The Non‐Redundant Contributions of Marr's Three Levels of Analysis for Explaining Information‐Processing Mechanisms

Abstract

Are all three of Marr's levels needed? Should they be kept distinct? We argue for the distinct contributions and methodologies of each level of analysis. It is important to maintain them because they provide three different perspectives required to understand mechanisms, especially information processing mechanisms. The computational perspective provides understanding of how a mechanism functions in broader environments that determine the computations it needs to perform (and may fail to perform). The representation and algorithmic perspective offer an understanding of how information about the environment is encoded within the mechanism and what are the patterns of organization that enable the parts of the mechanism to produce the phenomenon. The implementation perspective yields an understanding of the neural details of the mechanism and how they constrain function and algorithms. Once we adequately characterize the distinct role of each level of analysis, it is fairly straightforward to see how they relate. 1. Introduction The term level is used in a wide variety of ways. One use refers to levels of organization-a whole system is at a higher level than the parts that constitutes it and the activities the whole performs are at a higher level than those of its components (Craver & Bechtel, 2007). This is not the use Marr (1982) had in mind in distinguishing the computational, representational and algorithmic, and implementational levels. These are levels of analysis, not levels of organization and so, contrary to French et al. (this issue), Marr is not addressing topics such as the emergence of higher levels. The main question raised by the various papers in this issue is whether all three types of analysis are required and, if so, how they relate. The question of how they relate, we will argue, is fairly straightforward once we (1) characterize the distinctive role of each type of analysis and (2) show how each type of analysis makes an important, non-­-redundant contribution to understanding information processing mechanisms. As the explanatory relevance of the implementational level is generally not contested, we will not dwell on it. Within the context of a mechanistic framework of explanation, it specifies the parts (e.g., neurons) and operations (excitation or inhibition of other neurons) that are employed or recruited in the generation of the phenomenon of interest. Challenges to Marr's conception of levels focus on the representational and algorithmic and the computational levels of analysis. The idea of algorithms governing the transformations of representations is familiar from computer science but, as we will see, is not limited to the sorts of representations and algorithms used in digital computers. Rather, it allows for the

On computational explanations

“…According to Marr, the explanation is founded on (sometimes implicit) geometrical assumptions that reveal why a particular type of algorithm is appropriate for the job of computing depth from disparity in a 3D world populated by surface-bounded mid-size objects (Marr 1982; for a philosophical analysis in terms of why-questions, see Shagrir 2010a; Bechtel and Shagrir 2015). Marr describes in detail how spatial localization (each point stimulus in the physical world has a unique spatial location) and cohesiveness (surfaces are coherent) in the stimulus geometry explain why stereo algorithms that respect uniqueness (each point is matched to a unique point across retinae) and continuity (for most points, disparity should change only a little between adjacent points) work.…”

“…(2) If they are, then what kinds of explanations do they provide (Egan 1995;Shapiro 1997;Piccinini 2006b;Shagrir 2010a;Milkowski 2013;Bechtel and Shagrir 2015), and (3) in what sense do they involve a "special", "independent" or "autonomous" levels of explanation (Piccinini 2006b(Piccinini , 2011Kaplan 2011;Shagrir 2010a)?…”

“…For instance, there are debates on the question how the different levels are related to each other (Bechtel and Shagrir 2015;Milkowski 2013;Eliasmith and Kolbeck 2015;Love 2015), whether-and in what ways-the Marrian levels are independent or interrelated (Piccinini 2006a;Shagrir 2010a;Kaplan 2011;Bechtel and Shagrir 2015;Eliasmith and Kolbeck 2015), and how the bridges between different levels should be described (Love 2015). Moreover, there is an ongoing debate on the question of to what extent Marr's account provides a unificatory account (Eliasmith and Kolbeck 2015), and in what ways the tri-partite scheme fits with actual practices in cognitive and computational neuroscience (Shagrir 2010a;Piccinini 2011;Kaplan 2011;Warren 2012;Love 2015).…”

Sculpting Computational‐Level Models

“…According to Marr (), this hypothesis should be specified by a mathematical function f : I f → O f that specifies for each input i ∈ I f its corresponding output o ∈ O f . In addition to being a hypothesis about what cognitive capacities people have, a computational‐level explanation in a strict framework is a well‐characterized target explanandum (Bechtel & Shagrir, ; Cummins, ). It can be explained by an algorithm A : I A → O A (and subsequently an implementation) that implements the function, that is, I f = I A and .…”

The rise of cognitive science in the 20th century

“…Marr (1982: 24) proposed that explaining any information-processing system required answering three different sorts of questions about it. These could be described and conceptualized in terms of three explanatory levels or analyses (Bechtel and Shagrir 2015;Shagrir 2010). The computational level involved explaining the why or goal of a particular kind of processing: What is the problem that the system need to solve?…”