TTF: A Trapezoidal Temporal Fusion Framework for LTV Forecasting in Douyin

AI summary

Overview

Research area: Machine learning for time series forecasting, applied to channel-level user lifetime value (LTV) prediction in an industrial user-growth (paid user acquisition) setting at Douyin.

Technical level: Intermediate. The individual building blocks (moving averages, MLP backbones, RevIN-style scaling, positional encoding) are accessible, but the paper assumes familiarity with time series forecasting terminology, multi-variate forecasting benchmarks, and evaluation metrics such as MAPE.

Scope: The paper proposes the Trapezoidal Temporal Fusion (TTF) framework — a data-construction module, a multi-tower network (MT-FusionNet), and a training loss — for forecasting channel-level LTV curves from only 30 observed retention days, and reports its offline benchmarks and three months of online deployment results at Douyin.

What This Paper Is About

Internet companies spend heavily on paid acquisition channels, and sustainable growth requires the LTV generated by acquired users to exceed customer acquisition cost (CAC). Because CAC per channel is planned in advance while LTV is uncertain at acquisition time, the company needs an early, accurate forecast of each channel's LTV in order to allocate budget across channels and maximize the LTV/CAC ratio. This paper frames that forecast as a new kind of forecasting problem — many unaligned channel LTV series, each with a short observed input and a very long required output — and builds a framework to solve it.

Key Contributions

1. Trapezoidal multi-time series module. A new data structure/construction method for unaligned multi-time series. It concatenates several LTV series from the same channel with different activation dates into a two-dimensional window, so that longer-history series supplement the short input of the most recent series.
2. MT-FusionNet. A multi-tower structure that applies moving averages at multiple scales and passes each smoothed version (plus the original) through independently parameterized backbones, then fuses the tower outputs with a feed-forward network, aiming to make the model robust to heterogeneous and volatile data.
3. Utilitarian loss. A training loss compatible with the trapezoidal module that computes error only on the last series in the window — the series whose prediction is actually the objective — instead of averaging over all series, resolving an inconsistency between optimization and the real goal.
4. Production deployment and evaluation. The framework is deployed in Douyin's online system and provides channel-level LTV predictions to marketing strategists and budget planners; both offline experiments and online results are reported.

Main Findings

• MT-FusionNet improves every backbone tested. On the LTV_360 prediction task, adding MT-FusionNet reduced error for all three MLP-based backbones: TSMixer from 14.2% to 13.5% MAPE_p and from 9.8% to 9.2% MAPE_a; TiDE from 18.2% to 15.6% MAPE_p and from 13.3% to 10.8% MAPE_a; DLinear from 29.8% to 24.1% MAPE_p and from 22.6% to 20.6% MAPE_a.
• Best configuration beats the deployed statistical baseline. TSMixer with MT-FusionNet achieved the lowest MAPE_p (13.5%) and MAPE_a (9.2%) among all evaluated models, outperforming the statistical model (MAPE_p 16.1%, MAPE_a 11.1%), which is a rules-and-expert-knowledge framework that had been in production for many years.
• Trapezoidal input beats single-series input, but more series is not always better. Single-series input scored MAPE_p 15.7% / MAPE_a 12.3%; trapezoidal input with k = 180 series per window scored 13.5% / 9.2%; increasing to k = 360 degraded performance to 15.6% / 11.9%, which the authors attribute to possible overfitting or increased model complexity without proportional information gain.
• A moderate, mixed set of moving-average scales works best. The configuration w = [1, 3, 7, 14] gave the lowest MAPE_p (13.5%) and MAPE_a (9.2%). Relative to w = [1] (14.2% / 9.8%), this is a 4.9% relative improvement in MAPE_p and a 6.1% improvement in MAPE_a. Simply adding more towers did not consistently help — for example, w = [1, 3, 5, 7, 9, 11, 13, 15] scored 13.8% / 9.3% and w = [1, 7, 14, 21] scored 14.3% / 9.9%.
• Utilitarian loss provides a small but consistent gain. It scored 13.5% MAPE_p and 9.2% MAPE_a versus MSE loss at 13.8% and 9.4%, i.e. a 0.3% improvement in MAPE_p and 0.2% in MAPE_a.
• Positional encoding mostly affects the aggregate metric. With positional encoding, MAPE_p was unchanged at 13.5% while MAPE_a improved slightly from 9.2% to 9.1% (a 0.1% improvement).
• Qualitative curve behavior. In the prediction plots, MT-FusionNet variants aligned more closely with ground truth than their original versions, which showed a systematic positive bias and larger phase lag around local extrema; the design reduced bias, tracked short-term fluctuations better, and preserved the long-term trend. The largest qualitative gains appeared on DLinear, whose vanilla predictions were described as rigid and biased upward, failing to capture the gradual downward drift after 200 days.
• Online results. After three months of online deployment, compared to the previously deployed online model, MAPE_p decreased by 4.3% and MAPE_a decreased by 3.2%.

