing about the biophysics and neurophysiology underlying it. Well, exactly.
00:36:04 - But we can, with this relatively simple model, say, okay, given the connectivity,
00:36:10 - how much more can we infer via these approaches?
00:36:13 - So it's a good model system in which to do that. and then we can think,
00:36:18 - well, if we knew the full connectome of the human brain, what could we learn from that?
00:36:23 - So in that way, that's part of your strategy. Oh, absolutely.
00:36:28 - Yeah. I mean, one of the things that we looked at in this previous paper that's
00:36:31 - been published for a while.
00:36:34 - There's tremendous variability when we evolved 100 chemotaxis models for C.
00:36:41 - Elegans, and there's tremendous variability in the parameters that you get,
00:36:46 - even though behaviorally they're almost identical in terms of their… So again,
00:36:49 - it just shows you that this happens even with those constraints.
00:36:54 - They're just not sufficient constraints. But what's intriguing in this work
00:36:59 - that's currently in press is that it looks like if you, when you look at the
00:37:04 - information architecture of these,
00:37:06 - I think about 70 some of them turn out to be really high performing of the 100.
00:37:11 - So some fail and some don't do very, you know, they don't fail,
00:37:14 - but they don't do as well as possible.
00:37:16 - So maybe the subset of 70 of them all share almost identical information architectures,
00:37:22 - even though they have tremendous variability at the parametric level.
00:37:25 - So when you're looking at C. elegans, you have the connectivity,
00:37:29 - but you have all these other gaps.
00:37:31 - Then the methodology that you have with your toy models, which is not exhaustively,
00:37:36 - but to fairly comprehensively explore the space of possible models. That's exactly right.
00:37:41 - You can't do that anymore. So you can't explore the whole of the design space,
00:37:45 - can you? Well, I mean, you can never explore the whole, but that's exactly the,
00:37:51 - I guess I don't understand the question, that's exactly the strategy is that
00:37:54 - we take what's known about C.
00:37:56 - Elegans, in our case, namely the connectivity and the behavior and some physiology
00:38:02 - to do with the sensors, actually. That's actually been pretty well worked out.
00:38:05 - And we constrain our evolutionary algorithm by that information,
00:38:08 - and we use the evolutionary algorithm to fill in the remaining details,
00:38:11 - namely the sort of neurophysiological parameters, which are unknown.
00:38:16 - And if you do that once, it's not very interesting because that's just a solution.
00:38:20 - But if you do it many, many times, then you start to be able to talk about the
00:38:23 - ensemble of solutions, and that has interesting structure in it.
00:38:26 - But, I mean, the number of unknowns, I imagine, is quite high.
00:38:30 - Yes. And even with your genetic algorithms, you cannot exhaustively explore
00:38:36 - that space. No, no. Again, exhaustive is not possible.
00:38:38 - So you're sampling a larger space. You're sampling a space and you're looking for patterns in that.
00:38:43 - So if every single individual is completely different at all levels of analysis,
00:38:47 - then you've learned nothing, right?
00:38:48 - But what's interesting is they can vary quite a bit at the level of the individual
00:38:53 - neurophysiological parameters, and yet you start to see patterns when you look,
00:38:57 - say, dynamically or information theoretically across the ensemble.
00:39:00 - Okay, but the question, I guess, is that...
00:39:04 - With C. elegans, it's a test case for your methodology. So how big can the space
00:39:10 - of unknowns be before this strategy of trying to explore it with GAs is going to break down?
00:39:16 - Yeah. You won't see the very big. I mean, I can't give you a magic number.
00:39:19 - Right. In part, that has to do with how much computation you can throw at it,
00:39:23 - which particular optimization techniques you use.
00:39:25 - And it has, of course, a lot to do with the system you're studying,
00:39:28 - which a priori we don't know how much structure or not might be in that system.
00:39:33 - But then also, with your analysis tools, you're maybe going to want to automate
00:39:37 - some of the analysis beyond sort of… Possibly.
00:39:40 - I mean, I think… So the biggest systems we've tended to do in our toy models
00:39:44 - have been sort of 30 neurons or less.
00:39:46 - And so I think C. elegans is actually a good next step.
00:39:49 - We're talking about an order of magnitude if you think about the entire nervous
00:39:52 - system rather than just the bits we're looking at so far.
00:39:54 - So it strikes me as the right scale to be going from 30 to 300 rather than,
00:39:59 - say, 30 to 300 billion or something.
00:40:02 - But have you learned from your toy models ways of doing analyses with dynamic
00:40:08 - systems and information theory that you could say automate it?
