Diagnostics of inter-layer connectivity decay and minimal correction by residual connections in deep sequential networks

Deep sequential network design requires choosing the number and placement of residual connections, while architecture-search methods are resource-intensive and do not localize structural defects. The objective is to diagnose pre-training inter-layer coupling decay and use it for minimal residual-topology correction. The procedure analyzes off-diagonal Hessian blocks and introduces a global collapse index and a maximum local drop. A greedy algorithm places residual connections based on the profile without training or gradient-based architecture search. The method is evaluated on multilayer perceptrons with an artificial bottleneck on CIFAR-10. Sixteen configurations with 8, 12, 16, or 20 blocks and base width 64 or 128 were evaluated with three initializations each (48 runs), along with a 16-block architecture of base width 256, bottleneck width 16, and bottleneck position 8. The Spearman correlation between the maximum local drop and final accuracy is –0.692; the p -value is less than 0.001. After architectural adjustment, no significant association with accuracy is detected. With a fixed one-edge budget, guided placement yields higher accuracy than random placement; the p -value is 0.019 (exploratory analysis). Soft Jaccard coefficients range from 0.9583 to 0.9722. For adjacent target blocks, the 90 % confidence interval for the paired accuracy difference lies within the equivalence bounds; the larger p -value of the two one-sided tests is 0.014. The Hessian profile localizes a coupling drop and guides residual intervention rather than serving as an independent predictor of training quality. Conclusions obtained are limited to networks with an artificial bottleneck.