# PRIME: Mitigating Subgroup Optimization Competition in Shared CTR Top Networks with Plug-in Residual Input-Conditioned Mixture of Expert

arXiv: https://arxiv.org/abs/2608.30449 · HTML: https://mlsanity.com/paper/2608.30449/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Expert routing strategies, one of 12 directions in Mixture-of-experts.
- Builds on 30 of its 43 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Placed in

- Mixture-of-experts / [Expert routing strategies](https://mlsanity.com/moe/expert-routing-strategies/)

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models](https://mlsanity.com/paper/2401.06066/) (2024)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [Deep Interest Network for Click-Through Rate Prediction](https://mlsanity.com/paper/1706.06978/) (2017)
- [ST-MoE: Designing Stable and Transferable Sparse Expert Models](https://mlsanity.com/paper/2202.08906/) (2022)
- [Deep & Cross Network for Ad Click Predictions](https://mlsanity.com/paper/1708.05123/) (2017)
- [DCN V2: Improved Deep & Cross Network and Practical Lessons for Web-scale Learning to Rank Systems](https://mlsanity.com/paper/2008.13535/) (2020)
- [xDeepFM: Combining Explicit and Implicit Feature Interactions for Recommender Systems](https://mlsanity.com/paper/1803.05170/) (2018)
- [From Sparse to Soft Mixtures of Experts](https://mlsanity.com/paper/2308.00951/) (2023)
- [Auxiliary-Loss-Free Load Balancing Strategy for Mixture-of-Experts](https://mlsanity.com/paper/2408.15664/) (2024)
- [Neural Factorization Machines for Sparse Predictive Analytics](https://mlsanity.com/paper/1708.05027/) (2017)
- [Attentional Factorization Machines: Learning the Weight of Feature Interactions via Attention Networks](https://mlsanity.com/paper/1708.04617/) (2017)
- [FiBiNET: Combining Feature Importance and Bilinear feature Interaction for Click-Through Rate Prediction](https://mlsanity.com/paper/1905.09433/) (2019)
- [One Model to Serve All: Star Topology Adaptive Recommender for Multi-Domain CTR Prediction](https://mlsanity.com/paper/2101.11427/) (2021)
- [PEPNet: Parameter and Embedding Personalized Network for Infusing with Personalized Prior Information](https://mlsanity.com/paper/2302.01115/) (2023)
- [Field-weighted Factorization Machines for Click-Through Rate Prediction in Display Advertising](https://mlsanity.com/paper/1806.03514/) (2018)
- [BARS: Towards Open Benchmarking for Recommender Systems](https://mlsanity.com/paper/2205.09626/) (2022)
- [ReMoE: Fully Differentiable Mixture-of-Experts with ReLU Routing](https://mlsanity.com/paper/2412.14711/) (2024)
- [Open Benchmarking for Click-Through Rate Prediction](https://mlsanity.com/paper/2009.05794/) (2020)
- [MaskNet: Introducing Feature-Wise Multiplication to CTR Ranking Models by Instance-Guided Mask](https://mlsanity.com/paper/2102.07619/) (2021)
- [FinalMLP: An Enhanced Two-Stream MLP Model for CTR Prediction](https://mlsanity.com/paper/2304.00902/) (2023)
- [Towards Deeper, Lighter and Interpretable Cross Network for CTR Prediction](https://mlsanity.com/paper/2311.04635/) (2023)
- [APG: Adaptive Parameter Generation Network for Click-Through Rate Prediction](https://mlsanity.com/paper/2203.16218/) (2022)
- [Coupling Experts and Routers in Mixture-of-Experts via an Auxiliary Loss](https://mlsanity.com/paper/2512.23447/) (2025)
- [Hierarchical LoRA MoE for Efficient CTR Model Scaling](https://mlsanity.com/paper/2510.10432/) (2025)
- [Routing Manifold Alignment Improves Generalization of Mixture-of-Experts LLMs](https://mlsanity.com/paper/2511.07419/) (2025)
- [MoE-MLoRA for Multi-Domain CTR Prediction: Efficient Adaptation with Expert Specialization](https://mlsanity.com/paper/2506.07563/) (2025)

## Abstract (arXiv)

Click-through rate (CTR) models vary in feature-interaction design, yet their top networks usually remain a single multilayer perceptron shared by all examples. Heterogeneous user, item, and context subgroups therefore update the same parameters; weakly aligned learning signals make the aggregate gradient a compromise among competing directions. We study the competition on Avazu with 4 models and 4 semantic fields. Across all architectures, semantic subgroups show lower Top-NN gradient cosine similarity than random groups matched by sample size and label ratio, with reductions of 0.23-0.37. This competition motivates input-conditioned experts, but directly replacing an established Dense mapping changes its initial function, sharing pattern, and capacity, obscuring the source of gains. We introduce PRIME (Plug-in Residual Input-conditioned Mixture of Experts), a Dense-anchored mixture of low-rank residual experts. PRIME anchors the original prediction and uses zero-residual initialization to match the Dense baseline exactly at training onset. Input-dependent routing weights low-rank experts for example-specific logit corrections; multi-bag aggregation and EMA load biases stabilize conditional estimation. We evaluate PRIME on held-out Avazu and Criteo test sets across 13 CTR architectures and five paired seeds. Median paired AUC gains are +0.0022 and +0.0066, with LogLoss reductions of 0.0011 and 0.0081, respectively. On FiBiNET and DCNv2, PRIME outperforms APG in all ten seed-level AUC comparisons while using fewer parameters and lower inference latency on both backbones. These results show that function-preserving conditional residuals add input-dependent capacity while preserving the Dense path and its optimization stability. Code is available at https://github.com/YH-learning/PRIME.