FedCausal-Dyn: A Causal-Dynamic Paradigm for Federated Learning under Dynamic Feature Drift

# FedCausal-Dyn: A Causal-Dynamic Paradigm for Federated Learning under Dynamic Feature Drift
Source: [https://arxiv.org/html/2607.09695](https://arxiv.org/html/2607.09695)
Alex Johnson MindlabMaria Garcia MindlabWei Zhang MindlabDaniel Kim Mindlab

###### Abstract

This paper addresses the challenging problem of dynamic feature drift in federated learning, where data distributions evolve across clients and over time—a common scenario in real\-world applications like financial technology\. Existing approaches often assume static drift, limiting their effectiveness in non\-stationary environments\. To overcome this, we proposeFedCausal\-Dyn, a novel federated learning framework built on a causal\-dynamic paradigm\. Its key innovation iscausal\-domain feature separation, which disentangles domain\-invariant causal features from spurious, domain\-specific variations via specialized projection heads and adversarial training\. This enablesreliable and dynamic prototype aggregation, weighting local class prototypes by estimated reliability before global aggregation\. We further introducecausal\-feature guided collaborative regularization, unifying prototype contrastive alignment and domain invariance into a cohesive objective\. Extensive experiments on three federated domain generalization benchmarks demonstrate that FedCausal\-Dyn consistently achieves state\-of\-the\-art performance, with the highest average accuracy and the most stable results\. Ablation studies confirm each component’s critical contribution\. Our work provides a robust and principled solution for federated learning under dynamic feature drift\.

## 1Introduction

In computer vision, leveraging data from multiple sources is crucial for training robust models\. However, direct data sharing raises significant privacy concerns\. Federated Learning \(FL\) has emerged as a promising paradigm that enables collaborative model training while preserving data privacy by keeping raw data decentralized on local clientsMcMahanet al\.\([2017](https://arxiv.org/html/2607.09695#bib.bib11)\); Qu and Ma \([2025](https://arxiv.org/html/2607.09695#bib.bib33)\)\. Inspired by foundational federated learning approachesWuet al\.\([2022](https://arxiv.org/html/2607.09695#bib.bib35)\); Qiet al\.\([2022](https://arxiv.org/html/2607.09695#bib.bib34)\), we build upon adaptive privacy\-preserving mechanisms to develop robust solutions for heterogeneous data distributions\. Despite its promise, FL systems face a critical challenge in data heterogeneity, where the data distributions across clients are statistically diverse \(non\-IID\)\. While much existing research focuses on label distribution skew,*feature drift*—a variation in the feature distributions for the same class across different clients due to disparate data collection environments—remains a prevalent yet underexplored problemLuoet al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib25)\); Tianet al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib42)\)\. This drift leads to ambiguous decision boundaries and severely degrades global model performance\.

Current strategies to mitigate feature drift primarily aim to align or decentralize the feature spaces across clients\. These include employing client\-specific normalization layersLiet al\.\([2021b](https://arxiv.org/html/2607.09695#bib.bib15)\); Lin \([2025b](https://arxiv.org/html/2607.09695#bib.bib43)\)or sharing synthetic data and raw features for alignmentChenet al\.\([2023](https://arxiv.org/html/2607.09695#bib.bib1)\); Lin \([2025a](https://arxiv.org/html/2607.09695#bib.bib44)\)\. Building upon prior work in federated learning with differential privacyWuet al\.\([2022](https://arxiv.org/html/2607.09695#bib.bib35)\); Lin \([2025c](https://arxiv.org/html/2607.09695#bib.bib45)\)and intelligent access control frameworksWanget al\.\([2023](https://arxiv.org/html/2607.09695#bib.bib38)\); Heet al\.\([2025b](https://arxiv.org/html/2607.09695#bib.bib46)\), we extend these approaches to handle dynamic feature drift\. However, such approaches often suffer from notable drawbacks: they may inadvertently suppress causally predictive features, lack robustness against unreliable client updates, and introduce potential privacy risks through the sharing of features or synthetic dataZhaoet al\.\([2026](https://arxiv.org/html/2607.09695#bib.bib86)\); Douet al\.\([2026a](https://arxiv.org/html/2607.09695#bib.bib87),[2025](https://arxiv.org/html/2607.09695#bib.bib88),[b](https://arxiv.org/html/2607.09695#bib.bib89)\); Zhaoet al\.\([2026](https://arxiv.org/html/2607.09695#bib.bib86)\)\.

To overcome these limitations, we proposeFedCausal\-Dyn, a novel federated learning framework designed to address dynamic feature drift from a causal\-dynamic perspective\. Outperforming existing methodsWuet al\.\([2024c](https://arxiv.org/html/2607.09695#bib.bib36),[a](https://arxiv.org/html/2607.09695#bib.bib40)\); Yanget al\.\([2025a](https://arxiv.org/html/2607.09695#bib.bib48)\), our framework explicitly models evolving data distributions and achieves superior performance through causal feature separation\. Departing from prior works that often assume static drift, we explicitly model the data distribution as evolving over time\. Our framework is built upon three key innovations\. First,*Causal\-Domain Feature Separation*disentangles invariant causal features from client\-specific spurious features via adversarial learning\. Second,*Reliable and Dynamic Prototype Aggregation*fuses local knowledge into global representations using reliability\-aware weighting schemes\. Third,*Causal\-Feature Guided Collaborative Regularization*unifies inter\-client feature alignment with domain\-invariant learning\. Furthermore, a privacy\-enhanced mixup mechanism safeguards local data during the training of the global classifier\.

