Archives de catégorie : Neural coding

What is computational neuroscience? (XXXV) Metaphors as morphisms

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What is a metaphor? Essentially, a metaphor is an analogy that doesn’t say its name. We use metaphors all the time without even noticing it, as was beautifully demonstrated by Lakoff & Johnson (1980). When I say for example, “let me cast some light on this issue”, I am using a fairly sophisticated metaphor in which I make an analogy between understanding and seeing. In that analogy, an explanation allows you to understand, in the same way as light allows you to see. You might then reply: I see what you mean, it is clearer! Chances are that, in normal conversation, we would not have noticed that we both used a metaphor.

Metaphors are everywhere in neuroscience, and in biology more generally (see these posts). For example: evolution optimizes traits (see the excellent article of Gould & Lewontin (1979) for a counterpoint); the genome is a code for the organism (see Denis Noble (2011a; 2011b)); the brain runs algorithms, or is a computer (see also Paul Cisek (1999) or Francisco Varela); neural activity is a code.

These metaphors are so ingrained in neuroscientific thinking that many object to the very idea that they are metaphorical. The objection is that “evolution is optimization” or “brain runs algorithms” is not a metaphor, it is a theory. Or, for the more dogmatic, these are not metaphors, these are facts.

Indisputable truths belong to theology, not science, so any claim that a general proposition is a fact should be seen as suspect – it is an expression of dogmatism. But there is a case that we are actually talking about theories. In the case of neural codes or brains as computers, one might insist that the terms “code” or “computer” refer to abstract properties, not to concrete objects like a desktop computer. But this is a misunderstanding of what a metaphor, or more generally an analogy, is. When I am “casting light on this issue”, I am not referring to any particular lamp, but to an abstract concept of light which does not actually involve photons. The question is not whether words are actually some sort of photons, but whether the functional relation between light and seeing is similar to the functional relation between explanation and understanding. There is no doubt that these concepts are abstracted from actual properties of concrete situations (of light and perception), but so are the concepts of code and computer. In the metaphor, it is the abstract properties that are at stake, so the objection “it is not a metaphor, it is a theory” either misunderstands what metaphor is (a metaphor is a theory), or perhaps really means “the theory is correct” – again dogmatism.

For the mathematically minded, a mathematical concept that captures this idea is “morphism”. A morphism is a map that preserves structure. For example, a group homomorphism f from X to Y is such that f(a*b) = f(a) x f(b): the operation * defined on X is mapped to the operation x defined on Y (of course “metaphors are morphisms” is a metaphor!).

For example, in the “let me cast light on this issue” metaphor, I am mapping the domain of visual perception to the domain of linguistic discourse: light -> words; visual object -> issue ; seeing -> understanding. What makes the metaphor interesting is that some relations within the first domain are mapped to relations in the other domain: use of light on an object causes seeing; use of words on an issue causes understanding.

Another example in science is the analogy between the heart and a pump. Each element of the pump (e.g. valve, liquid) is mapped to an element of the heart, and the analogy is relevant because functional relations between elements of the pump are mapped to corresponding relations between elements of the heart. Thus, the analogy has explanatory power. What makes a metaphor or an analogy interesting is not the fact that the two domains are similar (they are generally not), but the richness of the structure preserved by the implied morphism.

In other words, a metaphor or an analogy is a theory that takes inspiration from another domain (e.g. computer science), by mapping some structure from one domain to the other. There is nothing intrinsically wrong with this, on the contrary. Why then is the term “metaphor” so vehemently opposed in science ? Because the term implies that the theory is questionable (hence, again, dogmatism). There are ways in which understanding is like seeing, but there are also ways in which it is different.

Let us consider the metaphor “the brain implements algorithms”, which I previously discussed. Some are irritated by the very suggestion that this might even be a metaphor. The rhetorical strategy is generally two-fold: 1) by “algorithm”, we mean some abstract property, not programs written in C++; 2) the definition of “algorithm” is made general enough that it is trivially true, in which case it is not a metaphor since it is literally true. As argued, (1) is a misunderstanding of linguistics because metaphor is about abstract properties. And if we follow (2), then nothing can be inferred from the statement. Thus, it is only to the extent that “the brain implements algorithms” is metaphorical that it is insightful (and it is to some extent, but in my view to a limited extent).

The key question, thus, is what we mean by “algorithm”. A natural starting point would be to take the definition from a computer science textbook. The most used textbook on the subject is probably Cormen et al., Introduction to algorithms. It proposes the following definition: “a sequence of computational steps that transform the input into the output”. One would need to define what “computational” means in this context, but it is not key for this discussion. With this definition, to say that the brain implements an algorithm means that there exists a morphism between brain activity and a sequence of computational steps. That is, intermediate values of the algorithm are mapped to properties of brain activity (e.g. firing rates measured over some time window) - this is the “encoding”. Then we claim that this mapping has the property that a computational step linking two values is mapped to the operation of the dynamics of the brain linking the two corresponding neural measurements. I explain in the third part of my essay on neural coding why this claim cannot be correct, at least not generally and only approximately (one reason is that a measurement of neural activity must be done on some time window, and thus cannot be considered as an initial state of a dynamical system, from which you could deduce the future dynamics). But this is not the point of this discussion. The point is that this claim, that there is a morphism between an algorithm and brain activity, is not trivial and it has explanatory value. In other words, it is interesting. This stems from the rich structure that is being mapped between the two domains.

