David Marr (neuroscientist)

Theories of cerebellum, hippocampus, and neocortex

Marr is best known for his work on vision, but before he began work on that topic he published three seminal papers proposing computational theories of the cerebellum (in 1969), neocortex (in 1970), and hippocampus (in 1971). Each of those papers presented important new ideas that continue to influence modern theoretical thinking.

The cerebellum theory^[3] was motivated by two unique features of cerebellar anatomy: (1) the cerebellum contains vast numbers of tiny granule cells, each receiving only a few inputs from "mossy fibers"; (2) Purkinje cells in the cerebellar cortex each receive tens of thousands of inputs from "parallel fibers", but only one input from a single "climbing fiber", which however is extremely strong. Marr proposed that the granule cells encode combinations of mossy fibre inputs, and that the climbing fibres carry a "teaching" signal that instructs their Purkinje cell targets to modify the strength of synaptic connections from parallel fibres. Neither of those ideas is universally accepted, but both form essential elements of viable modern theories .

The theory of neocortex^[4] was primarily motivated by the discoveries of David Hubel and Torsten Wiesel, who found several types of "feature detectors" in the primary visual area of the cortex. Marr proposed, generalising on that observation, that cells in the neocortex are flexible categorizers—that is, they learn the statistical structure of their input patterns and become sensitive to combinations that are frequently repeated.

The theory of hippocampus^[5] (which Marr called "archicortex") was motivated by the discovery by William Scoville and Brenda Milner that destruction of the hippocampus produced amnesia for memories of new or recent events but left intact memories of events that had occurred years earlier. Marr called his theory "simple memory": the basic idea was that the hippocampus could rapidly form memory traces of a simple type by strengthening connections between neurons. Remarkably, Marr's paper only preceded by two years a paper by Tim Bliss and Terje Lømo that provided the first clear report of long-term potentiation in the hippocampus, a type of synaptic plasticity very similar to what Marr hypothesized.^[6] (Marr's paper contains a footnote mentioning a preliminary report of that discovery.^[7]) The details of Marr's theory are no longer of great value because of errors in his understanding of hippocampal anatomy, but the basic concept of the hippocampus as a temporary memory system remains in a number of modern theories.^[8] At the end of his paper Marr promised a follow-up paper on the relations between the hippocampus and neocortex, but no such paper ever appeared.

Levels of analysis

Marr treated vision as an information processing system. He put forth (in concert with Tomaso Poggio) the idea that one must understand information processing systems at three distinct, complementary levels of analysis.^[9] This idea is known in cognitive science as Marr's Tri-Level Hypothesis:^[10]

• computational level: what does the system do (e.g.: what problems does it solve or overcome) and similarly, why does it do these things
• algorithmic/representational level: how does the system do what it does, specifically, what representations does it use and what processes does it employ to build and manipulate the representations
• implementational/physical level: how is the system physically realised (in the case of biological vision, what neural structures and neuronal activities implement the visual system)

After thirty years of the Vision (1982, W. H. Freeman and Company), Tomaso Poggio adds one higher level beyond the computational level, that is the learning.

I am not sure that Marr would agree, but I am tempted to add learning as the very top level of understanding, above the computational level. [...] Only then may we be able to build intelligent machines that could learn to see—and think—without the need to be programmed to do it.

— Tomaso Poggio, Vision (2010, The MIT Press), Afterword, P.367

Stages of vision

Marr described vision as proceeding from a two-dimensional visual array (on the retina) to a three-dimensional description of the world as output. His stages of vision include:

• a primal sketch of the scene, based on feature extraction of fundamental components of the scene, including edges, regions, etc. Note the similarity in concept to a pencil sketch drawn quickly by an artist as an impression.
• a 2.5D sketch of the scene, where textures are acknowledged, etc. Note the similarity in concept to the stage in drawing where an artist highlights or shades areas of a scene, to provide depth.
• a 3D model, where the scene is visualised in a continuous, 3-dimensional map.

2.5D sketch is related to stereopsis, optic flow, and motion parallax. The 2.5D sketch represents that in reality we do not see all of our surroundings but construct the viewer-centered three dimensional view of our environment. 2.5D Sketch is a so-called paraline drawing technique of data visualization and often referred to by its generic term "axonometric" or "isometric" drawing and is often used by modern architects and designers.^[11]