A model's depth can be measured either as computation-graph length or as concept-hierarchy depth

Goodfellow, Bengio & Courville note there are two main ways of measuring the depth of a model. The first counts the number of sequential instructions that must be executed to compute an output — the length of the longest path through the flowchart describing the computation; this depends on which operations count as a single step, so the same function can have different depths in different frameworks. The second measures depth as the depth of the graph of concepts, where later concepts are defined in terms of earlier ones. Because both the choice of elementary operations and the choice of representation differ, there is no single correct value for a model’s depth — it is framework- and viewpoint-dependent.

Examples

Under the computational-graph view, whether a logistic-regression step counts as one operation or several changes the measured depth. Under the concept-graph view, depth counts layers of learned abstraction (edges → parts → objects).

Assessment

Describe the two ways of measuring a model’s depth and give an example showing why the same model can be assigned different depths under each.