Methodology in Plain English

The problem setup. Each channel has many LTV series, one per activation date (the date new users were acquired). A series is the average LTV of that group on each retention day (Day 0 is the activation date). Because groups were acquired on different dates, their series start at different times and have different lengths — the "unaligned multi-time series" challenge. In the experiments, the model sees LTV over the first 30 retention days and must predict retention days 30 to 360, i.e. a 30-step input against a 330-step output, which the authors call the short-input long-output (SILO) problem. They also note real LTV series are volatile and non-stationary, with frequent fluctuations and higher variance than typical time series datasets.

Solving the short input with a "trapezoid." Instead of feeding one series, the trapezoidal module stacks k series from the same channel, ordered by activation date, into an l × k matrix. The most recent series has the shortest valid information length m; earlier series have longer valid history. Rows before a series' activation date are filled with zeros, and the series are aligned by actual calendar date. The stride s is the number of days between adjacent activation dates, and the info length of the j-th series is m + s × (k − j), with input length l = m + s × (k − 1). Because all series come from the same channel, the cross-series correlation is genuine — the authors contrast this with the weak cross-variate correlation that has made multivariate models underperform simple univariate baselines on common benchmarks.

Robust scaling. The input is normalized with a symmetric "normalization–denormalization" structure like RevIN, but using the median instead of the mean and the interquartile range (75th minus 25th percentile) instead of the standard deviation, so that outliers and spikes in the LTV curve do not distort the scaling.

Multi-scale towers. The normalized window is passed through moving averages at several scales using symmetric replicate padding to preserve length; the original data plus each smoothed version go to separate backbones with the same hyperparameters but non-shared, independently updated parameters (so d scales give d + 1 towers). Small windows (e.g. size 3) keep high-frequency detail while large windows (e.g. size 21) expose long-term trend. The tower outputs are concatenated along the time dimension, given sinusoidal positional encoding, and compressed back to the target horizon by a small feed-forward network (linear → activation/dropout → linear), followed by inverse robust scaling.

Covariates. Static covariates mark each window's channel; dynamic covariates include intrinsic time features (day/week/month/year) and one-hot holiday labels, since real LTV curves show prominent peaks or troughs on special dates.

Training loss. Ordinary MSE averages error over all series in the window, but the series have different info lengths, so the model tends to learn the longer-history series better than the one that matters. The utilitarian loss computes MSE only on the last series in the window — the most recently activated channel series — aligning optimization with the actual prediction target.

Evaluation. Experiments ran on Merlin, ByteDance's internal machine learning platform, using 60 selected acquisition channels (chosen in descending order of acquired-user count) covering 2021.1.1 to 2023.4.1 for training and 2023.4.1 to 2024.4.1 for testing, with results evaluated over 365 activation days. Two user-count-weighted metrics are used: MAPE_p, the point-wise MAPE of the LTV curve, and MAPE_a, the MAPE of the aggregated LTV_N (with N = 360).

Deployment. The system has three subsystems — offline data processing and model training, online serving, and a third-party system integrating repositories — and a four-step workflow: data preprocessing and dataset publication (on Dorado, ByteDance's big-data platform), data loading/training/evaluation (datasets in the Data Set Hub, models registered in the Model Hub), model loading and online inference, and persistence of predictions with version identifiers for auditing and rollback. Models are retrained weekly, with extra retraining triggered when monitoring detects performance drift (for example, a 2% increase in MAPE over a 7-day window), plus alerting and a rollback mechanism.