Since it is not trivial (as in fact any metaphor), a discussion will necessarily arise about whether and to what extent the implied mapping does in fact preserve structure between the two domains. You could accept this state of affairs and provide empirical or theoretical arguments. Or you could dismiss the metaphorical nature entirely. But by doing so, you are also dismissing what is interesting about the metaphor, that is, the fact that there might be a morphism between two domains. We could for example redefine “algorithm” in a more general way as a computable function, even if it is not what is usually meant by that (as the Cormen textbook shows). But in that case, the claim loses all explanatory value because no structure at all is transported between the two domains. We are just calling sensory signals “input” and motor commands “output” and whatever happens in between “algorithm”. In mathematical terms, this is a mapping but not a morphism.

Thus, metaphors are interesting because they are morphisms between domains, which is what gives them scientific value (they are models). The problem, however, is that metaphor is typically covert, and failure to recognize them as such leads to dogmatism. When one objects to the use of some words like “code”, “algorithm”, “representation”, “optimization”, a common reaction is that the issue “is just semantic”. What this means is that it is just about arbitrary labels, and the labels themselves do not really matter. As if scientific discourse were essentially uninteresting and trivial (we just observe things and give them names). This reaction reveals a naïve view of language where words are mappings (between objects and arbitrary labels), when what matters is the structured concepts that words refer to through morphisms, not just mappings. This is what metaphor is about.

Is the coding metaphor relevant for the genome?

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I have argued that the neural coding metaphor is highly misleading (see also similar arguments by Mark Bickhard in cognitive science). The coding metaphor is very popular in neuroscience, but there is another domain of science where it is also very popular: genetics. Is there a genetic code? Many scientists have criticized the idea of a genetic code (and of a genetic program). A detailed criticism can be found in Denis Noble’s book “The music of life” (see also Noble 2011 for a short review).

Many of the arguments I have made in my essay on neural coding readily apply to the “genetic code”. Let us start with the technical use of the metaphor. The genome is a sequence of DNA base triplets called “codons” (ACG, TGA, etc). Each codon specifies a particular amino-acid, and proteins are made of amino-acids. So there is a correspondence between DNA and amino-acids. This seems an appropriate use of the term “code”. But even it in this limited sense, it should be used with caution. The fact that a base triplet encodes an amino-acid is conditional on this triplet being effectively translated into an amino-acid (note that there are two stages, transcription into RNA, then translation into a protein). But in fact only a small fraction of a genome is actually translated, about 10% (depending on species); the rest is called “non-coding DNA”. So the same triplets can result in the production of an amino-acid, or they can influence the translation-transcription system in various ways, for example by interacting with various molecules involved in the production of RNA and proteins, thereby regulating transcription and translation (and this is just one example).

Even when DNA does encode amino-acids, it does not follow that a gene encodes a protein. What might be said is that a gene encodes the primary structure of proteins, that is, the sequence of amino-acids; but it does not specify by itself the shape that the protein will take (which determines its chemical properties), the various modifications that occur after translation, the position that the protein will take in the cellular system. All of those crucial properties depend on the interaction of the product of transcription with the cellular system. In fact, even the primary structure of proteins is not fully determined by the gene, because of splicing.

Thus, the genome is not just a book, as suggested by the coding metaphor (some have called the genome the “book of life”); it is a chemically active substance that interacts with its chemical environment, a part of a larger cellular system.

At the other end of the genetic code metaphor, genes encode phenotypes, traits of the organism. For example, the gene for blue eyes. A concept that often appears in the media is the idea of genes responsible for diseases. One hope behind the human genome project was that by scrutinizing the human genome, we might be able to identify the genes responsible for every disease (at least for every genetic disease). Some diseases are monogenic, i.e., due to a single gene defect, but the most common diseases are polygenic, i.e., are due to a combination of genetic factors (and generally environmental factors).

But even the idea of monogenic traits is misleading. There is no single gene that encodes a given trait. What has been demonstrated in some cases is that mutations in a single gene can impact a given trait. But this does not mean that the gene is responsible by itself for that trait (surprisingly, this fallacy is quite common in the scientific literature, as pointed out by Yoshihara & Yoshihara 2018). A gene by itself does nothing. It needs to be embedded into a system, namely a cell, in order to produce any phenotype. Consequently, the expressed phenotype depends on the system in which the gene is embedded, in particular the rest of the genome. There cannot be a gene for blue eyes if there are no eyes. So no gene can encode the color of eyes; this encoding is at best contextual (in the same way as “neural codes” are always contextual, as discussed in my neural coding essay).

So the concept of a “genetic code” can only be correct in a trivial sense: that the genome, as a whole, specifies the organism. This clearly limits the usefulness of the concept, however. Unfortunately, even this trivial claim is also incorrect. An obvious objection is that the genome specifies the organism only in conjunction with the environment. The deeper objection is that the immediate environment of the genome is the cell itself. No entity smaller than the cell can live or reproduce. The genome is not a viable system, and as such it cannot produce an organism, nor can it reproduce. An interesting experiment is the following: the nucleus (and thus the DNA) from an animal cell is transferred to the egg of an animal of another species (where the nucleus has been removed) (Sun et al., 2005). The “genetic code” theory would predict that the egg would develop into an animal of the donor species. What actually happens (this was done in related fish species) is that the egg develops into some kind of hybrid, with the development process closer to that of the recipient species. Thus, even in the most trivial sense, the genome does not encode the organism. Finally, since no entity smaller than the cell can reproduce, it follows that the genome is not the unique basis of heritability – the entire cell is (see Fields & Levin, 2018).