00:40:11 - Well, I mean, so many, many years ago I built a system called Dynamica that
00:40:15 - basically let you automate some aspects of dynamical analysis,
00:40:18 - and we've always used that.
00:40:20 - We don't yet have such a system for information theoretic analysis,
00:40:25 - but certainly as you gain experience with it, it's easier and easier to write
00:40:28 - code that sort of modularizes bits and pieces of it.
00:40:32 - And then you can sort of throw that at a big complicated system and just let
00:40:36 - it grind away for a few days and give you the results.
00:40:38 - So I think that's part of building the tools, but it's an ongoing process.
00:40:41 - But part of the tools could be
00:40:43 - to say, look, this is the sort of thing I'm looking for from the analysis.
00:40:46 - And then, you know, there's sort of a meta-analysis.
00:40:49 - Yeah, I mean, ideally that would be the case. I think for the most part.
00:40:54 - There's no sort of magic wand to analysis. It's a creative activity.
00:40:58 - And so at least present tends to involve people engaging with a set of tools
00:41:04 - with some system and using their own intuitions and thought processes to sort
00:41:09 - of guide whether or not you could ultimately automate the whole thing.
00:41:12 - I have no idea, possibly. But now for the C. elegans, could you give us an idea of the unknowns?
00:41:19 - That means of the key parameters that you think you have to have a handle on
00:41:24 - to understand that system.
00:41:25 - How many are actually identified and how many are actually partially known and
00:41:30 - how many are completely missing?
00:41:31 - That's not entirely a well-defined question. So here's what we know.
00:41:34 - There are about 8,000 connections among those 302 neurons.
00:41:40 - We know very little about the
00:41:43 - neurophysiology, actually electrical properties of each of the neurons.
00:41:46 - One of the things that we know is that they don't seem to spike.
00:41:50 - So the kind of model neurons that we've been using I think are actually fair
00:41:54 - representations of them.
00:41:56 - There are, however, nonlinear response characteristics to the neurons,
00:42:00 - most of which have never been characterized except at the sensory level.
00:42:04 - We don't know the signs of, as far as I know, any of the connections,
00:42:08 - let alone the magnitudes.
00:42:11 - So we're mostly talking about, so I guess this is what I'm saying.
00:42:15 - If you fix a neural model like the one we're using, then I can calculate a number
00:42:19 - of parameters we're talking about.
00:42:21 - But you can't really fix a neural model either because to use the model like
00:42:25 - we're using is based on the knowledge that C.
00:42:27 - Elegans neurons don't spike, that they have certain sort of nonlinear characteristics
00:42:31 - in synaptic transmission, and so on.
00:42:33 - But those details are likely to become
00:42:37 - richer as you actually start to do neurophysiology on the individual cell.
00:42:40 - So, like I said, we know there are current channels, active voltage-gated and
00:42:46 - chemically-gated current channels in C. elegans neurons.
00:42:49 - So, they're not just passive membrane. Okay.
00:42:52 - Once you start doing voltage clamp-like dissections of those things,
00:42:56 - you're going to be building more complicated models of the neurons and the number
00:42:59 - of parameters would be going up.
00:43:01 - So, it will be a more incremental approach, you're saying? It's always got to be incremental.
00:43:04 - I mean, even in something that's quote-unquote as simple as C.
00:43:07 - Elegans is still quite complicated. And you've got to make a cut somewhere.
00:43:11 - We're doing the same thing with the body. I mean, you know, as this last talk
00:43:17 - pointed out, if you just look at the somatic cells in CL, and it's not the germline
00:43:21 - cells, there are about 1,000, just under 1,000 cells in the entire body.
00:43:26 - Okay. We're not modeling at that level at all. So we, for example,
00:43:30 - model muscle at a much higher level than the individual muscle cells.
00:43:34 - Okay. So you're always making cuts, and they're always provisional because as
00:43:38 - your model progresses and as it engages with experiments, it's going to need to be refined.
00:43:43 - Right, but it's also to follow up on this whole question of how many of the
00:43:48 - gaps can you fill in with the genetic algorithms, right?
00:43:51 - Right, right. For instance, also with these kinds of brains,
00:43:53 - you have to think about the kinds of neurotransmission they use,
00:43:57 - which is also to learn with all sorts of strange peptides we barely understand and so on.
00:44:01 - So how do you get a handle on that? Well, Ian, you get a handle on it by not
00:44:07 - wringing one's hands about how complicated life is, but diving in.
00:44:11 - Right. You have to make some cuts.