Why This Matters

Impact on research. The authors state this is the first work to discuss unaligned multi-time series forecasting, and that existing models cannot handle such scenarios. The paper also argues that the inherent similarity of same-channel data sidesteps the weak cross-variate correlation problem that has limited multivariate forecasting models — a useful reframing for anyone working on grouped or staggered-origin series.

Real-world applications:

• Marketing budget allocation. Channel-level LTV forecasts combined with planned CAC per channel let marketers compute LTV/CAC ratios and reallocate spend toward channels that are expected to pay back.
• Paid acquisition planning. Because predictions are available early (from 30 days of retention data), acquisition decisions can be adjusted long before a year of retention data exists.
• Financial and business forecasting with staggered cohorts. Loan books, subscription cohorts, insurance policies, and any business where customers arrive on different dates but performance must be projected far forward face the same unaligned-series and short-input/long-output structure.
• Production forecasting systems. The deployment description — versioned datasets and models, weekly retraining, drift-triggered retraining, alerting, audit logging, rollback — is a concrete template for operating forecasting models in a business-critical pipeline.

Industry relevance. The work originates from and is deployed in Douyin's user growth business, and the reported online gains (MAPE_p down 4.3%, MAPE_a down 3.2% versus the previously deployed model) are measured over three months of production service, so the claims are tied to a live system rather than only offline benchmarks. The auxiliary contributions — the utilitarian loss and the trapezoidal input construction — are described as generalizable: the MT-FusionNet improved TSMixer, TiDE, and DLinear alike.

Future Directions

• Choosing the window size k automatically. The paper shows k = 180 outperformed both the single-series input and k = 360, attributing the degradation to overfitting or added complexity, but does not provide a rule for selecting the optimum; a principled or adaptive selection method is an obvious next step.
• Adapting the framework to other backbones and domains. The authors state the multi-tower structure is effective with other MLP-based models and suggest the framework may apply to other domains facing unaligned multi-time series forecasting, but they only test three MLP-based backbones here.
• Handling other kinds of non-stationarity. Robust scaling (median/IQR) and multi-scale smoothing address outliers and volatility, but the paper does not report experiments on regime changes or structural breaks in the LTV series beyond the holiday covariates.
• Extending beyond channel-level aggregation. The paper deliberately avoids user-level prediction because newly acquired users have sparse behavioral data; whether the trapezoidal structure could be combined with user-level signals as more data accumulates is left open.

Target Audience

Applied machine learning engineers and time series researchers working on industrial forecasting, especially those dealing with staggered or unaligned series, very long output horizons relative to input length, and high-volatility business metrics. It is also directly relevant to growth, marketing analytics, and MLOps practitioners who need channel-level LTV or CAC-based budget allocation models and want a description of how such a model is trained, deployed, monitored, and rolled back in production. Readers seeking theoretical analysis of forecasting models will find little here — the evidence is empirical and deployment-driven.

Authors’ abstract

In the user growth scenario, Internet companies invest heavily in paid acquisition channels to acquire new users. But sustainable growth depends on acquired users' generating lifetime value (LTV) exceeding customer acquisition cost (CAC). In order to maximize LTV/CAC ratio, it is crucial to predict channel-level LTV in an early stage for further optimization of budget allocation. The LTV forecasting problem is significantly different from traditional time series forecasting problems, and there are three main challenges. Firstly, it is an unaligned multi-time series forecasting problem that each channel has a number of LTV series of different activation dates. Secondly, to predict in the early stage, it faces the imbalanced short-input long-output (SILO) challenge. Moreover, compared with the commonly used time series datasets, the real LTV series are volatile and non-stationary, with more frequent fluctuations and higher variance. In this work, we propose a novel framework called Trapezoidal Temporal Fusion (TTF) to address the above challenges. We introduce a trapezoidal multi-time series module to deal with data unalignment and SILO challenges, and output accurate predictions with a multi-tower structure called MT-FusionNet. The framework has been deployed to the online system for Douyin. Compared to the previously deployed online model, MAPEp decreased by 4.3%, and MAPEa decreased by 3.2%, where MAPEp denotes the point-wise MAPE of the LTV curve and MAPEa denotes the MAPE of the aggregated LTV.