In summary, the genome does not encode much except for amino-acids (for about 10% of it). It should be conceptualized as a component that interacts with the cellular system, not as a “book” that would be read by some cellular machinery.

What is computational neuroscience? (XXXI) The problem of biological measurement (1)

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We tend to think of sensory receptors (photoreceptors, inner hair cells) or sensory neurons (retinal ganglion cells; auditory nerve fibers) as measuring physical dimensions, for example light intensity or acoustical pressure, or some function of it. The analogy is with physical instruments of measure, like a thermometer or a microphone. This confers a representational quality to the activity of neurons, an assumption that is at the core of the neural coding metaphor. I explain at length why that metaphor is misleading in many ways in an essay (Brette (2018) Is coding a relevant metaphor for the brain?). Here I want to examine more specifically the notion of biological measurement and the challenges it poses.

This notion comes about not only in classical representationalist views, where neural activity is seen as symbols that the brain then manipulates (the perception-cognition-action model, also called sandwich model), but also in alternative views, although it is less obvious. For example, one alternative is to see the brain not as a computer system (encoding symbols, then manipulating them) but as a control system (see Paul Cisek’s behavior as interaction, William Powers’ perceptual control theory, Tim van Gelder’s dynamical view of cognition). In this view, the activity of neurons does not encode stimuli. In fact there is no stimulus per se, as Dewey pointed out: “the motor response determines the stimulus, just as truly as sensory stimulus determines the movement.”.

A simple case is feedback control: the system tries to maintain some input at a target value. To do this, the system must compare the input with an internal value. We could imagine for example something like an idealized version of the stretch reflex: when the muscle is stretched, a sensory feedback triggers a contraction, and we want to maintain muscle length constant. But this apparently trivial task raises a number of deep questions, as more generally the application of control theory to biological systems. I suppose there is a sensor, a neuron that transduces some physical dimension into spike trains, for example the stretch of a muscle. There is also an actuator, which reacts to a spike by a physical action, for example contracting the muscle with a particular time course. I chose a spike-based description not just because it corresponds to the physiology of the stretch reflex, but also because it will illustrate some fundamental issues (which would exist also with graded transduction, but less obviously so).

Now we have a neuron, or a set of neurons, which receive these sensory inputs and send spikes to the actuator. For this discussion, it is not critical that these are actually neurons; we can just consider that there is a system there, and we ask how this system should be designed so as to successfully achieve a control task.

The major issue here is that the control system does not directly deal with the physical dimension. At first sight, we could think this is a minor issue. The physical dimension gets transduced, and we could simply define the target value in the transduced dimension (eg the current). But here we see that the problem is more serious. What the control system deals with is not simply a function of the physical dimension. More accurately, transduction is a nonlinear dynamical system influenced by a physical signal. The physical signal can be constant, for example, while the transduced current decays (adaptation) and the sensory neuron outputs spike trains, i.e., a highly variable signal. This poses a much more serious problem than a simple calibration problem. When the controlled physical value is at the target value, the sensory neuron might be spiking, perhaps not even at a regular rate. The control system should react to that particular kind of signal by not acting, while it should act when the signal deviates from it. But how can the control system identify the target state, or even know whether to act in one or the opposite direction?

Adaptation in neurons is often depicted as an optimization of information transmitted, in line with the metaphor of the day (coding). But the relevant question is: how does the receiver of this “information” knows how the neuron has adapted? Does it have to de-adapt, to somehow be matched to the adaptive process of the encoding neuron? (This problem has to do with the dualistic structure of the neural coding metaphor).

There are additional layers of difficulty. We have first recognized that transduction is not a simple mapping from a physical dimension to a biological (e.g. electrochemical) dimension, but rather a dynamical system influenced by a physical signal. Now this dynamical system depends on the structure of the sensory neuron. It depends for example on the number of ionic channels and their properties, and we know these are highly plastic and indeed quite variable both across time and across cells. This dynamical system also depends on elements of the body, or let’s say more generally the neuron’s environment. For example, the way acoustical pressure is transduced in current by an inner hair cell depends obviously on the acoustical pressure at the eardrum, but that physical signal depends on the shape the ear, which filters sounds. Properties of neurons change with time too, development and aging. Thus, we cannot assume that the dynamical transformation from physical signal to biological signal is a fixed one. Somehow, the control system has to work despite this huge plasticity and the dynamical nature of the sensors.

Let us pause for a moment and outline a number of differences between physical measurements, as with a thermometer, and biological measurements (or “sensing”):

  • The physical meter is calibrated with respect to an external reference, for example 0°C is when water freezes, while 100°C is when it boils. The biological sensor cannot be calibrated with respect to an external reference.
  • The physical meter produces a fixed value for a stationary signal. The biological sensor produces a dynamical signal in response to a stationary signal. More accurately, the biological sensor is a nonlinear dynamical system influenced by the physical signal.
  • The physical meter is meant to be stable, in that the mapping from physical quantity to measurement is fixed. When it is not, this is considered an error. The biological sensor does not have fixed properties. Changes in properties occur in the normal course of life, from birth to death, and some changes in properties are interpreted as adaptations, not errors.

