Conventional neural networks learn mainly through affine transformations followed by nonlinear activations, while elapsed time is often treated as an auxiliary feature or assumed to be uniformly sampled. This paper introduces Wave Function Backpropagation (WFB), a formulation that parameterizes neural responses with learnable amplitude, wavenumber, angular frequency and phase, and links an observed state to its temporal interval Δt via the phase of a differentiable spatiotemporal wave. Standard WFB gradients are derived and a spatial‑curvature correction based on the Laplacian of the wave response is proposed. WFB is instantiated in a deliberately feed‑forward trajectory predictor to serve as a controlled proof of concept; sequence learning is outside the scope of the evaluation. With motion features, STD‑WFB using real intervals reduces average displacement error (ADE) by 20.4% relative to the original feed‑forward network (FFN). In a position‑only evaluation that removes pre‑computed velocity and acceleration, real‑interval WFB reduces ADE by 10.4% and remains competitive with parameter‑matched ReLU controls, achieving 2.1% lower mean ADE than the matched FFN with explicit Δt. Shuffled‑interval WFB attains the lowest mean ADE, indicating that the wave representation itself is effective, though the gain is not solely attributable to interval alignment. These results establish WFB as a viable structured feed‑forward learning formulation and provide a clear basis for subsequent architectural studies.
Review: By embedding temporal information into wave parameters, WFB offers a physically intuitive yet fully differentiable approach, and the experiments demonstrate its advantage in trajectory prediction, suggesting a promising direction for temporal modeling.