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Levels of Analysis

 

      Although the physical reductionism and reconstructionism motivations behind computational cognitive neuroscience may appear sound and straightforward, this approach to understanding human cognition is challenged by the extreme complexity of and lack of knowledge about both the brain and the cognition it produces. As a result, many researchers have appealed to the notion of hierarchical levels of analysis to deal with this complexity. Clearly, some levels of underlying mechanism are more appropriate for explaining human cognition than others. For example, it appears foolhardy to try to explain human cognition directly in terms of atoms and simple molecules, or even proteins and DNA. Thus, we must focus instead on higher level mechanisms. However, exactly which level is the ``right'' level is an important issue that will only be resolved through further scientific investigation. The level presented in this book represents our best guess at this time.

          One approach toward thinking about the issue of levels of analysis was suggested by David Marr Marr82, who introduced the seductive notion of computational, algorithmic, and implementational levels by forging an analogy with the computer. Take the example of a program that sorts a list of numbers. One can specify in very abstract terms that the computation performed by this program is to arrange the numbers such that the smallest one is first in the list, the next largest one is next, and so on. This abstract computational level of analysis is useful for specifying what different programs do, without worrying about exactly how they go about doing it. Think of it as the ``executive summary.''

The algorithmic level then delves into more of the details as to how sorting actually occurs -- there are many different strategies that one could adopt, and they have various tradeoffs in terms of factors such as speed or amount of memory used. Critically, the algorithm provides just enough information to implement the program, but does not specify any details about what language to program it in, what variable names to use, and so on. These details are left for the implementational level -- how the program is actually written and executed on a particular computer using a particular language.

        Marr's levels and corresponding emphasis on the computational and algorithmic levels were born out of the early movements of artificial intelligence, cognitive psychology, and cognitive science, which were based on the idea that one could ignore the underlying biological mechanisms of cognition, focusing instead on identifying important computational or cognitive level properties. Indeed, these traditional approaches were based on the assumption that the brain works like a standard computer, and thus that Marr's computational and algorithmic levels were much more important than the ``mere details'' of the underlying neurobiological implementation.

    The optimality or rational analysis approach, which is widely employed across the ``sciences of complexity'' from biology to psychology and economics [AndersonAnderson1990Anderson90, e.g.,,], shares the Marr-like emphasis on the computational level. Here, one assumes that it is possible to identify the ``optimal'' computation or function performed by a person or animal in a given context, and that whatever the brain is doing, it must somehow be accomplishing this same optimal computation (and can therefore be safely ignored). For example, Anderson90 argues that memory retention curves are optimally tuned to the expected frequency and spacing of retrieval demands for items stored in memory. Under this view, it doesn't really matter how the memory retention mechanisms work, because they are ultimately driven by the optimality criterion of matching expected demands for items, which in turn is assumed to follow general laws.

Although the optimality approach may sound attractive, the definition of optimality all too often ends up being conditioned on a number of assumptions (including those about the nature of the underlying implementation) that have no real independent basis. In short, optimality can rarely be defined in purely ``objective'' terms, and so often what is optimal in a given situation depends on the detailed circumstances.

Thus, the dangerous thing about both Marr's levels and these optimality approaches is that they appear to suggest that the implementational level is largely irrelevant. In most standard computers and languages, this is true, because they are all effectively equivalent at the implementational level, so that the implementational issues don't really affect the algorithmic and computational levels of analysis. Indeed, computer algorithms can be turned into implementations by the completely automatic process of compilation. In contrast, in the brain, the neural implementation is certainly not derived automatically from some higher-level description, and thus it is not obviously true that it can be easily described at these higher levels.

In effect, the higher-level computational analysis has already assumed a general implementational form, without giving proper credit to it for shaping the whole enterprise in the first place. However, with the advent of parallel computers, people are beginning to realize the limitations of computation and algorithms that assume the standard serial computer with address-based memory -- entirely new classes of algorithms and ways of thinking about problems are being developed to take advantage of parallel computation. Given that the brain is clearly a parallel computer, having billions of computing elements (neurons), one must be very careful in importing seductively simple ideas based on standard computers.