From these differences, we realize that biological sensors do not provide physical measurements in the usual sense. The next question, then, is how can a biological system control a physical dimension with biological sensors that do not act as measurements of that dimension?

What is computational neuroscience? (XXVIII)The Bayesian brain

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Our sensors give us an incomplete, noisy, and indirect information about the world. For example, estimating the location of a sound source is difficult because in natural contexts, the sound of interest is corrupted by other sound sources, reflections, etc. Thus it is not possible to know the position of the source with certainty. The ‘Bayesian coding hypothesis’ (Knill & Pouget, 2014) postulates that the brain represents not the most likely position, but the entire probability distribution of the position. It then uses those distributions to do Bayesian inference, for example, when combining different sources of information (say, auditory and visual). This would allow the brain to optimally infer the most likely position. There is indeed some evidence for optimal inference in psychophysical experiments – although there is also some contradicting evidence (Rahnev & Denison, 2018).

The idea has some appeal. The problem is that, by framing perception as a statistical inference problem, it focuses on the most trivial type of uncertainty, statistical uncertainty. It is illustrated by the following quote: “The fundamental concept behind the Bayesian approach to perceptual computations is that the information provided by a set of sensory data about the world is represented by a conditional probability density function over the set of unknown variables”. Implicit in this representation is a particular model, for which variables are defined. Typically, one model describes a particular experimental situation. For example, the model would describe the distribution of auditory cues associated with the position of the sound source. Another situation would be described by a different model, for example one with two sound sources would require a model with two variables. Or if the listening environment is a room and the size of that room might vary, then we would need a model with the dimensions of the room as variables. In any of these cases where we have identified and fixed parametric sources of variation, then the Bayesian approach works fine, because we are indeed facing a problem of statistical inference. But that framework doesn’t fit any real life situation. In real life, perceptual scenes have variable structure, which corresponds to the model in statistical inference (there is one source, or two sources, we are in a room, the second source comes from the window, etc). The perceptual problem is therefore not just to infer the parameters of the model (dimensions of the room etc), but also the model itself, its structure. Thus, it is not possible in general to represent an auditory scene by a probability distribution on a set of parameters, because the very notion of a parameter already assumes that the structure of the scene is known and fixed.

Inferring parameters for a known statistical model is relatively easy. What is really difficult, and is still challenging for machine learning algorithms today, is to identify the structure of a perceptual scene, what constitutes an object (object formation), how objects are related to each other (scene analysis). These fundamental perceptual processes do not exist in the Bayesian brain. This touches on two very different types of uncertainty: statistical uncertainty, variations that can be interpreted and expected in the framework of a model; and epistemic uncertainty,  the model is unknown (the difference has been famously explained by Donald Rumsfeld).

Thus, the “Bayesian brain” idea addresses an interesting problem (statistical inference), but it trivializes the problem of perception, by missing the fact that the real challenge is epistemic uncertainty (building a perceptual model), not statistical uncertainty (tuning the parameters): the world is not noisy, it is complex.

A brief critique of predictive coding

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Predictive coding is becoming a popular theory in neuroscience (see for example Clark 2013). In a nutshell, the general idea is that brains encode predictions of their sensory inputs. This is an appealing idea because superficially, it makes a lot of sense: functionally, the only reason why you would want to process sensory information is if it might impact your future, so it makes sense to try to predict your sensory inputs.

There are substantial problems in the details of predictive coding theories, for example with the arbitrariness of the metric by which you judge that your prediction matches sensory inputs (what is important?), or the fact that predictive coding schemes encode both noise and signal. But I want to focus on the more fundamental problems. One has to with “coding”, the other with “predictive”.

It makes sense that brains anticipate. But does it make sense that brains code? Coding is a metaphor of a communication channel, and this is generally not a great metaphor for what the brain might do, unless you fully embrace dualism. I discuss this at length in a recent paper (Is coding a relevant metaphor for the brain?) so I won’t repeat the entire argument here. Predictive coding is a branch of efficient coding, so the same fallacy underlies its logic: 1) neurons encode sensory inputs; 2) living organisms are efficient; => brains must encode efficiently. (1) is trivially true in the sense that one can define a mapping from sensory inputs to neural activity. (2) is probably true to some extent (evolutionary arguments). So the conclusion follows. Critiques of efficient coding have focused on the “efficient” part: maybe the brain is not that efficient after all. But the error is elsewhere: living organisms are certainly efficient, but it doesn’t follow that they are efficient at coding. They might be efficient at surviving and reproducing, and it is not obvious that it entails coding efficiency (see the last part of the abovementioned paper for a counter-example). So the real strong assumption is there: the main function of the brain is to represent sensory inputs.

The second problem has to with “predictive”. It makes sense that an important function of brains, or in fact of any living organism, is to anticipate (see the great Anticipatory Systems by Robert Rosen). But to what extent do predictive coding schemes actually anticipate? First, in practice, those are generally not prediction schemes but compression schemes, in the sense that they do not tell us what will happen next but what happens now. This is at least the case of the classical Rao & Ballard (1999). Neurons encode the difference between expected input and actual input: this is compression, not prediction. It uses a sort of prediction in order to compress: other neurons (in higher layers) produce predictions of the inputs to those neurons, but the term prediction is used in the sense that the inputs are not known to the higher layer neurons, not that the “prediction” occurs before the inputs. Thus the term “predictive” is misleading because it is not used in a temporal sense.

