# X-VFL: A New Vertical Federated Learning Framework with Cross Completion and Decision Subspace Alignment

arXiv: https://arxiv.org/abs/2508.05568 · HTML: https://mlsanity.com/paper/2508.05568/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 28 references that are in the map.
- First posted on arXiv 7 Aug 2025.

## Builds on (most cited first, 21 of 21)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Ensemble Distillation for Robust Model Fusion in Federated Learning](https://mlsanity.com/paper/2006.07242/) (2020)
- [Age Progression/Regression by Conditional Adversarial Autoencoder](https://mlsanity.com/paper/1702.08423/) (2017)
- [Split learning for health: Distributed deep learning without sharing raw patient data](https://mlsanity.com/paper/1812.00564/) (2018)
- [SplitFed: When Federated Learning Meets Split Learning](https://mlsanity.com/paper/2004.12088/) (2020)
- [SPIDER: Near-Optimal Non-Convex Optimization via Stochastic Path Integrated Differential Estimator](https://mlsanity.com/paper/1807.01695/) (2018)
- [Mini-batch Stochastic Approximation Methods for Nonconvex Stochastic Composite Optimization](https://mlsanity.com/paper/1308.6594/) (2013)
- [PAGE: A Simple and Optimal Probabilistic Gradient Estimator for Nonconvex Optimization](https://mlsanity.com/paper/2008.10898/) (2020)
- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [Personalized Federated Learning with Feature Alignment and Classifier Collaboration](https://mlsanity.com/paper/2306.11867/) (2023)
- [Compressed-VFL: Communication-Efficient Learning with Vertically Partitioned Data](https://mlsanity.com/paper/2206.08330/) (2022)
- [Federated Learning for Healthcare Domain - Pipeline, Applications and Challenges](https://mlsanity.com/paper/2211.07893/) (2022)
- [FedCVT: Semi-supervised Vertical Federated Learning with Cross-view Training](https://mlsanity.com/paper/2008.10838/) (2020)
- [A Unified Analysis of Stochastic Gradient Methods for Nonconvex Federated Optimization](https://mlsanity.com/paper/2006.07013/) (2020)
- [Vertical Federated Knowledge Transfer via Representation Distillation for Healthcare Collaboration Networks](https://mlsanity.com/paper/2302.05675/) (2023)
- [Towards Communication-efficient Vertical Federated Learning Training via Cache-enabled Local Updates](https://mlsanity.com/paper/2207.14628/) (2022)
- [Coresets for Vertical Federated Learning: Regularized Linear Regression and K-Means Clustering](https://mlsanity.com/paper/2210.14664/) (2022)
- [Vertical Semi-Federated Learning for Efficient Online Advertising](https://mlsanity.com/paper/2209.15635/) (2022)
- [Vertical Federated Learning with Missing Features During Training and Inference](https://mlsanity.com/paper/2410.22564/) (2024)
- [VFed-SSD: Towards Practical Vertical Federated Advertising](https://mlsanity.com/paper/2205.15987/) (2022)

## Abstract (arXiv)

Vertical Federated Learning (VFL) enables collaborative learning by integrating disjoint feature subsets from multiple clients/parties. However, VFL typically faces two key challenges: i) the requirement for perfectly aligned data samples across all clients (missing features are not allowed); ii) the requirement for joint collaborative inference/prediction involving all clients (it does not support locally independent inference on a single client). To address these challenges, we propose X-VFL, a new VFL framework designed to deal with the non-aligned data samples with (partially) missing features and to support locally independent inference of new data samples for each client. In particular, we design two novel modules in X-VFL: Cross Completion (XCom) and Decision Subspace Alignment (DS-Align). XCom can complete/reconstruct missing features for non-aligned data samples by leveraging information from other clients. DS-Align aligns local features with completed and global features across all clients within the decision subspace, thus enabling locally independent inference at each client. Moreover, we provide convergence theorems for different algorithms used in training X-VFL, showing an O(1/√T) convergence rate for SGD-type algorithms and an O(1/T) rate for PAGE-type algorithms, where T denotes the number of training update steps. Extensive experiments on real-world datasets demonstrate that X-VFL significantly outperforms existing methods, e.g., achieving a 15% improvement in accuracy on the image CIFAR-10 dataset and a 43% improvement on the medical MIMIC-III dataset. These results validate the practical effectiveness and superiority of X-VFL, particularly in scenarios involving partially missing features and locally independent inference.