Progressive Approximation in Deep Residual Networks: Theory and Validation
The Universal Approximation Theorem (UAT) guarantees universal function approximation but does not explain how residual models distribute approximation across layers. We reframe residual networks as a layer-wise approximation process that builds an approximation trajectory from input to target, and prove the existence of progressive trajectories where error decreases monotonically with depth. It reveals that residual networks can implement structured, step-by-step refinement rather than end-to-end (E2E) black-box mapping. Building on this, we propose Layer-wise Progressive Approximation (LPA), a theoretically grounded training principle that explicitly aligns each layer with its residual ...
| Authors | Wei Wang, Xiao-Yong Wei, Qing Li |
|---|---|
| Primary category | cs.LG |
| Published | 27 April 2026 |
| Last updated at source | 27 April 2026 |
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