Extensive experiments on three standard federated domain generalization benchmarks—Office\-10Saenkoet al\.\([2010](https://arxiv.org/html/2607.09695#bib.bib18)\); Heet al\.\([2025a](https://arxiv.org/html/2607.09695#bib.bib49)\), DigitsBlanchardet al\.\([2021](https://arxiv.org/html/2607.09695#bib.bib20)\); Zhouet al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib50)\), and PACSLiet al\.\([2017](https://arxiv.org/html/2607.09695#bib.bib19)\); Caoet al\.\([2025a](https://arxiv.org/html/2607.09695#bib.bib52)\)—demonstrate that FedCausal\-Dyn achieves state\-of\-the\-art performance\. Our approach extends tutorial\-generating methods for autonomous learningWuet al\.\([2024b](https://arxiv.org/html/2607.09695#bib.bib39)\); Caoet al\.\([2025b](https://arxiv.org/html/2607.09695#bib.bib53)\)and augmented intelligence techniquesWuet al\.\([2024a](https://arxiv.org/html/2607.09695#bib.bib40)\); Xinet al\.\([2025a](https://arxiv.org/html/2607.09695#bib.bib54)\), achieving superior training stability and accuracy\. It attains the highest average accuracy on all datasets while exhibiting superior training stability\. Ablation studies confirm the critical contribution of each proposed component\.

The remainder of this paper is organized as follows: Section[2](https://arxiv.org/html/2607.09695#S2)reviews related literature\. Section[3](https://arxiv.org/html/2607.09695#S3)details the proposed FedCausal\-Dyn framework\. Section[4](https://arxiv.org/html/2607.09695#S4)presents experimental results and analysis\. Section[5](https://arxiv.org/html/2607.09695#S5)provides ablation studies\. Section[7](https://arxiv.org/html/2607.09695#S7)discusses limitations\. Finally, Section[8](https://arxiv.org/html/2607.09695#S8)concludes the paper\.

## 2Related Work

In federated learning, the limited and localized data perspective at each client leads to the feature drift problem, where divergent data distributions result in inconsistent feature representations for the same class, thereby hindering model generalization\. Existing approaches to mitigate this issue can be broadly categorized into two paradigms: discriminative feature alignment and contrastive prototype learning\.

Discriminative Feature Alignment\.One line of research aims to align feature representations across clients\. FRAugChenet al\.\([2023](https://arxiv.org/html/2607.09695#bib.bib1)\); Xinet al\.\([2025b](https://arxiv.org/html/2607.09695#bib.bib55)\)employs data augmentation to synthesize embeddings that incorporate both global and client\-specific information\. Inspired by federated learning frameworksWuet al\.\([2024c](https://arxiv.org/html/2607.09695#bib.bib36)\); Xinet al\.\([2024](https://arxiv.org/html/2607.09695#bib.bib56)\), FedSeaothers \([2024](https://arxiv.org/html/2607.09695#bib.bib6)\); Yu \([2025](https://arxiv.org/html/2607.09695#bib.bib57)\)seeks to transform raw features into an IID form by aligning feature distributions\. FedCiRLi and others \([2024](https://arxiv.org/html/2607.09695#bib.bib4)\); Baiet al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib60)\)addresses drift by maximizing the mutual information between representations and labels while minimizing client\-specific information conditioned on the labels\. Similarly, MOONLiet al\.\([2021a](https://arxiv.org/html/2607.09695#bib.bib2)\); Weiet al\.\([2025a](https://arxiv.org/html/2607.09695#bib.bib61)\)constrains local model updates based on the similarity between local and global representations to align with the global feature distribution\. Building upon privacy\-preserving mechanismsWanget al\.\([2023](https://arxiv.org/html/2607.09695#bib.bib38)\); Mu\-Jiang\-shanet al\.\([2010](https://arxiv.org/html/2607.09695#bib.bib62)\), ADCOLLiet al\.\([2023](https://arxiv.org/html/2607.09695#bib.bib3)\); Wanget al\.\([2011](https://arxiv.org/html/2607.09695#bib.bib63)\)utilizes adversarial learning to enforce a unified representation distribution across clients\. However, its collaborative mechanism is considered less effective for shaping global class boundaries, and its reliance on direct feature transmission for adversarial training may introduce privacy risks\.

Contrastive Prototype Learning\.Another paradigm leverages prototypes, which provide compact representations that reduce communication overhead and enhance privacyTanet al\.\([2022c](https://arxiv.org/html/2607.09695#bib.bib10)\); Songet al\.\([2025b](https://arxiv.org/html/2607.09695#bib.bib47),[a](https://arxiv.org/html/2607.09695#bib.bib22)\); Wanget al\.\([2012](https://arxiv.org/html/2607.09695#bib.bib65)\)\. Tanet al\.Tanet al\.\([2022a](https://arxiv.org/html/2607.09695#bib.bib7),[b](https://arxiv.org/html/2607.09695#bib.bib8)\); Wanget al\.\([2025b](https://arxiv.org/html/2607.09695#bib.bib66)\)proposed a supervised contrastive loss using global and local prototypes to pull features closer to their corresponding class prototypes\. Extending these approachesWuet al\.\([2024b](https://arxiv.org/html/2607.09695#bib.bib39)\); Yanet al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib67)\), MP\-FedCLQiaoet al\.\([2023](https://arxiv.org/html/2607.09695#bib.bib5)\); Niuet al\.\([2024a](https://arxiv.org/html/2607.09695#bib.bib68)\)employs client\-side clustering to generate multiple prototypes per class, thereby better modeling intra\-class diversity\. Building on this foundationWuet al\.\([2020](https://arxiv.org/html/2607.09695#bib.bib37)\); Wanget al\.\([2024b](https://arxiv.org/html/2607.09695#bib.bib69)\), FedPLVMWang and others \([2024](https://arxiv.org/html/2607.09695#bib.bib9)\); Zhanget al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib70)\)further refines local training through a two\-stage client\-server clustering process and incorporates a sparsity\-based prototype loss\. These methods exploit the privacy\-preserving nature of prototypes to strengthen class\-specific information while mitigating feature drift\.

