Cross-channel temporal fusion for retail customer lifetime value prediction: architecture, ablation, and causal validation of a gated BiGRU fusion network

Introduction Predicting customer lifetime value (CLV) in non-contractual retail settings is complicated by purchase sequence sparsity and heterogeneous engagement across marketing channels. Methods We propose the Cross-Channel Temporal Fusion Network (CCTFN), a dual-branch architecture combining a convolutional-recurrent temporal encoder (Conv1d → 2-layer BiGRU → 4-head attention pooling) with a residual static MLP via a per-household learned sigmoid gate, evaluated through a four-way ablation on 2,581,266 grocery transactions from 2,500 households using a strictly disjoint 547-day calibration/164-day holdout design with GroupKFold cross-validation (K = 5); causal validation employed propensity score matching (PSM) and difference-in-differences (DiD). Results The static branch alone (RMSE = 485.60, Spearman ρ = 0.8060) outperforms the full gated model (ρ = 0.7998) at N = 2,500; gated fusion outperforms concatenation by Δρ = 0.0042 (95% CI [0.0028, 0.0056]; paired t = 8.3, p < 0.01); channel-exposure variables account for only 1.50% of permutation importance yet PSM yields a causal ATT of $193.55 per household (22.8% uplift, 95% CI [$112.51, $276.70]), corroborated by DiD at $100.30. Discussion These results provide a transparent diagnostic of where temporal deep learning adds value relative to static feature engineering, and reveal a systematic asymmetry between the predictive and causal roles of channel-exposure features in retail CLV modeling.