However, it is relatively easy to imagine how predictive coding might be about temporal predictions, although the neural implementation is not straightforward (delays etc). So I want to make a deeper criticism. I started by claiming that it is useful to predict sensory inputs. I am taking this back (I can because I said it was superficial reasoning). It is not useful to know what will happen. What is useful is to know what might happen, depending on what you do. If there is nothing you can do about the future, what is the functional use of predicting it? So what is useful is to predict the future conditionally to a different set of potential actions. This is about manipulating models of the world, not representing the present.

What is computational neuroscience? (XXVII) The paradox of the efficient code and the neural Tower of Babel

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A pervasive metaphor in neuroscience is the idea that neurons “encode” stuff: some neurons encode pain; others encode the location of a sound; maybe a population of neurons encode some other property of objects. What does this mean? In essence, that there is a correspondence between some objective property and neural activity: when I feel pain, this neuron spikes; or, the image I see is “represented” in the firing of visual cortical neurons. The mapping between the objective properties and neural activity is the “code”. How insightful is this metaphor?

An encoded message is understandable to the extent that the reader knows the code. But the problem with applying this metaphor to the brain is only the encoded message is communicated, not the code, and not the original message. Mathematically, original message = encoded message + code, but only one term is communicated. This could still work if there were a universal code that we could assume all neurons can read, the “language of neurons”, or if somehow some information about the code could be gathered from the encoded messages themselves. Unfortunately, this is in contradiction with the main paradigm in neural coding theory, “efficient coding”.

The efficient coding hypothesis stipulates that neurons encode signals into spike trains in an efficient way, that is, it uses a code such that all redundancy is removed from the original message while preserving information, in the sense that the encoded message can be mapped back to the original message (Barlow, 1961; Simoncelli, 2003). This implies that with a perfectly efficient code, encoded messages are undistinguishable from random. Since the code is determined on the statistics of the inputs and only the encoded messages are communicated, a code is efficient to the extent that it is not understandable by the receiver. This is the paradox of the efficient code.

In the neural coding metaphor, the code is private and specific to each neuron. If we follow this metaphor, this means that all neurons speak a different language, a language that allows expressing concepts very concisely but that no one else can understand. Thus, according to the coding metaphor, the brain is a Tower of Babel.

Can this work?

Neural correlates of perception (what's wrong with them)

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Broadly speaking, neural correlates of a percept, e.g. seeing a face, are what happens with neurons when we see a face. For example, a bunch of neurons would fire when we see Jennifer Aniston. What do neural correlates teach us about perception, or more generally about the mind-body problem?

The interest in neural correlates of perception is largely subtended by the implicit belief that there must be a mapping between perception and brain state seen as a physical system. That is, the percept of seeing Jennifer Aniston's face corresponds to a particular brain state; the percept of a sound being at a particular spatial position corresponds to another one. There are considerable conceptual difficulties with this belief. Consider these two thoughts experiments.

1) Imagine we can instantaneously freeze the brain so that its components, ions, tissues, etc are preserved in the same state (it's a thought experiment!). Does the brain still experience seeing Jennifer Aniston's face?

2) Imagine we record the precise spatiotemporal activity of all neurons in response to Jennifer Aniston's face. Then we inactivate all synapses, and we replay the activity pattern optogenetically. Would the brain still experience seeing Jennifer Aniston's face?

Intuitively, our answer to both questions is negative. If you answered the second question positively, then consider this one:

2b) Imagine we record the precise spatiotemporal activity of all neurons in response to Jennifer Aniston's face. Then we replay the activity pattern on a set of light diodes. Would the diodes experience seeing Jennifer Aniston's face?

If our intuition is correct, then brain states, even understood more broadly as “firing patterns” are not constitutive of percepts. It appears that whatever a percept is, it must involve not just the state or even the activity of neurons, but the interaction between neurons. Therefore when we describe neural correlates of perception in terms of neural “activity”, we appear to be missing a crucial ingredient, which has to do with interactional properties of neurons. To be honest, I must admit here that “interactional properties of neurons” is a loosely defined concept, but apparently there seems to be a need for a concept that goes beyond the concept of activity “pattern”, a concept to be clarified (see afterthought below).

Underlying the problematic concept of neural correlates of perception is the representational view of perception; the idea that whatever we perceive must somehow be “represented” in the brain, like neural paintings of the world. I have pointed out the deep problems with the representational view on this blog (for example here and there) – and obviously I am not the first one to do so (see e.g. Gibson, Brooks, Merleau-Ponty, O'Regan etc). Let us simply reflect on the following one. When we look at Jennifer Anniston's face, we experience the percept of seeing her face at different moments. It seems as if at any instant, we are experiencing the same percept (along with others, of course). Possibly this is an illusion and experience is actually discrete in time, but in any case the perceptual “grain of time” is no more than a few tens of ms. Therefore when looking for neural correlates of the percept, then we cannot be happy to rely on average activity, over time or over trials. We do not experience percepts “on average”, but at any instant (this is related to my points on the rate vs. spike debate). What we should be looking for is something in the interactional properties of neurons that is invariant through the entire time during which the percept is experienced. The concept is quite different from the more traditional “neural paintings” concept.

So, in the current state of research, what neural correlates of perception tell us about perception, more specifically about the mind-body problem, is disappointingly: not so much.