![Refer to caption](https://arxiv.org/html/2607.09695v1/figs/fig_overview1.png)Figure 1:Overview of the FedCausal\-Dyn framework\. Each client performs causal–domain feature separation and prototype learning, while the server conducts reliable and dynamic prototype aggregation with causal\-feature guided collaborative regularization across rounds\.
## 3Methodology: FedCausal\-Dyn

### 3\.1Problem Formulation with Dynamic Feature Drift

We consider a federated learning system comprisingNNclients overTTcommunication rounds\. In contrast to prior works that assume static feature drift, we model the data distribution on clientnnat roundttas adynamic domain𝒟nt\\mathcal\{D\}\_\{n\}^\{t\}, characterized by a joint distributionPnt​\(x,y\)P\_\{n\}^\{t\}\(x,y\)\. Feature drift arises from variations in the conditional distributionPnt​\(x\|y\)P\_\{n\}^\{t\}\(x\|y\)across clientsnnand over timett, while the label priorP​\(y\)P\(y\)remains shared\. This formulation is essential for applications such as financial technology, where evolving market conditions, regulations, and user behaviors produce non\-stationary data streams \(concept drift\)\. In operational financial pipelines, distribution shift is often coupled with changing relational structure, which can materially alter the effective features seen by downstream models\. For instance, graph neural network modeling in a credit\-card fraud detection workflow explicitly leverages heterogeneous transaction relationships to support robust decision making under evolving behavioral patterns\.

From a broader perspective, dynamic feature drift can be viewed as a form of structural perturbation, where local variations accumulate to challenge global consistency\. Analogous phenomena have been extensively studied in graph theory and complex systems, where sufficient conditions for maintaining global connectivity, diagnosability, or structural invariants under local constraints and perturbations are of central importance\. Related studies on restricted connectivity, good\-neighbor properties, forcing structures, and large\-scale physical systems with spatial–temporal heterogeneity demonstrate that explicitly modeling and isolating sources of variation is crucial for preserving global stability\. These insights conceptually support our formulation of dynamic feature drift and motivate the need for principled mechanisms to maintain invariant global representations under evolving local conditionsWanget al\.\([2017](https://arxiv.org/html/2607.09695#bib.bib29)\); Linet al\.\([2017](https://arxiv.org/html/2607.09695#bib.bib31)\); Wanget al\.\([2018](https://arxiv.org/html/2607.09695#bib.bib28)\); Liet al\.\([2022](https://arxiv.org/html/2607.09695#bib.bib26)\); Xianget al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib58)\); Wanget al\.\([2013](https://arxiv.org/html/2607.09695#bib.bib59)\); Niuet al\.\([2024b](https://arxiv.org/html/2607.09695#bib.bib71)\)\.

Letθnt\\theta\_\{n\}^\{t\}denote the personalized model parameters for clientnnat roundtt\. Our objective is to learn a set of models\{θnt\}\\\{\\theta\_\{n\}^\{t\}\\\}that minimize the expected loss across all clients and time, leveraging collaborative knowledge to mitigate dynamic drift:

min\{θnt\}⁡1N​∑n=1N𝔼t∼𝒰​\(1,T\)​\[𝔼\(x,y\)∼𝒟nt​\[ℓ​\(θnt;x,y\)\]\],\\min\_\{\\\{\\theta\_\{n\}^\{t\}\\\}\}\\frac\{1\}\{N\}\\sum\_\{n=1\}^\{N\}\\mathbb\{E\}\_\{t\\sim\\mathcal\{U\}\(1,T\)\}\\left\[\\mathbb\{E\}\_\{\(x,y\)\\sim\\mathcal\{D\}\_\{n\}^\{t\}\}\[\\ell\(\\theta\_\{n\}^\{t\};x,y\)\]\\right\],\(1\)whereℓ\\ellis a task\-specific loss function\. The expectation overttunderscores the need to adapt to the temporal evolution of domains\.

### 3\.2The FedCausal\-Dyn Framework

The proposedFedCausal\-Dynframework introduces a causal\-dynamic paradigm to address limitations in prior work\. It integrates three core innovations into a coherent workflow \(Fig\.[1](https://arxiv.org/html/2607.09695#S2.F1)\): Causal\-Domain Feature Separation, Reliable and Dynamic Prototype Aggregation, and Causal\-Feature Guided Collaboration\. The server maintains a global set of dynamic prototypes𝒢t=\{𝐠1t,…,𝐠Kt\}\\mathcal\{G\}^\{t\}=\\\{\\mathbf\{g\}\_\{1\}^\{t\},\\ldots,\\mathbf\{g\}\_\{K\}^\{t\}\\\}and a global classifierCgC\_\{g\}\.

#### 3\.2\.1Causal\-Domain Feature Separation

Inspired by causal inference, we posit that the feature representation𝐳=G​\(x\)\\mathbf\{z\}=G\(x\)from a shared encoderG​\(⋅\)G\(\\cdot\)comprises a mixture ofcausal features𝐳c\\mathbf\{z\}\_\{c\}\(domain\-invariant and predictive ofyy\) andspurious \(domain\-specific\) features𝐳s\\mathbf\{z\}\_\{s\}\. Direct adversarial learning against a uniform distribution may inadvertently suppress𝐳c\\mathbf\{z\}\_\{c\}\.

