Before I try to answer the questions I asked at the end of the previous post , I will first describe the different types of approaches in computational neuroscience. Note that this does not cover everything in theoretical and quantitative neuroscience (see my first post).

David Marr, a very important figure in computational neuroscience, proposed that cognitive systems can be described at three levels:

1) The computational level: what does the system do? (for example: estimating the sound location of a sound source)

2) The algorithmic/representational level: how does it do it? (for example: by calculating the maximum of cross-correlation between the two monaural signals)

3) The physical level: how is it physically realized? (for example: with axonal delay lines and coincidence detectors)

Theories in computational neuroscience differ by which level is addressed, and by the postulated relationships between the three levels (see also my related post).

David Marr considered that these three levels are independent. Francisco Varela described this view as “computational objectivism”. This means that the goal of the computation is defined in terms that are external to the organism. The two other levels describe how this goal is achieved, but they have no influence on what is achieved. It is implied that evolution shapes levels 2 and 3 by imposing the first level. It is important to realize that theories that follow this approach necessarily start from the highest level (defining the object of information processing), and only then analyze the lower levels. Such approaches can be restricted to the first level, or the first two levels, but they cannot address only the third level, or the second level, because these are defined by the higher levels. It can be described as a “top-down” approach.

The opposite view is that both the algorithmic and computational levels derive from the physical level, i.e., they emerge from the interactions between neurons. Varela described it as “neurophysiological subjectivism”. In this view, one would start by analyzing the third level, and then possibly go up to the higher levels – this is a “bottom-up” approach. This is the logic followed by data-driven approaches that I criticized in my first post. I criticized it because this view fails to acknowledge the fact that living beings are intensely teleonomic, i.e., the physical level serves a project (invariant reproduction, in the words of Jacques Monod). This is not to say that function is not produced by the interaction of neurons – it has to, in a materialistic view. But as a method of scientific inquiry, analyzing the physical level independently of the higher levels, as if it were a non-living object (e.g. a gas), does not seem adequate – at least it seems highly hopeful. As far as I know, this type of approach has produced theories of neural dynamics, rather than theories of neural computation. For example, showing how oscillations or some other large scale aspect of neural networks might emerge from the interaction of neurons. In other words, in Marr’s hierarchy, such studies are restricted to the third level. Therefore, I would categorize them as theoretical neuroscience rather than computational neuroscience.

These two opposite views roughly correspond to externalism and internalism in philosophy of perception. It is important to realize that these are important philosophical distinctions, which have considerable epistemological implications, in particular on what is considered a “realistic” model. Computational objectivists would insist that a biological model must serve a function, otherwise it is simply not about biology. Neurophysiological subjectivists would insist that the models must agree with certain physiological experiments, otherwise they are empirically wrong.

There is another class of approaches in philosophy of perception, which can be seen as intermediate between these two, the embodied approaches. These consider that the computational level cannot be defined independently of the physical level, because the goal of computation can only be defined in terms that are accessible to the organism. In the more external views (Gibson/O’Regan), this means that the computational level actually includes the body, but the neural implementation is seen as independent from the computational level. For example, in Gibson’s ecological approach and in O’Regan’s sensorimotor theory, the organism looks for information about the world implicit in its sensorimotor coupling. This differs quite substantially from computational objectivism in the way the goal of the computation is defined. In computational objectivism, the goal is defined externally. For example: to estimate the angle between a sound source and the head. Sensorimotor theories acknowledge that the notion of “angle” is one of an external observer with some measurement apparatus, it cannot be one of an organism. Instead in sensorimotor approaches, direction is defined subjectively (contrary to computational objectivism), but still in reference to an external world (contrary to neurophysiological subjectivism), as the self-generated movement that would make the sound move to the front (an arbitrary reference point). In the more internal views (e.g. Varela), the notion of computation itself is questioned, as it is considered that the goal is defined by the organism itself. This is Varela’s concept of autopoiesis, according to which a living entity acts so as to maintain its own organization. “Computation” is then a by-product of this process. This last class of approaches is currently less developed in computational neuroscience.

The three types of approaches I have described are mostly between the relationships between the computational and physical levels, and they are tightly linked with different views in philosophy of perception. There is also another divide line between neural computation theories, which has to do with the relationship between the algorithmic and physical levels. This is related to the rate-based vs. spike-based theories of neural computation (see my series of posts on the subject).

In Marr’s view and in general in rate-based views, the algorithmic and physical levels are mostly independent. Because algorithms are generally described in terms of calculus with analog values, spikes are generally seen as implementing analog calculus. In other words, spikes only reflect an underlying analog quantity, the firing rate of a neuron, on which the algorithms are defined. The usual view is that spikes are produced randomly with some probability reflecting the underlying rate (an abstract quantity).

On the contrary, another view holds that algorithms are defined at the level of spikes, not of rates. Such theories include the idea of binding by synchrony (Singer/von der Malsburg), in which neural synchrony is the signature of a coherent object, the related idea of synfire chains (Abeles), and more recently the theories developed by Sophie Denève and by myself (there is also Thorpe’s rank-order coding theory, but it is more on the side of coding than computation). In these former two theories, spiking is seen as a decision. In Denève’s approach, the neuron spikes so as to reduce an error criterion. In my recent paper on computing with synchrony, the neuron spikes when it observes unlikely coincidences, which signals some invariant structure (in the sense of Gibson). In both cases, the algorithm is defined directly at the level of spikes.

In summary: theories of neural computation can be classified according to the implicit relationships between the three levels of analysis described by Marr. It is important to realize that these are not purely scientific differences (by this, I mean not simply about empirical disputes), but really philosophical and/or epistemological differences. In my view this is a big issue for the peer-reviewing system, because it is difficult to have a paper accepted when the reviewers or editors do not share the same epistemological views.