PatchTransferNet: A Mechanism-Driven Demand Forecasting Model

Classical time series forecasting models are mostly designed for slowly varying, smooth, continuous signals (M1). By contrast, retail demand is discrete and nonnegative, often intermittent or sparse. We model retail demand as an observation-driven counting process (M2), and then develop PatchTransferNet (PtNet), which translates the M2 recursion directly through mean-preserving convex decoding and aggregate-consistent supervision. Sparse series put the two targets in conflict. Per-day medians can be all zero under a positive window total, so daily supervision misses the total and aggregate supervision cannot distribute it. An idealized mixed-Poisson window turns this tension into a two-fingerprint rule. Firstly, the zero-mass share gates aggregate supervision on sparse populations, and then the benefit grows with the count autocorrelation $\rho$, the idealization places the crossing at ${\rho }_0=1/(W+1)$ for sales cycle $W$. The rule places the optimum correctly on all three demand datasets. Two of them sit at opposite ends of the $\lambda$ range, and the third splits by the reporting metric, where the daily caliber selects $\lambda =0$ and the official aggregate metric selects $\lambda =0.5$. On FreshRetailNet-50K, PtNet reaches 27.94% WAPE, beats every single-stage forecaster in all five seeds by at least 1.4 pt (worst seed $29.60$ vs. best baseline $31.06$), and shrinks its under-forecast to $-2.2\%$, matching the best two-stage pipeline. On the public M5 benchmark it ties the best published store-item-level score ($0.905$). When transplanted into a linear backbone on ten classical benchmarks, the anchor's gain tracks $R_{last}^2$, so each data type rewards its own inductive bias.