 

Afterthought: an interesting analogy is the concept of temperature in physics. Since temperature corresponds to the movement of particles, you cannot really define the temperature of a physical object at any given time. Temperature corresponds to the activity, not the position or nature of the particles. What's more, the concept of temperature makes no sense except when considering the interaction between agitated particles. Temperature is perhaps an example of “interactional property” of a set of particles.

Why do neurons spike?

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Why do neurons produce those all-or-none electrical events named action potentials?

One theory, based on the coding paradigm, is that the production of action potentials is like analog-to-digital conversion, which is necessary if a cell wants to communicate to a distant cell. It would not be necessary if neurons were only communicating with their neighbors. For example, in the retina, most neurons do not spike but interact through graded potentials, and only retinal ganglion cells produce spikes, which travel over long distances (note that there is actually some evidence of spikes in bipolar cells). In converting graded signals into discrete events, some information is lost, but that is the price to pay in order to transmit any signal at all over a long distance. There is some theoretical work on this trade-off by Manwani and Koch (1999).

Incidentally, this theory is sometimes (wrongly) used to argue that spike timing does not matter because spikes are only used as a proxy for an analog signal, which is reflected by the firing rate. This theory is probably not correct, or at least incomplete.

First, neurons start spiking before they make any synaptic contact, and that activity is important for normal development (Pineda and Ribera, 2009). Apparently, normal morphology and mature properties of ionic channels depend on the production of spikes. In many neuron types, those early spikes are long calcium spikes.

A more convincing argument to me is the fact that a number of unicellular organisms produce spikes. For example, in paramecium, calcium spikes are triggered in response to various sensory stimuli and trigger an avoidance reaction, where the cell swims backward (reverting the beating direction of cilia). An interesting point here is that those sensory stimuli produce graded depolarizations in the cell, so from a pure coding perspective, the conversion of that signal to an all-or-none spike in the same cell seems very weird, since it reduces information about the stimuli. Clearly, coding is the wrong perspective here (as I have tried to argue in my recent review on the spike vs. rate debate). The spike should not be seen as a code for the stimulus, but rather as a decision or action, in this case to reverse the beating direction. This argues for another theory, that action potentials mediate decisions, which are by definition all-or-none.

Action potentials are also found in plants. For example, mimosa pudica produces spikes in response to various stimuli, for example if it is touched, and those spikes mediate an avoidance reaction where the leaves fold. Those are long spikes, mostly mediated by chloride (which is outward instead of inward). Again the spike mediates a timed action. It also propagates along the plant. Here spike propagation allows organism-wide coordination of responses.

It is also interesting to take an evolutionary perspective. I have read two related propositions that I found quite interesting (and neither is about coding). Andrew Goldsworthy proposed that spikes started as an aid to repair a damaged membrane. There is a lot of calcium in the extracellular space, and so when the membrane is ruptured, calcium ions rush into the cell, and they are toxic. Goldsworthy argues that the flow of ions can be reduced by depolarizing the cell, while repair takes place. We can immediately make two objections: 1) if depolarization is mediated by calcium then this obviously has little interest; 2) to stop calcium ions from flowing in, one needs to raise the potential to the reversal potential of calcium, which is very high (above 100 mV). I can think of two possible solutions. One is to trigger a sodium spike, but it doesn't really solve problem #2. Another might be to consider evenly distributed calcium channels on the membrane, perhaps together with calcium buffers/stores near them. When the membrane is ruptured, lots of calcium ions enter through the hole, and the concentration increases locally by a large amount, which probably immediately starts damaging the cell and invading it. But if the depolarization quickly triggers the opening of calcium channels all over the membrane, then the membrane potential would increase quickly with relatively small changes in concentration, distributed over the membrane. The electrical field then reduces the ion flow through the hole. It's an idea, but I'm not sure the mechanism would be so efficient in protecting the cell.

Another related idea was proposed in a recent review. When the cell is ruptured, cellular events are triggered to repair the membrane. Brunet and Arendt propose that calcium channels sensitive to stretch have evolved to anticipate damage: when the membrane is stretched, calcium enters through the channels to trigger the repair mechanisms before the damage actually happens. In this theory, it is the high toxicity of calcium that makes it a universal cellular signal. The theory doesn't directly explain why the response should be all-or-none, however. An important aspect, maybe, is cell-wide coordination: the opening of local channels must trigger a strong enough depolarization so as to make other calcium channels open all over the membrane of the cell (or at least around the stretched point). If the stretch is very local, then this requires an active amplification of the signal, which at a distance is only electrical. In other words, fast coordination at the cell-wide level requires a positive electrical feedback, aka an action potential. Channels must also close (inactivate) once the cellular response has taken place, since calcium ions are toxic.

Why would there be sodium channels? It's actually obvious: sodium ions are not as toxic as calcium and therefore it is advantageous to use sodium rather than calcium. However, this is not an entirely convincing response since in the end, calcium is in the intracellular signal. But a possible theory is the following: sodium channels appear whenever amplification is necessary but no cellular response is required at that cellular location. In other words, sodium channels are useful for quickly propagating signals across the cell. It is interesting to note that developing neurons generally produce calcium spikes, which are then converted to sodium spikes when the neurons start to grow axons and make synaptic contacts.

These ideas lead us to the following view: the primary function of action potentials is cell-wide coordination of timed cellular decisions, which is more general than fast intercellular communication.