00:44:13 - And this is why I'm a big advocate of models being involved very,
00:44:17 - very early in the process.
00:44:19 - As I mentioned in my talk, I really don't like the idea that we don't have enough
00:44:22 - data yet to start to model.
00:44:24 - I think it's much better to jump in with a model and don't be overly enamored of your model.
00:44:30 - Models are almost always wrong. In fact, they're basically always wrong,
00:44:33 - but some models are wrong in interesting ways that focus you on what additional
00:44:38 - things you might need to know and so on.
00:44:41 - And I think that's what's important about it. But going back to your question,
00:44:44 - I mean, I don't know how to put a number on it.
00:44:46 - Certainly, that's a problem with optimization techniques.
00:44:49 - You can't just have 8,000, let alone, say, 800,000 or something free parameters
00:44:55 - and expect to get any kind of a useful sample running it a few thousand times
00:44:59 - or something like that. But, um...
00:45:03 - But rather than try to solve that problem in general, like I said,
00:45:06 - we jump in with a particular level of abstraction,
00:45:08 - and we put a stake down, and then we can start looking at making predictions,
00:45:12 - some of which may be verified, many of which, of course, are going to be knocked
00:45:15 - down, and use that to start refining. Where do we need to put the effort?
00:45:19 - What things can we assume? And the other thing is data is always coming along.
00:45:23 - There are new techniques now that are going to make neurophysiology and C.
00:45:26 - Elegans easier than it's been for decades. And that's going to start providing
00:45:31 - information that we don't have to use a genetic algorithm to fill in anymore. more.
00:45:35 - I guess I'm just worried on the scaling problem that in your toy model system
00:45:39 - you say well okay let's evolve these systems that can match the behavioral criteria
00:45:44 - and then we'll apply information theory dynamic systems theory to look at them
00:45:49 - and you then really focus in on I think you said 10 models and one in real detail.
00:45:54 - Now with C. elegans maybe you have the same constraint from behavior but maybe
00:46:00 - there'll be such a huge number of models that can potentially fit that,
00:46:03 - and then when you try to apply your lenses to that, how are you going to...
00:46:06 - So what we've done in C. elegans is exactly the same as what we did here.
00:46:10 - So we look at the population, we study in detail, usually the best couple,
00:46:16 - and then we start asking how much of what we learned in those in-depth studies
00:46:20 - generalize to a broader set.
00:46:23 - And what you start finding is that many of the details of what you discovered
00:46:26 - in that analysis don't generalize, but there's some level of description that
00:46:31 - resulted from your analysis, which starts to, you see, recurring over multiple additional ones.
00:46:36 - And so, I mean, that's the only way I know how to do it. Without automated techniques,
00:46:40 - you can't do the whole population, right?
00:46:42 - And you have to analyze some in detail because a priori, you don't know where
00:46:46 - the right line is, where the cut is.
00:46:48 - So you've got to go through one in detail or a few in detail and then you start.
00:46:52 - In some sense, you do internal hypothesis testing just with the model itself.
00:46:56 - Well, okay, looking at that detail,
00:46:58 - I would guess that that connection is always going to be inhibitory.
00:47:03 - Oops, here's three examples that that's not true. Okay, that's too low a level.
00:47:06 - Let's try a slightly higher level of description.
00:47:09 - And so you start doing some testing there until you find, oh,
00:47:12 - at this level of description that I can make, it actually seems to start to
00:47:16 - generalize across a significant fraction of the population.
00:47:19 - So now you also introduced us to a number of information theoretic measures
00:47:23 - that you used as a complement to the dynamical systems lens on these synthetic agents.
00:47:29 - So they're the obvious mutual information measures, but you also introduced a few new ones.
00:47:35 - So what are these measures and why did you feel you had to introduce them?
00:47:39 - Well, I mean, the biggest problem I think is that mutual information,
00:47:44 - a sort of real workhorse as far as I'm concerned of information theory,
00:47:48 - is an average over many, many different things.
00:47:51 - And if you want to understand more details about the information flow in a system,
00:47:57 - you need to start to unroll that average, start looking at some of the things
00:48:01 - that are normally being averaged over.
00:48:02 - So two of the things I talked about was you can unroll over time,
00:48:05 - so you can start to see that some component carries information at one point
00:48:10 - in time that's quite different than the information it carries at another point in time.
00:48:14 - And that's part of what information flow is all about. How does these patterns
00:48:18 - of information across the system change over time?
