AI RESEARCH
Progressive Approximation in Deep Residual Networks: Theory and Validation
arXiv CS.LG
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ArXi:2604.24154v1 Announce Type: new 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.