# PPDL: A Real-world Industrial User Retention Ratio Forecasting Framework Integrating Physical Priors with Deep Learning

arXiv: https://arxiv.org/abs/2609.13789 · HTML: https://mlsanity.com/paper/2609.13789/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 12 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [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)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecasting](https://mlsanity.com/paper/2402.05956/) (2024)
- [Reinforcing User Retention in a Billion Scale Short Video Recommender System](https://mlsanity.com/paper/2302.01724/) (2023)
- [Stratified Expert Cloning for Retention-Aware Recommendation at Scale](https://mlsanity.com/paper/2504.05628/) (2025)

## Abstract (arXiv)

In multi-channel paid user acquisition, early and accurate prediction of user retention at the channel level is crucial for optimizing budget allocation. User retention curves display a pronounced temporal pattern: an initial period of high churn transitions into long-term stability. This pattern is further characterized by regular fluctuations attributable to seasonality and exhibits high serial autocorrelation. These intrinsic properties make such curves highly suitable for analysis within a time-series forecasting framework. However, forecasting user retention ratio for large-scale short-video platform faces three major challenges: significant heterogeneity across channels, pronounced global trend of decay followed by saturation, and short look-back windows. To address these challenges, we propose PPDL, a novel forecasting framework that integrates physical priors with deep learning. We first introduce a trend-residual decomposition component. The trend is modeled using the Weibull distribution, whose parameters are learned via a Multilayer Perceptron (MLP). Secondly, for the residual component, we design an auxiliary embedding module on top of a deep learning backbone to maintain the channel identity awareness. Finally, to enhance the model's sensitivity to trends, we design a Multiscale Trend-penalized loss function. The proposed approach PPDL is validated through comprehensive experiments on industrial-scale datasets, covering three applications with an average of 30+ channels each. Experimental results show that PPDL achieves improvements across different backbones and significantly outperforms existing online solutions.