Topology-Dependent Loss Plateau Persistence in Neural Network Training: A Modified Decay Law and Falsifiable Prediction

Neural network training under stochastic gradient descent is expected to exhibit exponential decay of the loss toward a noise-limited minimum. Recent experiments, however, show persistent loss plateaus in architectures with structured connectivity (residual blocks, dense layers, graph motifs) at epochs far exceeding simple noise expectations. We propose a minimal phenomenological recurrence for local gradient coherence on the parameter graph that reproduces standard exponential loss decay in unstructured (fully-connected) networks but predicts delayed convergence and nonzero loss plateaus when repeated local motifs are present in the architecture. The model is parameterized by a single topology-dependent memory strength α(μ) and yields closed-form expressions for the loss L(e) with a calculable plateau height and build-up epoch scale. Matched-pair training runs (identical parameter count, dataset, optimizer, and learning rate, differing only in motif density) provide a direct falsification protocol. If no separation is observed, the model is ruled out; if plateaus emerge as predicted, it offers a new diagnostic for topology-induced memory in neural network optimization dynamics.