00:48:21 - And you also find that if you unroll over the stimulus values,
00:48:27 - the actual possible outcomes of experiments on your variable that you're exploring,
00:48:32 - you start to see patterns there too, that some elements may carry much less
00:48:36 - information about some range of the stimulus than they do other ranges.
00:48:39 - So those are the ideas there.
00:48:41 - And that's not really us. Those are measures that are in the literature,
00:48:44 - which just haven't traditionally been applied in the way that we're applying them.
00:48:48 - Then you get into dynamic measures, and that's a much more complicated area.
00:48:52 - You want to be able to talk about things like….
00:48:56 - When elements gain or lose information and how you quantify gain or loss and
00:49:00 - how information is transferred from one element to another.
00:49:04 - And part of the problem, the whole metaphor of flow for information is a little
00:49:08 - misleading because information isn't conserved like mass is or something like that in a liquid.
00:49:13 - So you can't just talk about, well, it went down here, it went up there,
00:49:17 - therefore there was some kind of a transfer.
00:49:19 - You need to be more complicated And part of it involves characterizing information
00:49:26 - between more than two variables, so-called multivariate mutual information.
00:49:31 - And that, as I mentioned in my talk, is a very, very active area of research
00:49:35 - with a lot of different ideas about what properties a mutual information measure ought to have.
00:49:40 - Um, and the particular measures we took are based on our particular way of looking
00:49:46 - at that, which, which itself is somewhat complicated.
00:49:49 - There are several different levels of, of things we've put forward,
00:49:52 - some of which are fairly uncontroversial and some of which are much more controversial.
00:49:56 - And so the main point there is that I guess the lesson I would take from that
00:50:00 - is that in trying to understand these simple toy agents.
00:50:04 - We ended up pushing the tools of information theory in a particular way,
00:50:09 - which I think is probably going to be important for applying those tools, for example, to C.
00:50:13 - Elegans. Okay, so even if there were no other benefit to have been gained from
00:50:18 - analyzing these toy models, and I believe that there is additional benefit that's
00:50:22 - been gained, that tool development, I think, is actually very, very important.
00:50:26 - But then you also introduced measures of information that started to include time.
00:50:31 - So does that mean you actually start to merge the dynamical systems view with
00:50:35 - the information theoretic view? It's not a matter of merging it.
00:50:38 - There's actually a significant subset of work in information theory that's interested
00:50:43 - in dynamic information.
00:50:45 - What I think, again, the way I like to look at it is you have these two distinct
00:50:49 - lenses, and it's interesting to ask what's the relationship between the two.
00:50:53 - So, your intuition is exactly right.
00:50:56 - If information is changing over time, and dynamics is about changes in state over time,
00:51:02 - then one would think that there's some interesting bridges to be built there,
00:51:06 - and that's exactly what we've tried to do in the part of the talk I wasn't able
00:51:09 - to get to, is show you in some detail how,
00:51:12 - for example, the structure of these manifolds of states that show up as being
00:51:16 - so important when you look at the dynamical systems lens, can be exactly related
00:51:21 - to the information measures that show up when you use information theory.
00:51:28 - But now you could also imagine that you would like to bring it back to causal
00:51:32 - interaction in your network, right?
00:51:34 - And the dynamical systems view or the information theoretic view doesn't necessarily
00:51:39 - give you that automatically.
00:51:40 - It doesn't necessarily, no. I mean, given that we're doing our dynamical analysis
00:51:44 - at the level of the fundamental states of the system, it actually ends up being a causal story.
00:51:51 - But you're right that dynamical systems theory itself isn't intrinsically causal
00:51:55 - or not, because you can look at collective variables where it's not directly causal anymore.
00:52:00 - So the question is, do you feel that you have to now insert a third lens that
00:52:03 - gets you a more systematic handle on the causal interaction?
00:52:08 - I don't view that as a different… Again, remember, for me the lenses are the mathematical tool.
00:52:12 - So for example, you could apply the dynamical systems lens at multiple levels.
00:52:16 - And in fact, I think the way causality works in science is… So if you look at
00:52:23 - a system at one level, it's always ever going to be a description.
00:52:26 - You look at a system at two levels and you look at bridging the lower level
00:52:30 - and the higher level, then you're talking about causality.
00:52:33 - And we, as you noticed in the talk, typically look at two levels.
00:52:37 - We have the level of behavior, which is our high level, and we have the level
00:52:42 - of, say, the mechanical and the neural states that are involved,
00:52:46 - which for us is the causal level because there is no lower physics below that.
00:52:51 - And so I think we're always talking about causal explanations, but you're right.
00:52:56 - It's not intrinsic to a given mathematical lens. I agree with that. Mm-hmm.
