Marr’s three levels of inquiry

Assignment

Levels of inquiry in computational neuroscience

In order to understand a device that performs an information-processing task, one needs to employ a hierarchy of explanations.  In other words,

… computational neuroscience also involves [three different] levels of analysis. First, there is the level of what a neural subsystem does and why. Does it see or does it hear? Does it control the arm or the head? And what function does it compute in order to perform this function? Answering these what and why questions leads to what Marr called a ‘computational theory’ of the system. The theory specifies the function computed and why it is computed, without saying what representations and procedures are used in computing it. Specifying the representations and procedures is the job of the ‘algorithmic theory’. Finally, an ‘implementation theory’ specifies the mechanisms by which the representations and algorithms are implemented. [Piccinini and Shagrir 2014]

 

In brief, Marr’s Three Levels of Inquiry are

  • Computational: What computations does the central nervous system perform and why?
  • Algorithmic: What representations and procedures are used in the neural computation?
  • Implementation: What the physiological mechanisms that bring about these representations and carry out these algorithms?

It seems to me that the “vision” of contemporary neuroscience is to have an “multi-level explanation” of information processing by the nervous system that is “integrated” in the sense that explanations of different mechanistic levels are “linked.”  Consider,

Nervous systems as well as artificial computational systems have many levels of mechanistic organization. They contain large systems like the brain and the cerebellum, which decompose into subsystems like the cortex and the brainstem, which decompose into areas and nuclei, which in turn decompose into maps, columns, networks, circuits, neurons, and subneuronal structures. Computational neuroscience studies neural systems at all of these mechanistic levels, and then it attempts to discover how the properties exhibited by the components of a system at one level, when they are suitably organized into a larger system, give rise to the properties exhibited by that larger system. If this process of linking explanations at different mechanistic levels is carried out, the hoped result is an integrated, multi-level explanation of neural activity. [Piccinini and Shagrir 2014, p. 28.]

But what do “we” mean by the linking of different mechanistic levels of explanation?  Is this linkage a one-way “bottom up” inheritance as in the philosophical position known as reductionism?  Is it possible that the linkage is two-way, “top down” as well as “bottom up”?

Let’s say that in my experience, 90% of physicist believe that the linkage between different mechanistic levels is “bottom up” only, while 90% of psychologists believe the linkage works both ways: “bottom up” and “top down.”   What is the significance of that observation?

Representation versus processing of information

Marr also emphasizes a duality between representation and processing of information

Vision is therefore, first and foremost, an information-processing task, but we cannot think of it just as a process. For if we are capable of knowing what is where in the world, our brains must somehow be capable of representing this information — in all its profusion of color and form, beauty, motion and detail.  The study of vision must therefor include not only the study of how to extract from images the various aspects of the world the are useful to us, but also an inquiry into the nature of the internal representations by which we capture this information and thus make it available as a basis for decisions about our thoughts and actions.  This duality — the representation and the processing of information — lies at the heart of most information-processing tasks and will profoundly shape our investigation of the particular problems posed by vision.

Modern representational theories conceive of the mind as having access to systems of internal representations; mental states are characterized by asserting what the internal representations currently specify, and mental processes by how such internal representations are obtained and how they interact.

Marr’s vision for computational vision

After a historical introduction to various aspects of visual perception (trichromatism of color vision, stereoscopic/binocular vision, parallel channels tuned to different spatial frequencies), Marr explains how the time-dependence of mental ration of 3D images led visual psychologists to seriously consider the idea of visual representations.

But what of explanation?  In the 1920’s electrophysiologists were able to record voltage changes that accompanied transmission of nerve signals.  The character of somatic sensations depended on which peripheral nerve fibers carried the message, as one might have expected from anatomical studies.   When single unit recordings became possible, the notion of somatosensory receptive fields was developed, followed by the concept of visual receptive fields of retinal ganglion cells and visual cortical neurons (center-surround properties, edge detection, parallel on-off channels, and so on).

The observation of feature detectors in the frog and rabbit retina strongly suggested that questions of psychological interest could be illuminated and perhaps even explained by neurophysiological experiments.