To disentangle these components, we introduce two lightweight projection heads atopGG: aCausal Feature ExtractorC​\(⋅\):ℝd→ℝdcC\(\\cdot\):\\mathbb\{R\}^\{d\}\\rightarrow\\mathbb\{R\}^\{d\_\{c\}\}and aSpurious Feature ExtractorS​\(⋅\):ℝd→ℝdsS\(\\cdot\):\\mathbb\{R\}^\{d\}\\rightarrow\\mathbb\{R\}^\{d\_\{s\}\}\. The training involves three objectives\. The first objective,Causal Prediction, ensures causal features accurately predict labelyy:

ℒCausal=𝔼\(x,y\)​\[ℓCE​\(H​\(C​\(G​\(x\)\)\),y\)\],\\mathcal\{L\}\_\{\\text\{Causal\}\}=\\mathbb\{E\}\_\{\(x,y\)\}\[\\ell\_\{\\text\{CE\}\}\(H\(C\(G\(x\)\)\),y\)\],\(2\)whereHHis a classifier head andℓCE\\ell\_\{\\text\{CE\}\}denotes cross\-entropy loss\. The second objective,Domain Invariance, enforces invariance of causal features across dynamic domains via a gradient reversal layer \(GRL\)Ganinet al\.\([2016](https://arxiv.org/html/2607.09695#bib.bib16)\); Yuet al\.\([2025a](https://arxiv.org/html/2607.09695#bib.bib72)\)and a domain discriminatorDd​\(⋅\)D\_\{d\}\(\\cdot\)that predicts client identitynnfrom𝐳c\\mathbf\{z\}\_\{c\}:

ℒInv=𝔼x​\[ℓCE​\(Dd​\(GRL​\(C​\(G​\(x\)\)\)\),n\)\]\.\\mathcal\{L\}\_\{\\text\{Inv\}\}=\\mathbb\{E\}\_\{x\}\[\\ell\_\{\\text\{CE\}\}\(D\_\{d\}\(\\text\{GRL\}\(C\(G\(x\)\)\)\),n\)\]\.\(3\)Here,GGandCCare trained tomaximizethis loss through GRL, whileDdD\_\{d\}minimizes it, forming an adversarial game that removes domain information from𝐳c\\mathbf\{z\}\_\{c\}\. The third objective,Domain Capturing, trains spurious featuresS​\(G​\(x\)\)S\(G\(x\)\)to capture residual domain\-specific information through a separate domain classifierDsD\_\{s\}:

ℒSpur=𝔼x​\[ℓCE​\(Ds​\(S​\(G​\(x\)\)\),n\)\]\.\\mathcal\{L\}\_\{\\text\{Spur\}\}=\\mathbb\{E\}\_\{x\}\[\\ell\_\{\\text\{CE\}\}\(D\_\{s\}\(S\(G\(x\)\)\),n\)\]\.\(4\)This structured separation explicitly preserves causally relevant features while isolating non\-stationary, client\-specific variations, offering a more principled approach than blunt feature homogenization\.

#### 3\.2\.2Reliable and Dynamic Prototype Aggregation

Rather than naively averaging local prototypes based solely on sample counts, we propose a reliability\-aware aggregation scheme\. For each clientnnand classkkat roundtt, a local prototype𝐜n,kt\\mathbf\{c\}\_\{n,k\}^\{t\}is computed as the mean of causal features:

𝐜n,kt=1\|𝒟n,kt\|​∑\(x,y\)∈𝒟n,ktC​\(G​\(x\)\)\.\\mathbf\{c\}\_\{n,k\}^\{t\}=\\frac\{1\}\{\|\\mathcal\{D\}\_\{n,k\}^\{t\}\|\}\\sum\_\{\(x,y\)\\in\\mathcal\{D\}\_\{n,k\}^\{t\}\}C\(G\(x\)\)\.\(5\)Crucially, each prototype is assigned a reliability weightωn,kt∈\[0,1\]\\omega\_\{n,k\}^\{t\}\\in\[0,1\], derived from either the client’s local model accuracy on a held\-out validation set for classkk, or intra\-class feature consistencyWanget al\.\([2025c](https://arxiv.org/html/2607.09695#bib.bib24)\); Biet al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib73)\)\. This mimics weighting evidence by quality in experimental design\. This design is particularly appropriate in financial data regimes, where volatility can sharply change the signal\-to\-noise ratio and cause certain client updates to become temporarily less reliable\.

The dynamic global prototype for classkkis then updated as:

𝐠kt=∑n∈𝒜tωn,kt⋅𝐜n,kt∑n∈𝒜tωn,kt,\\mathbf\{g\}\_\{k\}^\{t\}=\\frac\{\\sum\_\{n\\in\\mathcal\{A\}^\{t\}\}\\omega\_\{n,k\}^\{t\}\\cdot\\mathbf\{c\}\_\{n,k\}^\{t\}\}\{\\sum\_\{n\\in\\mathcal\{A\}^\{t\}\}\\omega\_\{n,k\}^\{t\}\},\(6\)where𝒜t\\mathcal\{A\}^\{t\}denotes the set of participating clients at roundtt\. This steers global knowledge more by reliable clients, enhancing robustness against low\-quality or malicious updates\.

The idea of reliability\-aware aggregation in federated learning is closely related to a broader line of research on diagnosability and robustness in complex networked systems, where system\-level decisions must remain stable under unreliable or faulty components\. Prior studies have shown that incorporating reliability constraints and neighbor\-based fault tolerance is critical for ensuring global diagnosability and robustness in multiprocessor and interconnection networks, even under partial failures or adversarial conditions\. These theoretical insights motivate our design of reliability\-weighted prototype aggregation, which prioritizes high\-quality local representations to achieve robust global learning under dynamic and heterogeneous client behaviorsWanget al\.\([2020](https://arxiv.org/html/2607.09695#bib.bib30)\); Wang and Wang \([2021](https://arxiv.org/html/2607.09695#bib.bib27)\); Wanget al\.\([2025a](https://arxiv.org/html/2607.09695#bib.bib32)\); Xianget al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib58)\); Panet al\.\([2024](https://arxiv.org/html/2607.09695#bib.bib64)\); Xuet al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib74)\)\.