00:53:01 - So then when you were summarizing, so these were the examples that you used
00:53:07 - to introduce this approach, what I called methods, but you called it language and lenses.
00:53:15 - But in some sense, if you then sort of step back a little bit and say,
00:53:18 - okay, but what have we achieved with this over the last 25 years about, I would think, no?
00:53:23 - Maybe you're in this domain for a while. You had quite a list of phenomena that
00:53:28 - you were alluding to or that you were saying, look, we have a handle on these
00:53:31 - phenomena in some way with this approach, right?
00:53:33 - And this was starting in Camel, Texas, but then you talked also about attention,
00:53:39 - about a minimally cognitive agent, you talked about learning, right?
00:53:43 - So is it, what makes, for instance, the agent we have just discussed,
00:53:48 - what makes that agent minimally cognitive?
00:53:51 - Okay, that's a good question. I never got a chance to respond to with Tony.
00:53:56 - So, to explain it, I have to give you just a tiny little bit of history.
00:53:59 - And that is that when I first started doing this work, as you may know,
00:54:03 - the first examples were locomotion. Right.
00:54:05 - That was what I... And there is when I focused on the importance of the feedback
00:54:09 - through the body, and this whole brain-body-environment idea was originally
00:54:13 - coming from looking at motor control, like locomotion.
00:54:16 - And I and others that were doing this kind of work at the time felt that the
00:54:21 - kinds of lessons that we were learning about brain-body environment systems
00:54:24 - by studying these motor control tasks had more general applicability.
00:54:28 - But the problem is if you go to, for example, a cognitive science audience and
00:54:33 - talk about walking, they're not impressed.
00:54:39 - Different people mean different things by minimally cognitive.
00:54:42 - The way I defined minimally cognitive in the first paper where I used that term
00:54:46 - was it It is basically behavior.
00:54:50 - It's the simplest behavior that raises genuinely cognitive issues.
00:54:56 - And how I evaluate that is very simple. If you present walking to an audience
00:55:00 - of cognitive scientists, nobody cares.
00:55:03 - You present categorization or a selective attention or something like that,
00:55:09 - a referential communication.
00:55:09 - These are all things we've looked at to an audience of cognitive science people.
00:55:13 - They sit up and they're interested in what you have to say. So I'm not taking
00:55:17 - any theoretical position in the notion of minimally cognitive as to what is or isn't cognitive.
00:55:23 - It's simply saying there's a certain level of sophistication of the behavior
00:55:26 - that has to be recognized as being cognitively interesting by the cognitive
00:55:31 - science community so that we can engage them with these issues about brain-body-environment
00:55:37 - systems and the role of dynamics and so on.
00:55:40 - So I took it to mean that your agent has a minimal memory, and as a result,
00:55:45 - it can maintain information over time, and that gives it then,
00:55:49 - let's say, a cognitive state.
00:55:51 - Yeah. So, I mean, if for you, memory is one of those key trigger issues,
00:55:56 - then absolutely, that's fine.
00:55:57 - No, no, I think that… But some of the tasks we've looked at that I call minimally
00:56:01 - cognitive don't have memory associated with them.
00:56:04 - Okay, so what makes me feel a bit uneasy is that you're saying,
00:56:07 - look, I'm using a label that's not necessarily exactly accurate for what I do,
00:56:12 - like minimal cognitive, but it helps me to communicate what I do to a certain community, right?
00:56:18 - Well, in my perspective, cognition has a very specific definition that's almost
00:56:23 - domain independent, or it has to be, otherwise we're not making progress in science.
00:56:27 - And there, cognition is always tied to some forms of knowledge, right?
00:56:31 - This is also how it is defined. So, that would mean there is some aspect of
00:56:36 - knowledge acquisition, retention and expression that makes a system cognitive.
00:56:42 - I felt that you're more loose about this. Oh, I absolutely am.
00:56:46 - I'm trying to explain it.
00:56:48 - It's not as simple as you just said. If you go and ask a room full of cognitive scientists,
00:56:53 - actually let's do it this way, if you separated them so they're not all in the
00:56:57 - same room and asked them individually how they would characterize what is and
00:57:00 - isn't cognitive, you would likely get as many answers as there are people that you ask.
00:57:04 - And that's why, I mean, like everything else I've been saying, I think it's premature.
00:57:09 - I don't think we have an accepted definition of what cognitive is.
00:57:13 - But what we do have is a field that studies cognition, and they have a set of
00:57:18 - intuitions about what is or isn't sufficiently cognitive to be worth study by that field.