A description of that activity of a single nerve cell which is transmitted to and influences other nerve cells and of a nerve cell’s response to such influences from other cells, is a complete enough description for functional understanding of the nervous system. There is nothing else “looking at” or controlling this activity, which must therefore provide a basis for understanding how the brain controls behaviour’ (Barlow, 1972, p. 380).

According to Marr, in the 1950s and 1960s

… the eventual success of a reductionist approach seemed likely.  Hubel and Wiesel’s (1962, 1968) pioneering studies had shown the way; single-unit studies on stereopsis (Barlow, Blakemore, and Pettigrew, 1967) and on color (DeValois, Abramov, and Mead, 1967; Gouras, 1968) seemed to confirm the close links between perception and single-cell recordings, and the intriguing results of Gross, Rocha-Miranda; and Bender (1972), who found “hand-detectors” in the inferotemporal cortex, seemed to show that the application of the reductionist approach would not be limited just to the early parts of the visual pathway. (p. 27)

But these initial coups were not followed by equally dramatic discoveries in the 1970s.

No neurophysiologists had recorded new and clear high-level correlates of perception. The leaders of the 1960s had turned away from what they had been doing—Hubel and Wiesel concentrated on anatomy, Barlow turned to psychophysics, and the mainstream of neurophysiology concentrated on development and plasticity (the concept that neural connections are not fixed) or on a more thorough analysis of the cells that had already been discovered (for example, Bishop, Coombs, and Henry, 1971; Schiller, Finlay, and Volman, 1976a, 1976b), or on cells in species like the owl (for example, Pettigrew and Konishi, 1976). None of the new studies succeeded in elucidating the function of the visual cortex.

As Marr reflected on these events, he decided that neurophysiology and psychophysics “have as their business to describe the behavior of cells or of subjects [by observing the the neural implementation of vision in the cerebral cortex] but not to explain such behavior” (emphasis added).  Explanations of the function of visual cortex would have to be sought at higher levels of inquiry (computational and algorithmic).

The message was plain. There must exist an additional level of understanding at which the character of the information-processing tasks carried out during perception are analyzed and understood in a way that is independent of the particular mechanisms and structures that implement them in our heads. This was what was missing—the analysis of the problem as an information-processing task. Such analysis does not usurp an understanding [at the level of neural implementation] … but it is a necessary complement to them, since without it there can be no real understanding of the function of all those neurons.

Understanding complex information processing systems

Almost never can a complex system of any kind be understood as a simple extrapolation from the properties of its elementary components. … If one hopes to achieve a full understanding of a system as complicated as a nervous system … then one must be prepared to contemplate different kinds of explanation at different levels of description that are linked, at least in principle, into a cohesive whole, even if linking the levels in complete detail is impractical. For the specific case of a system that solves an information-processing problem, there are in addition the twin strands of process and representation….

–David Marr

As originally presented, Marr’s Three Levels of Inquiry for understanding complex information processing systems are

marr3

He uses the example of a cash register to illustrate these different levels of inquiry.  To make sure you understand this approach, make an attempt to apply these levels of inquiry to another example from daily life.

Representation is a choice

A representation is a formal system for making explicit certain entities or types of information, together with a specification of how the system does this.  … However, the notion that one can capture some aspect of reality by making a description of it using a symbol and that to do so can be useful seems to me a fascinating and powerful idea. … But … the choice of which to use is important and cannot be taken lightly. It determines what information is made explicit and hence what is pushed further into the background, and it has a far-reaching effect on the ease and difficulty with which operations may subsequently be carried out on that information.

–David Marr

Questions for Discussion

Writing prompt (200 words):  What are some examples (from daily life) of how a choice of representation can determine what information is made explicit and what information is pushed further into the background?

Writing prompt (200 words): Do you think Hilary Putnam would agree that mental states are characterized by asserting what the internal representations currently specify?

Further reading

Masland, R.H. and Martin, P.R., 2007. The unsolved mystery of vision. Current Biology, 17(15), pp.R577-R582.

Niell, C.M., 2013. Vision: more than expected in the early visual system. Current biology, 23(16), pp.R681-R684.