Notes on consciousness. (V) 4 key questions about consciousness and the mind-body problem

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It is fair to say that we have little idea about how neural activity gives rise to consciousness, and about the relationship between neural activity and conscious states (i.e., what you are experiencing). This is the mind-body problem. In my opinion, there has been relatively little fundamental progress on this question because it has been addressed mainly within the computationalist framework (ie in terms of information processing), which is very inappropriate for this question (this is partly Chalmers' criticism). So below I am listing a number of unanswered questions on this matter, which I believe requires a very different kind of approach. First of all, let me remark that because being conscious is always being conscious of something, understanding consciousness is largely about understanding perception at the phenomenal level (perception in the broadest sense, e.g., perceiving your thoughts).

1) How can perception be stable?

Why is it that a pure tone feels like a stable percept when 1) the acoustic wave is time-varying, 2) the activity of neurons everywhere in the brain is dynamic? The same can be said of all senses; in vision, the eyes move at high frequency even when fixating an object, and there is no visual percept if they are forced to be still. More generally: if there is a mapping between states of the brain and percepts, then why is it that percepts are not changing all the time?

A thought experiment. Imagine the state of the brain is held fixed. Someone scratches her nose and time is stopped. Would you still experience something? Any conscious experience seems to require a change, not just a state. This suggests that the relevant mapping is actually not from brain states to percepts, but from brain activity to percepts. This immediately raises a problem, because a conscious state can be defined at any point in time, but it is not immediate that brain activity can (as this would reduce activity to state). This is not a fatal problem, though, for there is a precedent in physics: a gas is composed of individual particles, but the pressure of a gas at a given instant cannot be defined as a function of the state of the particles at that moment, because pressure corresponds to the force exerted by the particles impacting a surface. It might be that the relation between neural activity and conscious states is of a similar kind as the relation between mechanics and thermodynamics.

Two more thoughts experiments. 1) Record the firing of all neurons in the brain, then play them on a set of unconnected light diodes, does that set feel the same experience? 2) (adapted from Chalmers) Replace randomly every other neuron in the brain by an artificial neuron that interacts with other neurons in exactly same way as the neuron it replaces, would there be a conscious experience? My personal answers would be: (1) no and (2) yes, and this suggests to me that the right substrate to look at is not neural activity as a state (e.g. firing rates of all neurons) but neural activity as an interaction between neurons.

 

2) What is time for a conscious brain?

A fundamental property of consciousness is its unity: a single conscious entity sees, hears and thinks. If visual and auditory areas where independent and, say, control speech, then one conscious entity would report visual experience and another conscious entity would report auditory experience. It could not be a single conscious entity since the two relevant parts are physically disconnected. Thus the unity of consciousness requires an interdependence between all the elements that compose it. This is, as I understand it, the issue that is addressed by a number of biological theories of consciousness, for example Edelman's “reentrant loops” or Tononi's integrated information theory.

However, as far as I know, there is another crucial aspect to this problem, which is the unity of consciousness, or lack of it, in time. There is no general unity of consciousness across time: two things that happen at, say, 1 minute of interval produce distinct percepts, not a single one. Clearly, consciousness is dynamic. But the big question is: how can there be a unique conscious state at any given moment in time when all the elements of the conscious network interact with some delay (since they are physical elements), typically of a few milliseconds? And what is time for such a network? Imagine there is a (physical) visual event at time t1 and an auditory event at time t2. At what time do they occur for the network, as they are sensed at different times by all its elements?Why is it that electricity changes on a millisecond timescale in the brain but conscious states seem to change at a much slower rate?

 

3) How can there be an intrinsic relation between neural activity and percepts?

Why is it that a particular pattern of neural activity produces the experience of redness? Most biological explanations are of this kind: I experience redness because when some red object is presented, neurons fire in that specific way. This is the coding perspective. The problem in the coding perspective is of course: who decodes the code? Ultimately, this kind of explanation is strongly dualist: it is implicitly assumed that, at some point, neural activity is transformed into the redness experience by some undetermined process that must be of a very different nature.

I would like to point out that proposals in which perception lies in the interaction between the organism and the environment (e.g. the sensorimotor theory) do not solve this problem either. I can close my eyes and imagine something red. It could be that redness corresponds to a particular way in which visual inputs change when I move my eyes or the surface, which I am anticipating or imagining, but this does not explain what is intrinsically red about the pattern of neural activity now. If we cannot explain it without referring to what happened before, then we are denying that the pattern of neural activity itself determines experience, and again this is a strong dualist view.

An experiment of thought. Consider two salamanders, and each of them has only one neuron, which is both a sensory neuron and motor neuron; say, its firing produces a particular movement. The salamanders are very similar, but their visual receptors are tuned to different wavelengths. In the first salamander, the neuron reacts to red stimuli; in the second salamander, the neuron reacts to blue stimuli. What might happen in terms of visual experience when the neuron fires? Does the first salamander see red and the other see blue? If we think that neural activity alone determines experience, then in fact the two salamanders should experience exactly the same thing – and this is also independent of the sensorimotor contingencies in this case.

 

4) What is the relationship between the structure of experience and the structure of neural activity?