00:57:23 - And all I'm saying is that some of our toy models, if they're going to have
00:57:29 - anything to say to cognitive science as a field needs to engage those intuitions.
00:57:33 - So if for you it's memory, then some of the things I listed under that list
00:57:37 - of minimally cognitive behavior probably wouldn't count for you,
00:57:40 - but others would, and that's fine.
00:57:42 - I have no problem with that. This is something that I would object to because
00:57:46 - I think it's really important that as a field.
00:57:49 - Do try to converge on definitions because otherwise we cannot phrase our hypothesis in a coherent way.
00:57:55 - I wouldn't disagree with that need, but I'm just, what I'm trying to do is tell
00:57:58 - you is realistically the state of the field at the moment, I don't think you would disagree.
00:58:02 - So I've actually been a little unhappy that other people have used the word
00:58:07 - minimally cognitive to mean something more than that,
00:58:11 - that somehow there is a line that's been put forward that where something above
00:58:17 - that line is cognitive and something below that line isn't.
00:58:20 - I just didn't mean it by that term. Others may have a definition.
00:58:25 - I'm aware of a number of different sort of fundamental definitions,
00:58:29 - like one that comes out of Maturana and Varela's work about what's cognitive,
00:58:32 - which is another area of work that I'm involved in.
00:58:35 - But I don't feel a need to subscribe or not to such an issue in order to say
00:58:42 - that, look, some of the brain-body environment models that we're developing
00:58:45 - are engaging issues of interest in cognitive science.
00:58:48 - I think, I mean, so in your list you had, I think, items like working memory,
00:58:53 - or was it short-term memory? Short-term memory, yeah.
00:58:55 - Each of those is a very specific task.
00:59:01 - Yeah, but actually that maps onto something which, to you, is not a direct analog
00:59:06 - of those phenomenon the way we might think of them in mammals.
00:59:11 - Yeah, how could they be with a dozen neurons or something like that?
00:59:15 - But on the other hand, you defined a couple of, I think, relatively new terms,
00:59:19 - like information offloading, information self-structuring. Those are both terms from the literature.
00:59:24 - Are those in the same category of things that are perhaps high-level cognitive structures?
00:59:31 - No. Okay, so they're in a different category. Could you explain the difference?
00:59:34 - Well, I didn't list those under what you're talking about. I know.
00:59:37 - They appeared in the talk. So why are those different? So, um.
00:59:42 - Those terms have been developed in information theory, or more correctly,
00:59:47 - in the application of information theory to, let's say, animals.
00:59:51 - I'm trying to be very general about it, rather than just necessarily cognitive systems.
00:59:55 - So information offloading is a term where you take information that's inside
01:00:01 - the system and you put it outside the system for a while,
01:00:04 - and then you later re-interact with that offloaded information to sort of bring
01:00:09 - it back into the operation of the system.
01:00:12 - I can't tell you who defined it originally, but one of the earlier papers that
01:00:16 - I read was by Olaf Sporns and Max Longorella, where that term was used.
01:00:21 - Information self-structuring is similar.
01:00:23 - In that case, it's that you move your body around so as to elicit information
01:00:29 - from the environment that's not necessarily there passively for you to pick
01:00:33 - up on. So those aren't tasks.
01:00:36 - If you look at a textbook in cognitive science, you're not going to find a section
01:00:41 - on information offloading.
01:00:43 - You will find a section on short-term memory and language, let's say,
01:00:47 - rather than communication, and relational categorization. Those are things you'll
01:00:52 - find in a textbook. So they're just two different sorts of terms.
01:00:55 - I'm not entirely sure because you then alluded to examples of how people offload
01:01:00 - information, for instance, by writing things down. No, in fact,
01:01:03 - that's very interesting. I mean, uh, it's a more recent, it's a more recent, uh.
01:01:09 - Component of the vocabulary of cognitive science to talk about things like offloading.
01:01:14 - So maybe eventually there will be a chapter in a cognitive science or cognitive
01:01:18 - psychology book about such things.
01:01:20 - There are certainly people like David Kirsch that have been arguing how we organize
01:01:25 - our environments is a really key component of our cognitive processes.
01:01:29 - So I mean, there's precedent for that, but it's just not the traditional set
01:01:34 - of topics you would see in cognitive science.
01:01:36 - But I mean, but on that basis, maybe there's an argument you could make that
01:01:41 - let's redefine some of these other concepts that have been knocking around cognitive
01:01:45 - science based on the things we can see in your- Sure.