    On the other end of the spectrum, various researchers have emphasized the implementational level as primary over the computational and algorithmic. They have argued that cognitive models should be assembled by making extremely detailed replicas of neurons, thus guaranteeing that the resulting model contains all of the important biological mechanisms [BowerBower1992Bower92, e.g.,,]. The risk of this approach is complementary to those that emphasize a purely computational approach: without any clear understanding of which biological properties are functionally important and which are not, one ends up with massive, complicated models that are difficult to understand, and that provide little insight into the critical properties of cognition. Further, these models inevitably fail to represent all of the biological mechanisms in their fullest possible detail, so one can never be quite sure that something important is not missing.

  Instead of arguing for the superiority of one level over the other, we adopt a fully interactive, balanced approach, which emphasizes forming connections between data across all of the relevant levels, and striking a reasonable balance between the desire for a simplified model and the desire to incorporate as much of the known biological mechanisms as possible. There is a place for both bottom-up (i.e., working from biological facts ``up'' to cognition), top-down (i.e., working from cognition ``down'' to biological facts), and, most important, interactive approaches, where one tries to simultaneously take into account constraints at the biological and cognitive levels.

For example, it can be useful to take a set of facts about how neurons behave, encode them in a set of equations in a computer program, and see how the kinds of behaviors that result depend on the properties of these neurons. It can also be useful to think about what cognition should be doing in a particular case (e.g., at the computational level, or on some other principled basis), and then derive an implementation that accomplishes this, and see how well that characterizes what we know about the brain, and how well it does the cognitive job it is supposed to do. This kind of interplay between neurobiological, cognitive and principled (computational and otherwise) considerations is emphasized throughout the text.

  figure478
Figure: The two basic levels of analysis used in this text, with an intermediate level to help forge the links.

        To summarize our approach, and to avoid the unintended associations with Marr's terminology, we adopt the following hierarchy of analytical levels (figure 1.2). At its core, we have essentially a simple bi-level physical reductionist/reconstructionist hierarchy, with a lower level consisting of neurobiological mechanisms, and an upper level consisting of cognitive phenomena. We will reduce cognitive phenomena to the operation of neurobiological mechanisms, and show, through simulations, how these mechanisms produce emergent cognitive phenomena. Of course, our simulations will have to rely on simplified, abstracted renditions of the neurobiological mechanisms.

  To help forge links between these two levels of analysis, we have an auxiliary intermediate level consisting of principles presented throughout the text. We do not think that the brain nor cognition can be fully described by these principles, which is why they play an auxiliary role and are shown off to one side of the figure. However, they serve to highlight and make clear the connection between certain aspects of the biology and certain aspects of cognition. Often, these principles are based on computational-level descriptions of aspects of cognition. But, we want to avoid any implication that these principles provide some privileged level of description (i.e., like Marr's view of the computational level), that tempts us into thinking that data at the two basic empirical levels (cognition and neurobiology) are less relevant. Instead, these principles are fundamentally shaped by, and help to strike a good balance between, the two primary levels of analysis.        The levels of analysis issue is easily confused with different levels of structure within the nervous system, but these two types of levels are not equivalent. The relevant levels of structure range from molecules to individual neurons to small groups or columns of neurons to larger areas or regions of neurons up to the entire brain itself. Although one might be tempted to say that our cognitive phenomena level of analysis should be associated with the highest structural level (the entire brain), and our neurobiological mechanisms level of analysis associated with lower structural levels, this is not really accurate. Indeed, some cognitive phenomena can be traced directly to properties of individual neurons (e.g., that they exhibit a fatiguelike phenomenon if activated too long), whereas other cognitive phenomena only emerge as a result of interactions among a number of different brain areas. Furthermore, as we progress from lower to higher structural levels in successive chapters of this book, we emphasize that specific computational principles and cognitive phenomena can be associated with each of these structural levels. Thus, just as there is no privileged level of analysis, there is no privileged structural level -- all of these levels must be considered in an interactive fashion.  


next up previous contents
Next: Scaling Issues Up: Basic Motivations for Computational Previous: Reconstructionism

Randall C. O'Reilly
Fri Apr 28 14:15:16 MDT 2000