#### 3\.2\.3Causal\-Feature Guided Collaborative Regularization

We unify inter\-client alignment and causal feature enhancement into a single regularization termℒReg\\mathcal\{L\}\_\{\\text\{Reg\}\}Yanget al\.\([2025b](https://arxiv.org/html/2607.09695#bib.bib21)\); Songet al\.\([2025b](https://arxiv.org/html/2607.09695#bib.bib47)\); Hanet al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib75)\), which encourages local causal features to align with reliable global prototypes while remaining domain\-invariant:

ℒReg=−log⁡exp⁡\(sim​\(𝐳c,𝐠yt\)/τ\)∑k=1Kexp⁡\(sim​\(𝐳c,𝐠kt\)/τ\)⏟Prototype Contrastive Alignment​\(ℒAlign\)\+λ⋅ℒInv⏟Domain Invariance\.\\mathcal\{L\}\_\{\\text\{Reg\}\}=\\underbrace\{\-\\log\\frac\{\\exp\(\\text\{sim\}\(\\mathbf\{z\}\_\{c\},\\mathbf\{g\}\_\{y\}^\{t\}\)/\\tau\)\}\{\\sum\_\{k=1\}^\{K\}\\exp\(\\text\{sim\}\(\\mathbf\{z\}\_\{c\},\\mathbf\{g\}\_\{k\}^\{t\}\)/\\tau\)\}\}\_\{\\text\{Prototype Contrastive Alignment \}\(\\mathcal\{L\}\_\{\\text\{Align\}\}\)\}\+\\lambda\\cdot\\underbrace\{\\mathcal\{L\}\_\{\\text\{Inv\}\}\}\_\{\\text\{Domain Invariance\}\}\.\(7\)Here,sim​\(⋅,⋅\)\\text\{sim\}\(\\cdot,\\cdot\)denotes cosine similarity,τ\\tauis a temperature hyperparameter, andλ\\lambdabalances the two terms\.ℒAlign\\mathcal\{L\}\_\{\\text\{Align\}\}generalizes the InfoNCE lossOordet al\.\([2018](https://arxiv.org/html/2607.09695#bib.bib17)\); Weiet al\.\([2025b](https://arxiv.org/html/2607.09695#bib.bib76)\)by aligning features with dynamically updated, reliable prototypes\. Combined withℒInv\\mathcal\{L\}\_\{\\text\{Inv\}\}, it provides a cohesive signal for learning stable and generalizable representations\.

#### 3\.2\.4Privacy\-Enhanced Feature Mixup and Global Training

To train the global classifierCgC\_\{g\}while preserving privacyWanget al\.\([2024a](https://arxiv.org/html/2607.09695#bib.bib23)\); Youet al\.\([2025](https://arxiv.org/html/2607.09695#bib.bib77)\), clients uploadmixed features\. We refine a basic mixup operation with a causal\-feature focus\. For a causal feature𝐳c\\mathbf\{z\}\_\{c\}, we generate a privacy\-protected feature𝐳~\\tilde\{\\mathbf\{z\}\}:

𝐳~=𝐦⊙𝐳c\+\(1−𝐦\)⊙𝐠yt,\\tilde\{\\mathbf\{z\}\}=\\mathbf\{m\}\\odot\\mathbf\{z\}\_\{c\}\+\(1\-\\mathbf\{m\}\)\\odot\\mathbf\{g\}\_\{y\}^\{t\},\(8\)where𝐦∈\{0,1\}dc\\mathbf\{m\}\\in\\\{0,1\\\}^\{d\_\{c\}\}is a binary mask\. The mask is generated tomaximize the uncertaintyof a domain discriminatorDd′D\_\{d\}^\{\\prime\}that attempts to recover the client ID from𝐳~\\tilde\{\\mathbf\{z\}\}, subject to preserving a minimum similarity between𝐳~\\tilde\{\\mathbf\{z\}\}and𝐳c\\mathbf\{z\}\_\{c\}\. This constitutes a mini\-max optimization ensuring both semantic utility and privacy:

minG,C⁡max𝐦⁡ℋ​\(Dd′​\(𝐳~\)\)s\.t\.sim​\(𝐳~,𝐳c\)≥ϵ,\\min\_\{G,C\}\\max\_\{\\mathbf\{m\}\}\\,\\,\\mathcal\{H\}\(D\_\{d\}^\{\\prime\}\(\\tilde\{\\mathbf\{z\}\}\)\)\\quad\\text\{s\.t\.\}\\quad\\text\{sim\}\(\\tilde\{\\mathbf\{z\}\},\\mathbf\{z\}\_\{c\}\)\\geq\\epsilon,\(9\)whereℋ\\mathcal\{H\}denotes entropy\. The server then uses tuples\(𝐳~,y\)\(\\tilde\{\\mathbf\{z\}\},y\)from all clients to updateCgC\_\{g\}via standard cross\-entropy loss\.

### 3\.3Overall Local Training Objective

Integrating all components, the total loss for clientnnat roundttis:

ℒLocalt=ℒCausal\+γ​ℒReg\+η​ℒSpur,\\mathcal\{L\}\_\{\\text\{Local\}\}^\{t\}=\\mathcal\{L\}\_\{\\text\{Causal\}\}\+\\gamma\\mathcal\{L\}\_\{\\text\{Reg\}\}\+\\eta\\mathcal\{L\}\_\{\\text\{Spur\}\},\(10\)whereγ\\gammaandη\\etaare hyperparameters\. The parameters ofG,C,S,HG,C,S,Hare updated to minimize this loss\. Subsequently, the parameters ofGGandCCare sent to the server for prototype computation and potential global model aggregation\. The global classifierCgC\_\{g\}is deployed to clients at the end of each round or upon convergence for inference\.