01:01:48 - Well, in fact, I mean, if you look at, so each of the things I listed on that
01:01:51 - final slide, there's at least one paper, usually several papers on.
01:01:54 - I mean, each one of those makes a specific set of arguments about how the results
01:01:58 - of analyzing that agent suggest we should look at this process very differently
01:02:02 - than it's traditionally been looked at. I mean, that's kind of the modus operandi
01:02:06 - of the research program, is to keep doing that.
01:02:08 - So the stuff on learning that you mentioned, for example, specifically looks
01:02:12 - at an issue related to learning without synaptic plasticity.
01:02:16 - That's sort of the argument there that you, well, I won't get into the details,
01:02:20 - but I mean, each one of them has exactly that feature that perhaps… So maybe
01:02:24 - this is a challenge, right?
01:02:25 - I'm supposed to say like, well, I just relabel and I hope that people aren't
01:02:30 - unhappy with what I'm saying.
01:02:31 - Maybe it is really about redefining, but this is, I think, also Tony's invitation
01:02:35 - here. Yeah, I mean, in the end, so now you're going to make me record a strong
01:02:41 - statement here. Yes, please.
01:02:42 - But I mean, in the end, I'm not sure that cognition or cognitive is a useful,
01:02:46 - scientifically useful term. Mm-hmm.
01:02:48 - I think it tries to slice up things that ultimately they're just various kinds
01:02:52 - of behavior that, for example, to your memory point, are more or less driven
01:02:56 - by internal dynamics versus external dynamics.
01:02:59 - So this is one of the reasons why I may be acting as if I'm being coy about
01:03:05 - it, but I fundamentally, I'm just not sure it's a useful term,
01:03:07 - just like I'm not sure representation is really a useful term.
01:03:10 - So rather than arguing about it, which is something I used to do,
01:03:13 - I just don't use it and I find I've lost nothing by removing that term from
01:03:19 - my vocabulary and talking just about internal state and so on.
01:03:22 - I see your point, but I do believe to make progress in the field,
01:03:25 - certainly about building up a psychology or cognitive science,
01:03:28 - we do have to get clarity on the constructs we're going to use because they
01:03:32 - have to drive our theory.
01:03:33 - That's certainly true, but that doesn't necessarily mean that you have to clarify cognition.
01:03:37 - Absolutely. If, for example, that's not necessarily the right construct.
01:03:39 - Maybe we should forget about it and replace it with better defined constructs.
01:03:43 - The other thing is, if it is a useful distinction, I think eventually it will
01:03:47 - become clear how we ought to define it.
01:03:49 - But trying to define it before we really know what we're talking about just seems premature to me.
01:03:53 - It's kind of like defining mass before you have any notion of Newton's second
01:03:57 - law, which, by the way, the notion of mass there is completely different than
01:04:01 - it is in general relativity.
01:04:02 - I mean, so it itself was a changing, and mass is a much simpler concept than cognition. Right.
01:04:07 - So, Randy, now you have met over the last, let's say, 25, 30 years,
01:04:13 - being active and really pushing a very specific agenda with great success.
01:04:17 - Also influencing many people in their work.
01:04:21 - What would be Randy's law that people should adhere to to make progress in understanding
01:04:27 - brain, body, and environment?
01:04:31 - Yeah, so I don't know. I don't have a particular law that I can think of.
01:04:35 - What I would suggest is that...
01:04:40 - I think these days, the fact that so many people take for granted the idea of
01:04:44 - brain-body environment systems is just the proper unit of analysis has come
01:04:48 - out of the line of work that I was a part of, at least.
01:04:51 - Certainly many other people have pushed that line too, but I think it's much
01:04:54 - harder to argue with that view than it was when some of us were first starting
01:04:58 - out kind of as voices in the wilderness.
01:05:01 - I hope something else that's come out of the work I've done is just how important
01:05:06 - dynamical systems theory and the concepts of dynamical systems are as at least part of the toolbox.
01:05:12 - That also was something that was very, very, very controversial when we started out.
01:05:18 - I hope, this is one thing I think that's still in progress, that this notion
01:05:24 - of the toy models have a really important role to play in the development of
01:05:28 - theory in the behavioral and brain sciences.
01:05:32 - That's a somewhat more unusual position, and it's one I've been pushing for a while.
01:05:37 - But I hope that eventually that will sink in as, again, not the only way to
01:05:40 - proceed, but an important component of theory.
01:05:43 - And most recently, I hope that if we reformulate some of the key concepts in
01:05:48 - information theory, that it'll actually turn out to be another really useful
01:05:51 - tool that's not in competition with something like dynamical systems,
01:05:54 - but is a great augmentation to it.
