X-VFL: Vertical Federated Learning Framework

• X-VFL is a vertical federated learning framework that addresses non-aligned samples by integrating cross completion to recover missing features.
• The framework replaces concatenation-based fusion with an averaging strategy to align local and collaborative decision spaces, enabling local independent inference.
• Experimental evaluations demonstrate up to 43% accuracy improvements and significantly reduced performance gaps between clients under missing data conditions.

X-VFL is a vertical federated learning framework proposed to relax two assumptions that are standard in canonical VFL: perfectly aligned samples across all parties and mandatory joint inference across all parties. In its most specific current usage, the term refers to the framework introduced in “X-VFL: A New Vertical Federated Learning Framework with Cross Completion and Decision Subspace Alignment,” which targets non-aligned data samples with partially missing features and supports locally independent inference for each client (Yao et al., 7 Aug 2025). More broadly, the surrounding VFL literature uses “X-VFL” only informally, if at all, for extended or cross-silo variants of vertical federated learning, so the 2025 framework gives the term its clearest technical instantiation to date (Li et al., 2023).

1. Terminological scope and problem context

Vertical federated learning (VFL) is the feature-partitioned branch of federated learning: parties share the same sample space, or an aligned intersection of it, but hold disjoint feature spaces, and one active party typically holds labels. Classical VFL therefore depends on entity alignment, commonly through Private Set Intersection, and proceeds by exchanging intermediate representations and their gradients rather than raw features or model updates as in horizontal federated learning (Wei et al., 2022).

Within survey literature, the name “X-VFL” was not originally standardized. One survey describes it informally as an “extension beyond the canonical two-party, single-domain setting,” including multi-party, cross-silo, or cross-domain variants (Li et al., 2023). Other surveys explicitly note that they do not define a framework named X-VFL and instead discuss VFL generically (Yang et al., 2023). The 2025 X-VFL framework is therefore best understood not as a longstanding umbrella term, but as a named architecture that addresses two deployment bottlenecks: partially missing features in non-aligned samples and the inability of standard VFL systems to support single-client inference without collaborative interaction (Yao et al., 7 Aug 2025).

That focus is closely aligned with recent data-oriented analyses of practical VFL. Precise record matching is reported to be rare in potential real-world pairings, while fuzzy and semi-precise regimes are much more common; the same survey also emphasizes that imbalanced feature distributions are prevalent and that some practical scenarios remain under-served by existing algorithms (Wu et al., 12 Feb 2025). X-VFL should therefore be read as a response to the practical misalignment between idealized VFL assumptions and real cross-silo data conditions.

2. Formal setting and architectural design

The X-VFL paper considers $m$ clients $\{C_i\}_{i=1}^m$ and a label holder, or server. Client $i$ stores local features $X_i \in \mathbb{R}^{n_i \times d_i}$, where $d_i$ is the local feature dimension and $n_i$ is the number of local records. In classical VFL, all clients share the same sample index set, so for each sample index $t$, $(x_{1t}, \dots, x_{mt})$ corresponds to the same entity and the server holds its label $y_t$ (Yao et al., 7 Aug 2025).

X-VFL generalizes this to a mixed-alignment setting. For client $i$, the dataset is partitioned as $\{C_i\}_{i=1}^m$0, where $\{C_i\}_{i=1}^m$1 denotes aligned samples and $\{C_i\}_{i=1}^m$2 denotes non-aligned samples. Non-aligned samples may contain partially missing local features. The paper introduces a missing rate $\{C_i\}_{i=1}^m$3 to quantify this partial missingness. In the special case of two clients each holding $\{C_i\}_{i=1}^m$4 features from an original $\{C_i\}_{i=1}^m$5-feature sample, $\{C_i\}_{i=1}^m$6 recovers the fully missing-feature setting (Yao et al., 7 Aug 2025).

The modeling architecture departs from the canonical concatenation-based top model. Each client uses a local bottom model

$\{C_i\}_{i=1}^m$7

which produces a local embedding. The server uses a top model

$\{C_i\}_{i=1}^m$8

Instead of concatenating client embeddings, X-VFL aggregates them by averaging,

$\{C_i\}_{i=1}^m$9

so that each $i$0 has the same dimensionality as $i$1. This design is the key architectural choice that makes local and global prediction spaces compatible and thereby enables locally independent inference at each client (Yao et al., 7 Aug 2025).

This averaging-based fusion differs materially from the standard split-learning formulation typically summarized as $i$2 followed by a host-side fusion model. In conventional VFL, the host receives all client embeddings and computes predictions jointly, while gradients $i$3 are returned to the clients; X-VFL preserves the split-learning interaction pattern but changes the fusion structure and augments it with completion and alignment modules (Wei et al., 2022).