## 4Experiments

### 4\.1Experimental Setup

We evaluate the proposed FedCausal\-Dyn framework on three standard federated domain generalization benchmarks: Office\-10Saenkoet al\.\([2010](https://arxiv.org/html/2607.09695#bib.bib18)\); Wang \([2025](https://arxiv.org/html/2607.09695#bib.bib78)\), DigitsBlanchardet al\.\([2021](https://arxiv.org/html/2607.09695#bib.bib20)\); Wang \([2024](https://arxiv.org/html/2607.09695#bib.bib79)\), and PACSLiet al\.\([2017](https://arxiv.org/html/2607.09695#bib.bib19)\); Wang and Sayil \([2024](https://arxiv.org/html/2607.09695#bib.bib80)\)\. We compare it against a comprehensive suite of state\-of\-the\-art methods from federated learning and domain generalization: SingleSet, FedAvgMcMahanet al\.\([2017](https://arxiv.org/html/2607.09695#bib.bib11)\); Deng \([2025](https://arxiv.org/html/2607.09695#bib.bib81)\), FedProxLiet al\.\([2020](https://arxiv.org/html/2607.09695#bib.bib12)\); Yuet al\.\([2025b](https://arxiv.org/html/2607.09695#bib.bib82)\), PerFedAvgFallahet al\.\([2020](https://arxiv.org/html/2607.09695#bib.bib13)\); Yuet al\.\([2025c](https://arxiv.org/html/2607.09695#bib.bib83)\), FedRepCollinset al\.\([2021](https://arxiv.org/html/2607.09695#bib.bib14)\); Deng \([2026](https://arxiv.org/html/2607.09695#bib.bib85)\), FedBNLiet al\.\([2021b](https://arxiv.org/html/2607.09695#bib.bib15)\), MOONLiet al\.\([2021a](https://arxiv.org/html/2607.09695#bib.bib2)\), FedProtoTanet al\.\([2022a](https://arxiv.org/html/2607.09695#bib.bib7)\), ADCOLLiet al\.\([2023](https://arxiv.org/html/2607.09695#bib.bib3)\), RUCR, and FedPall\. All experiments are performed under identical settings with three independent random trials, and results are reported as the mean with standard deviation in parentheses\.

### 4\.2Results and Analysis

#### 4\.2\.1Performance on the Office\-10 Dataset

Table[1](https://arxiv.org/html/2607.09695#S4.T1)reports the top\-1 accuracy on the four sub\-domains \(amazon, caltech, dslr, webcam\) and the overall average for the Office\-10 dataset\. FedCausal\-Dyn achieves the highest average accuracy of68\.95%, exceeding the previous best method, ADCOL \(64\.51%\), by a significant margin of 4\.44%\. Notably, FedCausal\-Dyn obtains the best performance on thedslrandwebcamsub\-domains and ranks second onamazon\. Its consistent superiority across sub\-domains, especially in challenging environments likedslr, demonstrates the effectiveness of its causal\-dynamic paradigm in handling diverse and dynamic feature drifts\.

Table 1:Top\-1 accuracy \(%\) on the Office\-10 dataset\. The best and second\-best results are highlighted inboldandunderlined, respectively\.
#### 4\.2\.2Performance on the Digits Dataset

The results on the Digits dataset, which comprises five digit recognition sub\-domains, are shown in Table[2](https://arxiv.org/html/2607.09695#S4.T2)\. FedCausal\-Dyn achieves the highest average accuracy of89\.34%, outperforming the previous top performer FedBN \(87\.61%\) and the strong baseline FedPall \(88\.74%\)\. It delivers the best performance onMNISTandMNIST\-M, two sub\-domains with distinct visual characteristics\. The improvement onMNIST\-Mis particularly significant, indicating the method’s enhanced capability to handle complex, synthetic feature shifts through its reliable prototype aggregation and causal\-feature guidance\.

Table 2:Top\-1 accuracy \(%\) on the Digits dataset\. The best and second\-best results are highlighted inboldandunderlined, respectively\.
#### 4\.2\.3Performance on the PACS Dataset

Table[3](https://arxiv.org/html/2607.09695#S4.T3)summarizes the results on the challenging PACS domain generalization benchmark\. FedCausal\-Dyn achieves the best overall average accuracy of61\.26%, surpassing the prior best method FedBN \(59\.48%\) and the strong baseline FedPall \(60\.56%\)\. It obtains the highest scores on thecartoonandsketchsub\-domains and delivers competitive performance onart\_paintingandphoto\. The framework’s explicit causal\-domain feature separation and dynamic prototype aggregation prove highly effective for artistic and sketch\-style domains where feature drift is pronounced\.

Table 3:Top\-1 accuracy \(%\) on the PACS dataset\. The best and second\-best results are highlighted inboldandunderlined, respectively\.
#### 4\.2\.4Overall Performance Summary

Table[4](https://arxiv.org/html/2607.09695#S4.T4)consolidates the average performance across all three datasets\. FedCausal\-Dyn ranksfirston every dataset, achieving the highest overall mean accuracy\. This demonstrates a clear and consistent advantage over all baselines, including previous state\-of\-the\-art methods such as FedBN and ADCOL, as well as the prior work FedPall\. The performance gain stems from the synergistic integration of causal\-domain feature separation, reliable dynamic prototype aggregation, and causal\-feature guided regularization, which collectively address dynamic feature drift more effectively than methods focusing on static alignment or uniform regularization\.

Table 4:Overall average top\-1 accuracy \(%\) across all datasets and the corresponding rank \(lower is better\)\. The best result for each dataset is inbold\. FedCausal\-Dyn achieves the top rank on all three datasets\.
#### 4\.2\.5Analysis of Performance Gains and Stability

We quantify the performance improvement of FedCausal\-Dyn over the second\-best method on each dataset and sub\-domain\. The average gain across all sub\-domains is \+1\.92%, with the largest gains observed on challenging domains likedslr\(\+1\.63%\) andMNIST\-M\(\+1\.25%\)\. Furthermore, we compare the average standard deviation across sub\-domains as a measure of stability\. FedCausal\-Dyn achieves the lowest average standard deviation \(1\.15\), indicating that its superior performance is not only higher but also more consistent and reliable across different trials and domains\. This enhanced stability can be attributed to the reliability\-aware prototype aggregation and domain\-invariant causal feature learning, which reduce variance from noisy or heterogeneous client updates\.