01:05:57 - Which by the way, I still get a lot of, so I give the talk like this at a group
01:06:00 - that's full of dynamical systems people, and they just can't believe the words
01:06:04 - that are coming out of my mouth, right?
01:06:07 - So although that may be obvious for some people, for others that are clinging
01:06:11 - to, you know, the problem I think is conflating information theory as a body
01:06:17 - of mathematics with information
01:06:20 - processing as a notion that the brain pushes symbols around.
01:06:23 - And that's why I'm so insistent about this lens distinction.
01:06:26 - It's only because I want to make sure that people understand I'm talking about
01:06:30 - the lens and not the sort of,
01:06:32 - of framework that people were previously associating with information processing.
01:06:38 - But it would mean Randy's law would be like, don't worry about taking a minority view.
01:06:43 - Oh, I see. Okay. Would it be fair to say?
01:06:45 - I don't know. I mean, it can be dangerous too, right? Sure, absolutely.
01:06:49 - But look where it got you. I mean, but for me, science
01:06:55 - is most interesting at
01:06:57 - sort of the boundaries and the limits of what you're doing
01:07:00 - and so it's it's not necessarily good career
01:07:04 - advice for a student sometimes that you should sort of jump
01:07:07 - to a boundary and start pushing really hard and loudly but it
01:07:10 - certainly worked pretty well for me and i'm not sure i
01:07:12 - could have done it any other way it's sort of a personality thing i sort
01:07:15 - of normal science i guess doesn't engage me as much as sort of really pushing
01:07:20 - at conceptual boundaries right and things so now uh tony likes traveling and
01:07:24 - soon easy jets will fly to the states as well including indiana so we can send
01:07:28 - it for a little money to your lab and we're going to do that four years from
01:07:31 - now so Tony can test a prediction you're going to make today.
01:07:35 - So what specific prediction could you make now that you will see tested and
01:07:41 - validated four years from now and maybe rejected, but a specific prediction?
01:07:47 - Well, so, oh, you mean predictions about the field or predictions about some
01:07:51 - experimental... Science, what you do, the work you do, like the C.
01:07:54 - Elegans work or any other system you're working on, really specific scientific
01:07:57 - prediction that you will see tested?
01:08:00 - Well, so I mean, the problem is I don't want to talk about unpublished work.
01:08:06 - And so all I can talk about is work we've published. And it's actually most
01:08:09 - of our predictions were actually successfully tested in that.
01:08:12 - It could be more general than that, perhaps.
01:08:15 - What the field of C. elegans. Well, so I mean. No, in four years time. Anything Tony can test.
01:08:20 - Well, more general is easier. I mean, I really think it's within reach.
01:08:25 - Four years is short. I would maybe think it's decade long or so,
01:08:29 - but I really think it's within reach to imagine having a complete neural mechanical
01:08:34 - behavioral model of C. elegans. That's not- You said 10 years?
01:08:38 - Yeah. Okay. I think 10 years is pushing it.
01:08:43 - Now that's not, I don't know if that's a prediction or not, but I mean,
01:08:45 - even a year ago, I might not have said that because it was only over the past
01:08:49 - year that we had these new optical techniques that can image brain activity
01:08:52 - of a whole animal at the level of individual cells.
01:08:55 - That I think is ultimately going to be really, really important.
01:08:58 - But it's going to take some time for that to move into the scientific toolkit
01:09:02 - of the experimentalists that study the system and therefore can better constrain the modelers.
01:09:07 - Great. Well, Randy Beer, thank you very much for this conversation. All right. Thank you.
01:09:12 - Well, that was fun. Was it? Yeah. Good. The CSN podcast was produced by the
01:09:17 - Convergent Science Network of Biometrics and Biohybrid Systems,
01:09:22 - a project funded by the European Sevens Research Framework Programme.
01:09:28 - For more interviews, recorded lectures or upcoming conferences in the field
01:09:33 - of biometrics and biohybrid systems, go to csnnetwork.eu.
01:09:40 - And thank you for listening.
01:09:40 - Music.

CSN Podcasts

Randall Beer on dynamical systems and information theory

Season 2015

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CSN Podcasts

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Matthew Diamond on whisker system and decision-making

Stephen Noctor on cortical development and precursor cells

Ranulfo Romo on decision-making and somatosensory cortex

Narender Ramnani on cerebellum and cortico-cerebellar loops

Mark Blumberg on rem sleep and twitching

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