Subjective experience is highly structured. There might be some dispute about how rich it actually is, but it is at least as rich as what you can describe with words. A striking fact about language is that the meaning of sentences is not only implied by the words but also by the relations between them, i.e., the syntax. For example, a visual scene is composed of objects with spatial relations between them, and with attributes (a red car in front of a small house). In fact, there must be more to it than syntax, there must also be semantics: if neural activity completely determines subjective experience, it must not only specify that there is a car, but also what a car is. A useful notion in psychology of perception is the concept of “affordance” introduced by James Gibson: the affordance of an object is what it allows you to do (e.g. a car affords driving). Affordances are potentialities of interaction, and they gives some meaning (rather than labels) to perceptual objects. This brings an inferential structure to experience (if I did that, this would happen).

This stands in sharp contrast with the central perceptual concept in neuroscience, the notion that “cell assemblies” represent particular percepts. A cell assembly is simply a set of neurons, and their co-activation represents a particular percept (say, a particular face). Let us say that one neuron represents “red”, another represents “car”, then the assembly of the two neurons represents the red car. The problem with this concept is that it is very poorly structured. It cannot represent relations between objects, for example. This type of representation is known as the “bag-of-words” model in language processing: a text is represented by its set of words, without any syntactic relationship; clearly, the meaning of the text is quite degraded. The concept of cell assembly is simply too unstructured to represent experience.

If we are looking for a mapping between neural activity and percepts, then 1) we must find a way to define some structure on neural activity, and 2) the mapping must preserve that structure (in mathematical terms, we are looking for a morphism, not a simple mapping).

I can summarize this discussion by pointing out that to make progress on the mind-body problem, there are two crucial steps: 1) to understand the articulation between physical time and the time of consciousness, 2) to understand the articulation between the structure of neural activity and the structure of phenomenal experience.

Notes on consciousness. (IV) The phenomenal content of neural activity

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This post is about the mind-body problem. Specifically, what is the relationship between the activity of the brain and the phenomenal content of conscious experience? It is generally thought that experience is somehow produced by the electrical activity of neurons. The caricatural example of this idea is the concept of the “grandmother cell”: a neuron lights up when you think of your grandmother, or conversely the activation of that neuron triggers the experience of, say, the vision of your grandmother's face. The less caricatural version is the concept of cell assemblies, where the single cell is replaced by a set of neurons. There are variations around this theme, but basically, the idea is that subjective experience is produced by the electrical activity of neurons. There actually is some experimental evidence for this idea, coming from the electrical stimulation of the brain of epileptic patients (read any book by Oliver Sacks). Electrical stimulation is used to locate the epileptic focus in those patients, and depending on where the electrode is in the brain, electrical stimulation can trigger various types of subjective experiences. Epileptic seizures themselves can produce such experiences, for example auditory experiences of hearing specific musics. Migraines can also trigger perceptual experiences (called “aura”), in particular visual hallucinations. So there is some support for the idea of a causal relationship between neural activity and subjective experience.

The obvious question, of course, is: why? At this moment, I have no idea why neural activity should produce any conscious experience at all. We do not believe that the activity of the stomach causes any subjective experience for the stomach, or the activity of any set of cells, including cardiac cells, which also have an electrical activity (but of course, maybe we are wrong to hold this belief).

I propose to start with a slighly more specific question: why does neural activity cause subjective experience of a particular quality? Any conscious experience is an experience of something (a property called intentionality in philosophy), for example the vision of your grandmother's face. Why is it that a particular spatio-temporal pattern of activity in a neural network produces, for that neural network, the experience of seeing a face? One type of answer is to say that this particular pattern has been associated with the actual visual stimulus of the face, ie, it “encodes” the face, and so the meaning of those neurons lighting up is the presence of that visual stimulus. This is essentially the “neural coding” perspective. But there is a big logical problem here. What if the visual stimulus is not present, but the neurons that “encode” the face light up either naturally (memory, dream) or by electrode stimulation? Why would that produce a visual experience rather than anything else? If experience is produced by neural activity alone, then it should not matter what external stimulus might cause those neurons to fire, or what happened in the past to those neurons, or even what world the neurons live in, but only which neurons fire now. Which neurons fire now should entirely determine, by itself, the content of subjective experience. Again the problem with the neural coding perspective is that it is essentially dualist: at some stage, there is some other undefined process that “reads the code” and produces subjective experience. The problem we face here is that the firing of neurons itself must intrinsically specify the experience of seeing a face, independent of the existence of an outside world.

I will try to be more specific, with a very simple example. Imagine there is just one neuron, and two stimuli in the world, A and B. Now suppose, by conditioning or even simply by anatomical assumption, that stimulus A makes the neuron fire. A neural coder would say: this neuron codes for stimulus A, and therefore this neuron's firing causes the experience of A. But you could also assume a different situation, maybe a different organism or the same organism conditioned in a different way, where stimulus B, and not A, makes the neuron fire. If neural activity is what causes subjective experience, then this neuron's firing should produce exactly the same experience in both cases, even though different stimuli cause them to fire. This example can be vastly generalized, and the implication is that any two patterns of neural activity that are identical up to a permutation of neurons should produce the same subjective experience for that set of neurons.

As if all this were not puzzling enough, I will now end on a disturbing experiment of thought. Imagine we measure the entire pattern of neural activity of someone experiencing the vision of his grandmother. Then we build a set of blinking red lights, one for each neuron, programmed so as to light up at the same time as the neurons did. The red lights don't even need to be connected to each other. The electrical activity of this set of lights is thus the same as the activity of the neural network. Therefore, by the postulate that electrical activity is what causes subjective experience, the set of lights should experience the sight of the grandmother, with the impression of being the grandson. Would it?