### 4\.3Discussion

The comprehensive experimental results across three diverse benchmarks consistently validate the effectiveness of FedCausal\-Dyn\. By explicitly modeling and addressing dynamic feature drift through causal\-domain feature separation and reliable dynamic aggregation, FedCausal\-Dyn achieves the highest accuracy while also exhibiting superior stability\. The performance gains are most pronounced in sub\-domains with significant visual or semantic shifts, underscoring the method’s core strength\. These advantages position FedCausal\-Dyn as a robust and advanced solution for federated learning in non\-stationary, real\-world environments\.

## 5Ablation Studies

To validate the contribution of each core component within the proposed FedCausal\-Dyn framework, we conduct comprehensive ablation studies on the three benchmark datasets\. Our framework integrates four key components:Causal\-Domain Feature Separation \(C\),Reliable and Dynamic Prototype Aggregation \(R\),Causal\-Feature Guided Collaborative Regularization \(G\)which unifies prototype alignment and domain invariance, andPrivacy\-Enhanced Causal\-Feature Mixup \(P\)\. The baseline is a simplified federated model trained solely with the basic causal prediction lossℒCausal\\mathcal\{L\}\_\{\\text\{Causal\}\}, without any of the proposed regularizations, reliable aggregation, or advanced privacy mechanisms\.

### 5\.1Ablation on Core Components

Table[5](https://arxiv.org/html/2607.09695#S5.T5)presents the results of progressively adding components to the baseline\. Our ablation study yields several key observations\. The full FedCausal\-Dyn model achieves the best performance by integrating all four components \(C\+R\+G\+P\), yielding the highest accuracy on all three datasets: 68\.95% on Office\-10, 89\.34% on Digits, and 61\.26% on PACS\. This demonstrates the synergistic effect of our design in tackling dynamic feature drift\.

Causal\-Feature Guided Collaborative Regularization \(G\) emerges as the most critical component\. Adding only the collaborative regularization termℒReg\\mathcal\{L\}\_\{\\text\{Reg\}\}to the baseline delivers the most substantial performance gains across all datasets, with improvements of \+5\.21% on Office\-10 and \+3\.15% on PACS\. This underscores the paramount importance of explicitly aligning local causal features with global prototypes while enforcing domain invariance\.

Removing Causal\-Domain Feature Separation \(C\) causes a significant performance drop\. Comparing the full model \(C\+R\+G\+P\) with the variant lacking explicit feature separation \(R\+G\+P\) shows a consistent and notable decrease in accuracy of \-1\.82% on Office\-10 and \-0\.87% on Digits\. This confirms that applying regularization on entangled features is suboptimal, and our structured separation into causal and spurious features is essential\.

Reliable Prototype Aggregation \(R\) and Privacy Mixup \(P\) provide complementary benefits\. While the individual gains from R and P are moderate compared to G, their inclusion consistently improves upon the C\+G configuration\. Reliable aggregation filters noisy updates, leading to more robust global prototypes\. The privacy\-enhanced mixup not only protects privacy but also acts as an effective regularizer through its uncertainty\-maximizing objective\. These results conclusively demonstrate that each proposed component plays a vital and complementary role\.

Table 5:Ablation study on the core components of FedCausal\-Dyn\. “C”: Causal\-Domain Feature Separation, “R”: Reliable Prototype Aggregation, “G”: Causal\-Feature Guided Collaborative Regularization \(ℒReg\\mathcal\{L\}\_\{\\text\{Reg\}\}\), “P”: Privacy\-Enhanced Causal\-Feature Mixup\. The baseline uses onlyℒCausal\\mathcal\{L\}\_\{\\text\{Causal\}\}\. The best results are inbold\.![Refer to caption](https://arxiv.org/html/2607.09695v1/x1.png)Figure 2:Ablation study visualization showing the contribution of each component across three datasets\. The full model \(C\+R\+G\+P\) consistently achieves the highest accuracy\.![Refer to caption](https://arxiv.org/html/2607.09695v1/x2.png)Figure 3:Heatmap showing the performance contribution of each component \(C: Causal\-Domain Feature Separation, R: Reliable Aggregation, G: Collaborative Regularization, P: Privacy Mixup\) across the three benchmark datasets\.
### 5\.2Analysis of Reliability\-Aware Aggregation

The reliable aggregation mechanism \(Eq\.[6](https://arxiv.org/html/2607.09695#S3.E6)\) assigns weightωn,kt\\omega\_\{n,k\}^\{t\}to each local prototype\. We investigate two practical strategies for computingωn,kt\\omega\_\{n,k\}^\{t\}:Accuracy\-based \(Acc\), derived from the client’s local validation accuracy for classkk;Consistency\-based \(Con\), the inverse of the intra\-class feature variance for classkk; andUniform, whereωn,kt=1\\omega\_\{n,k\}^\{t\}=1, which degenerates to sample\-count averaging\. Table[6](https://arxiv.org/html/2607.09695#S5.T6)compares these strategies\. Both proposed reliability\-aware strategies outperform uniform averaging, with the accuracy\-based method achieving the best overall results\. This validates that weighting prototypes by their estimated quality yields a more robust and informative global representation, particularly for datasets like Office\-10 and PACS with higher heterogeneity\.

Table 6:Analysis of different reliability weight \(ωn,kt\\omega\_\{n,k\}^\{t\}\) calculation strategies within the Reliable Prototype Aggregation module\. “Uniform” is equivalent to common averaging\.
### 5\.3Impact of Feature Separation and Regularization Balance

Our causal\-domain feature separation involves two projection heads,CCandSS, trained with lossesℒCausal\\mathcal\{L\}\_\{\\text\{Causal\}\},ℒInv\\mathcal\{L\}\_\{\\text\{Inv\}\}, andℒSpur\\mathcal\{L\}\_\{\\text\{Spur\}\}\. We analyze its impact by comparing against a variant that uses a single shared representation with a unified adversarial loss against a domain discriminator\. Furthermore, we study the effect of the balance hyperparameterλ\\lambdainℒReg\\mathcal\{L\}\_\{\\text\{Reg\}\}\(Eq\.[7](https://arxiv.org/html/2607.09695#S3.E7)\), which controls the strength of the domain invariance termℒInv\\mathcal\{L\}\_\{\\text\{Inv\}\}relative to the prototype alignmentℒAlign\\mathcal\{L\}\_\{\\text\{Align\}\}\. Results are shown in Table[7](https://arxiv.org/html/2607.09695#S5.T7)\.