3. Cross Completion and decision-subspace alignment

X-VFL is organized around two modules: Cross Completion (XCom) and Decision Subspace Alignment (DS-Align). XCom addresses missing local features in non-aligned samples, while DS-Align forces local and global decisions to be mutually consistent within the decision subspace, defined as the output space of the top model $i$4 (Yao et al., 7 Aug 2025).

For two clients $i$5 and $i$6, with bottom models $i$7 and $i$8 and embeddings $i$9 and $X_i \in \mathbb{R}^{n_i \times d_i}$0, XCom introduces feature completers $X_i \in \mathbb{R}^{n_i \times d_i}$1 and $X_i \in \mathbb{R}^{n_i \times d_i}$2:

$X_i \in \mathbb{R}^{n_i \times d_i}$3

Completed features are then re-encoded as

$X_i \in \mathbb{R}^{n_i \times d_i}$4

For partially missing features, completion is applied only on missing indices, while observed features are retained (Yao et al., 7 Aug 2025).

The decision loss is defined as

$X_i \in \mathbb{R}^{n_i \times d_i}$5

Term activation depends on the alignment pattern. For aligned samples, all terms are active. For non-aligned samples, only the terms consistent with observed and reconstructed feature availability are used (Yao et al., 7 Aug 2025).

DS-Align adds two consistency objectives. The first aligns decisions from reconstructed and original features:

$X_i \in \mathbb{R}^{n_i \times d_i}$6

The second aligns single-client decisions with the averaged collaborative decision:

$X_i \in \mathbb{R}^{n_i \times d_i}$7

The total objective is

$X_i \in \mathbb{R}^{n_i \times d_i}$8

with $X_i \in \mathbb{R}^{n_i \times d_i}$9 (Yao et al., 7 Aug 2025).

Component	Role	Key relation
XCom	Reconstruct missing local features	$d_i$0
DS-Align1	Match reconstructed and original decisions	$d_i$1
DS-Align2	Match local and averaged decisions	$d_i$2

The multi-client generalization preserves the same logic. For $d_i$3 clients,

$d_i$4

and collaborative prediction uses

$d_i$5

The corresponding multi-client decision and alignment losses extend by summing over clients and over reconstructed/global combinations (Yao et al., 7 Aug 2025).

4. Training procedure, optimization, and inference modes

Training follows a split-learning-style round structure. For each mini-batch, clients compute embeddings $d_i$6 and $d_i$7, perform cross completion to obtain $d_i$8, merge completions with masks, re-encode $d_i$9, and send the necessary embeddings to the server. The server forms the averaged embeddings required by the active loss terms, computes $n_i$0, $n_i$1, and $n_i$2, and backpropagates the total loss. Gradients are returned to the clients to update $n_i$3 and $n_i$4, while the server updates $n_i$5 (Yao et al., 7 Aug 2025).

The paper analyzes two optimizer classes for the nonconvex objective

$n_i$6

Under average smoothness and bounded stochastic-gradient variance,

$n_i$7

$n_i$8

an SGD-type update

$n_i$9

satisfies

$t$0

while a PAGE-type variance-reduced method satisfies

$t$1

The corresponding communication-round complexities are stated as $t$2 for SGD-type methods and $t$3 for PAGE-type methods when targeting $t$4 (Yao et al., 7 Aug 2025).

A central novelty of X-VFL is its support for multiple inference modes. In independent inference without missing features, client $t$5 computes $t$6 and prediction is obtained via $t$7. In collaborative inference, clients send embeddings and the server predicts from the averaged embedding $t$8. For missing-feature cases, XCom reconstructs local missing features and DS-Align is intended to keep the resulting local decision faithful to the collaborative one (Yao et al., 7 Aug 2025).

This design directly contrasts with conventional VFL, where the forward pass is built around host-side fusion of all client embeddings and the backward pass routes $t$9 back to each party. Standard VFL therefore assumes that inference is either collaborative or host-centric; X-VFL changes the representation geometry so that a single local embedding can inhabit the same decision subspace as the collaborative average (Wei et al., 2022).

5. Experimental evaluation and observed behavior

The experimental study covers image datasets—CIFAR-10, TinyImageNet restricted to five classes, and UTKFace—and tabular datasets—MIMIC-III, Bank, and Avazu. Features are vertically partitioned across clients; for images this is done by spatial blocks or channels, and for tabular data by feature columns. The experiments vary aligned overlap ratios of $(x_{1t}, \dots, x_{mt})$0, $(x_{1t}, \dots, x_{mt})$1, and $(x_{1t}, \dots, x_{mt})$2, and missingness rates $(x_{1t}, \dots, x_{mt})$3 (Yao et al., 7 Aug 2025).

Baselines include Vanilla Standalone, Vanilla VFL, IAVFL, and FedCVT. Classification accuracy is the primary metric, evaluated under independent and collaborative inference, under different missingness levels, and under client-data imbalance (Yao et al., 7 Aug 2025).

