# Contextual Deconvolution for Variance-Stable Demand Sensing: Kernel-Modulated Operators in Promotional Retail

arXiv: https://arxiv.org/abs/2607.25664 · HTML: https://mlsanity.com/paper/2607.25664/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 40 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Builds on (most cited first, 12 of 12)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Transformers in Time Series: A Survey](https://mlsanity.com/paper/2202.07125/) (2022)
- [TimeMixer: Decomposable Multiscale Mixing for Time Series Forecasting](https://mlsanity.com/paper/2405.14616/) (2024)
- [N-HiTS: Neural Hierarchical Interpolation for Time Series Forecasting](https://mlsanity.com/paper/2201.12886/) (2022)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [Adaptive piecewise polynomial estimation via trend filtering](https://mlsanity.com/paper/1304.2986/) (2013)
- [Applying Deep Learning to the Newsvendor Problem](https://mlsanity.com/paper/1607.02177/) (2016)
- [Orbit: Probabilistic Forecast with Exponential Smoothing](https://mlsanity.com/paper/2004.08492/) (2020)

## Abstract (arXiv)

Machine learning demand forecasts optimize statistical accuracy yet leave excess operational volatility that inflates safety stock and amplifies the Bullwhip effect. We introduce Contextual Deconvolution (CD), a two-stage estimator that reframes demand sensing as a convex decomposition: a kernel-modulated banded operator separates transient promotion-driven shocks from a smooth structural baseline, and hierarchical partial pooling enables catalog-scale deployment without per-SKU training. The operator is data-derived, not imposed---it reduces to the identity wherever the promotional response is impulsive (most of M5, all of Favorita) and contributes only where genuine multi-day carryover exists, so the gains rest on the structural decomposition itself. Evaluating strictly out-of-sample on 30,490 M5 SKUs and 2,845 Favorita items, with calendar-aware baselines given CD's identical future calendar, we anchor the contribution on a full inventory-cost accounting: CD lowers safety stock, holding cost, and order variance but under-provisions event spikes, reducing total cost only when holding costs exceed ~20% of stockout costs (95% CI [17%,25%]); otherwise it is an operational-stability and inventory-capital layer, not an expected-cost minimizer. Its accuracy contribution is reliability rather than central tendency: across eleven baselines, CD attains the lowest cross-sectional dispersion of per-SKU error and mis-forecasts by more than 200% on 0.8% of SKUs versus 9.9--20.6% for every baseline, ranking first on both in all four M5 draws. Because the Variance Ratio and std-based safety stock are minimized by any sufficiently smooth forecast, we treat them as diagnostics, not objectives. A supporting analysis shows the learned demand operators are non-normal, yet CD's compact parametric kernel matches their operational performance interpretably.