Sculpting Computational‐Level Models

Abstract

In this commentary, I advocate for strict relations between Marr's levels of analysis. Under a strict relationship, each level is exactly implemented by the subordinate level. This yields two benefits. First, it brings consistency for multilevel explanations. Second, similar to how a sculptor chisels away superfluous marble, a modeler can chisel a computational-level model by applying constraints. By sculpting the model, one restricts the (potentially infinitely large) set of possible algorithmic- and implementational-level theories.

On the Relation Between Marr's Levels: A Response to Blokpoel (2017)

“…Our example is somewhat different from the example cited by Blokpoel (). He discusses Bayesian inverse planning (BIP) as an account of how one might infer an agent's goals from its actions (and knowledge of the probabilistic relations between actions and goals).…”

“…In other words, van Rooij's argument is that restricting inputs effectively renders tractable some computational‐level theories that would otherwise be intractable. This is a position that we, and Blokpoel (), endorse. However, restricting inputs typically increases the space of potential algorithms because algorithms that might be unreasonable on the full set of inputs may be reasonable when the set of inputs is restricted.…”

“…Given the above arguments, we propose an alternative account (to that of Blokpoel, ) concerning the relationship between levels. In order to ensure consistency between levels, Blokpoel proposes:for all inputs i within the cognitive capacity's domain, where is a computational‐level theory and is a corresponding algorithmic‐level theory.…”

“…In formal terms, it is of course possible to fold r into the computational level so as to preserve the position of Blokpoel (), viz. :However, this formulation adds unnecessary complication to the computational‐level specification—one must consider resources and their availability as a further input to the computational level.…”

“…A subsidiary argument made by Blokpoel () is that “each computational‐level constraint limits the set of possible algorithms” (p. 8). While this may well be true of some computational‐level constraints, it is not true of all computational‐level constraints.…”