The reported headline result is that X-VFL significantly outperforms existing methods, including an approximately $(x_{1t}, \dots, x_{mt})$4 improvement in accuracy on CIFAR-10 and an approximately $(x_{1t}, \dots, x_{mt})$5 improvement on MIMIC-III. The robustness claims are similarly explicit. On UTKFace at $(x_{1t}, \dots, x_{mt})$6, baseline independent accuracy drops by approximately $(x_{1t}, \dots, x_{mt})$7 from the no-missing condition, whereas X-VFL shows less than a $(x_{1t}, \dots, x_{mt})$8 drop relative to its own $(x_{1t}, \dots, x_{mt})$9 accuracy. On the same dataset, the gap between independent and collaborative inference is reported as less than $y_t$0 for X-VFL, specifically $y_t$1 versus $y_t$2, while the baselines exhibit more than a $y_t$3 accuracy drop when switching to independent mode (Yao et al., 7 Aug 2025).

The paper also studies imbalanced client data. In a setting where client $y_t$4 holds $y_t$5 of the data and client $y_t$6 holds $y_t$7, baselines show a large performance gap, approximately $y_t$8 on MIMIC-III, between the data-rich and data-poor clients. X-VFL reduces that gap to $y_t$9, and on CIFAR-10 slightly improves the data-poor client’s accuracy, which the paper attributes to XCom leveraging embeddings from the data-rich client. The same qualitative trends persist in four-client experiments (Yao et al., 7 Aug 2025).

Implementation details are also specified. For image tasks, client bottom models are residual networks and the server top model is a 6-layer fully connected neural network. For tabular tasks, both bottom and top models are 3-layer fully connected neural networks. Batch size is $i$0 in the two-client setting and $i$1 in the multi-client setting. Dataset-specific ranges are reported for $i$2 and $i$3, and PAGE-type as well as SGD-type optimizers are used (Yao et al., 7 Aug 2025).

6. Security posture, limitations, and relation to the broader VFL literature

X-VFL does not alter a foundational fact about VFL: communication still occurs through intermediate embeddings and backpropagated gradients rather than raw data. The paper states that XCom requires sharing embeddings $i$4 and optionally $i$5 across clients and server, and that the framework is compatible with secure aggregation of embeddings or gradients, encrypted channels such as TLS, and differential privacy noise on embeddings or gradients. At the same time, it also states that no specific privacy mechanism is implemented (Yao et al., 7 Aug 2025).

That omission is significant in light of the broader VFL security literature. Standard VFL has been shown to face feature leakage from intermediate embeddings, label leakage through host-generated gradients, reconstruction attacks, and inference attacks targeting membership or attributes (Wei et al., 2022). A dedicated privacy–utility evaluation study reports that model inversion and most label inference attacks can often be mitigated by existing protections, but model completion remains difficult to prevent, especially in split-learning-style systems and multi-class settings (Kang et al., 2022). Since X-VFL preserves embedding exchange and introduces additional reconstruction pathways through XCom, the security properties of completion-enhanced VFL remain an open issue rather than a resolved one.

The framework also inherits broader deployment constraints identified by recent surveys. Real-world VFL commonly exhibits semi-precise or fuzzy alignment, feature imbalance, and stringent trustworthiness requirements, while some scenarios—especially latent VFL without shared keys—still have no viable algorithmic solutions in the survey literature (Wu et al., 12 Feb 2025). X-VFL squarely addresses partially missing features and local inference, but it does so within a regime that still assumes meaningful cross-client signal for completion and supervised training via a label-holding server. This suggests a practical scope narrower than the full spectrum of under-served VFL scenarios.

The limitations stated in the X-VFL paper are correspondingly concrete. The convergence analysis relies on average smoothness and bounded variance assumptions. Sharing embeddings may still leak information, and adding stronger privacy mechanisms such as differential privacy, homomorphic encryption, or secure aggregation would increase communication or computation costs. Cross completion assumes useful correlations across client feature spaces, so domain shift may degrade reconstruction quality. The method also introduces hyperparameters $i$6 and $i$7 that require tuning, and high-dimensional embeddings can remain bandwidth-intensive despite the PAGE-based reduction in communication rounds (Yao et al., 7 Aug 2025).

Within the evolution of VFL research, X-VFL is therefore best characterized as a structural extension of split-learning-style vertical federation rather than a replacement for the classical framework. Its novelty lies in making partially observed, non-aligned samples trainable through feature completion, and in aligning local and collaborative prediction geometries tightly enough to support independent inference. In the current literature, those two properties distinguish it from concatenation-based VFL, distillation-only local-inference methods, and earlier semi-supervised completion methods such as FedCVT (Yao et al., 7 Aug 2025).