David Marr and Marr’s Three Levels
by girayhavur
David Courtnay Marr (January 19, 1945 – November 17, 1980) was a British neuroscientist and psychologist. Marr integrated results from psychology, artificial intelligence, andneurophysiology into new models of visual processing. His work was very influential in Computational Neuroscience and led to a resurgence of interest in the discipline.
Born in Woodford, Essex, and educated at Rugby School; he was admitted at Trinity College, Cambridge on 1 October 1963 (having been awarded the Lees Knowles Rugby Exhibition). He was awarded the Coutts Trotter Scholarship in 1966 and obtained his BA in mathematics the same year and got his Ph.D. in physiology under Professor G.S. Brindley in 1972. His interest turned from general brain theory to visual processing. His doctoral dissertation was submitted in 1969 and described his model of the function of the cerebellum based mainly on anatomical and physiological data garnered from a book by J.C. Eccles. A similar model was later independently proposed by James S. Albus. Subsequently he worked at theMassachusetts Institute of Technology, where he took on a faculty appointment in the Department of Psychology in 1977 and was subsequently made a tenured full professor in 1980. Marr proposed that understanding the brain requires an understanding of the problems it faces and the solutions it finds. He emphasized the need to avoid general theoretical debates and instead focus on understanding specific problems.
Marr died of leukemia in Cambridge, Massachusetts. Marr’s findings are collected in the book Vision: A computational investigation into the human representation and processing of visual information (ISBN 0-7167-1567-8), which was published after his death and re-issued in 2010 by The MIT Press (see References). He was married to Lucia M. Vaina of Boston University’s Department of Biomedical Engineering and Neurology. The Marr Prize, one of the most prestigious awards in computer vision, is named in his honor.
David Marr presents his variant on the “three levels” story. His summary of “the three levels at which any machine carrying out an information-processing task must be understood”:
- Computational theory: What is the goal of the computation, why is it appropriate, and what is the logic of the strategy by which it can be carried out?
- Representation and algorithm: How can this computational theory be implemented? In particular, what is the representation for the input and output, and what is the algorithm for the transformation?
- Hardware implementation: How can the representation and algorithm be realized physically? [Marr (1982), p. 25]
Taking seriously the explanatory centrality of explanation in terms of representation and algorithm, we might try to recast what’s importantly correct in Marr’s account in something like the following way: The number of actual algorithmic levels of organization in any given information-processing system (including the brain) is an entirely empirical matter about that particular system. It could of course be zero (as some eliminativists would have us think), but it could also be far more than one (as in the nested virtual machines in a real computer). But for each of those levels of organization or decomposition, there are three perspectives that we can take toward it — or if you prefer, three general kinds of questions that we can pose about it, or three kinds of explanations of it we might try to give: questions about that structure itself; questions about the functional, context-dependent properties of the parts and relations in that structure and their contribution to the functioning of the system as a whole; and questions about the implementation of the primitive parts of that algorithmic structure. Or to put it in a way even closer to Marr’s, we might see the three perspectives of algorithm, content of computation, and implementation as having something like the following questions associated with them:
- Format and algorithm: What is the syntactic structure of the representations at this level, and what algorithms are used to transform them? What is the real structure of the virtual machine? What’s the program? From this perspective, the questions are explicitly information-processing questions. Further, it’s this level of functional decomposition of the system which specifies the level of organization with which we are currently concerned, and to which the other two perspectives are related.
- Content, function, and interpretation: What are the relational or global functional roles of the main processes described at this level? What tasks are being performed by these processes, and why? These are centrally questions about the interpretation and global function of the parts and procedures specified in our algorithmic analysis.
- Implementation: How are the primitives of the current level implemented? By another computationally characterized virtual machine? Directly in the hardware? How much decomposition (in terms of kinds of primitives, structures, abilities, etc.) is there between the current level and what is implementing it? How much of the work is done by the postulated primitives of this level as opposed to being done explicitly by the analyzed processes? The shift from algorithm to implementation is thus centrally one of levels of organization or functional decomposition; i.e. of what happens when we try to move down a level of organization.
CogRobo 