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The Effective Depth Paradox: Evaluating the Relationship between Architectural Topology and Trainability in Deep CNNs

This paper investigates the relationship between convolutional neural network (CNN) topology and image recognition performance through a comparative study of the VGG, ResNet, and GoogLeNet architectural families. Utilizing a unified experimental framework, the study isolates the impact of depth from confounding implementation variables. A formal distinction is introduced between nominal depth ($D_{\mathrm{nom}}$), representing the physical layer count, and effective depth ($D_{\mathrm{eff}}$), an operational metric quantifying the expected number of sequential transformations. Empirical results demonstrate that architectures utilizing identity shortcuts or branching modules maintain optimization stability by decoupling $D_{\mathrm{eff}}$ from $D_{\mathrm{nom}}$. These findings suggest that effective depth serves as a superior framework for predicting scaling potential and practical trainability, ultimately indicating that architectural topology - rather than sheer layer volume - is the primary determinant of gradient health in deep learning models.

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