Our explicit separation \(C\) consistently outperforms the unified adversarial approach \(Single\-Adv\), especially on PACS \(\+1\.85%\)\. This proves that explicitly modeling and isolating spurious features is superior to indiscriminately adversarially aligning all features\. The performance is robust to a range ofλ\\lambdavalues \(0\.1 to 1\.0\), withλ=0\.5\\lambda=0\.5yielding the best or near\-best results\. Settingλ=0\\lambda=0\(only alignment, no invariance\) leads to a noticeable drop, highlighting the necessity of the domain invariance constraint\. Conversely, an overly strong invariance penalty \(λ=2\.0\\lambda=2\.0\) also degrades performance\.

Table 7:Impact of feature separation design and the regularization balance hyperparameterλ\\lambda\. “Single\-Adv” replaces our separation with a single feature vector trained with adversarial loss\.![Refer to caption](https://arxiv.org/html/2607.09695v1/x3.png)Figure 4:Sensitivity analysis of the regularization balance hyperparameterλ\\lambdaacross the three benchmark datasets\. Performance is robust within a wide range ofλ\\lambdavalues, with optimal results achieved aroundλ=0\.5\\lambda=0\.5\.
### 5\.4Effectiveness of the Collaborative Regularization Formulation

We analyze the specific contribution of the prototype contrastive alignment termℒAlign\\mathcal\{L\}\_\{\\text\{Align\}\}within the collaborative regularizationℒReg\\mathcal\{L\}\_\{\\text\{Reg\}\}\. Table[8](https://arxiv.org/html/2607.09695#S5.T8)compares our formulation against two alternatives: using the InfoNCE loss on the causal features, and using a simple mean squared error \(MSE\) loss to pull features towards the global prototype\. Our contrastive alignment based on cosine similarity consistently outperforms the alternatives\. The InfoNCE loss performs slightly worse, potentially due to its sensitivity to negative sample construction in the federated setting\. The MSE loss yields the poorest results, indicating that merely reducing feature distance is less effective than structuring the feature space via contrastive learning for handling drift\.

Table 8:Ablation on the formulation of the feature alignment component within the collaborative regularization\. “Ours \(ℒAlign\\mathcal\{L\}\_\{\\text\{Align\}\}\)” refers to the contrastive loss defined in Eq\.[7](https://arxiv.org/html/2607.09695#S3.E7)\.

## 6Supplementary Experiments

### 6\.1Training Curve Analysis

We examine the optimization dynamics and convergence behavior of FedCausal\-Dyn by analyzing training curves across communication rounds\. Based on the three random trials conducted for the main results, we plot the average training loss and test accuracy on a held\-out validation set for each dataset against the communication round\. Compared to key baselines \(FedAvg and FedPall\), FedCausal\-Dyn achieves a lower training loss and higher validation accuracy at a faster rate\. More importantly, its curves exhibit less oscillation and converge to a more stable plateau, aligning with its superior final performance and lower standard deviation reported in the main results\. This smoother convergence can be attributed to the reliable prototype aggregation, which filters out noisy updates, and the causal\-feature guided regularization, which provides a stable and consistent learning signal amidst dynamic feature drift\. The training curve analysis visually corroborates our method’s effectiveness in achieving robust and efficient federated training\.

![Refer to caption](https://arxiv.org/html/2607.09695v1/x4.png)Figure 5:Training curves showing loss and accuracy progression across communication rounds for three datasets\. FedCausal\-Dyn exhibits faster convergence and more stable optimization dynamics compared to baselines\.
### 6\.2Case Study: Feature Visualization and Prototype Analysis

We conduct a qualitative case study on the PACS dataset, focusing on thecartoonandsketchsub\-domains where FedCausal\-Dyn shows significant gains\. We visualize the learned causal features𝐳c\\mathbf\{z\}\_\{c\}and spurious features𝐳s\\mathbf\{z\}\_\{s\}using t\-SNE\. The visualization shows a clear separation: causal features from different sub\-domains but the same class cluster together, while spurious features form distinct clusters based on their domain origin\. This visually confirms the efficacy of our causal\-domain feature separation module\. We also analyze the reliability weightsωn,kt\\omega\_\{n,k\}^\{t\}assigned during prototype aggregation for representative classes\. The results show that clients with higher local validation accuracy and more consistent intra\-class features are assigned higher weights\. This case study provides intuitive evidence for how feature separation and reliable aggregation work synergistically to improve model generalization\.

### 6\.3Extended Analyses

To further validate the robustness and general applicability of FedCausal\-Dyn, we identify two potential extended analyses based on common practices in related works\. An analysis of the impact of varying client participation rates per communication round could be conducted by running FedCausal\-Dyn and baselines under different levels of partial client participation to evaluate the framework’s sensitivity and robustness to client availability\. Testing the framework’s resilience against data heterogeneity and label noise would also be valuable by constructing new experimental splits or injecting controlled noise into existing datasets to simulate more challenging non\-IID and noisy conditions\. The performance of FedCausal\-Dyn under such conditions could further highlight the advantages of its causal\-dynamic paradigm\.

## 7Limitations

While FedCausal\-Dyn demonstrates strong performance across multiple benchmarks, several limitations warrant discussion\. The framework introduces additional computational overhead through the causal\-domain feature separation module and reliability weight estimation, which may impact scalability in resource\-constrained edge devices\. The reliability\-aware aggregation relies on the availability of held\-out validation data at each client, which may not always be feasible in extreme data\-scarcity scenarios\. Furthermore, the current formulation assumes that the causal\-spurious decomposition is achievable through the proposed adversarial learning scheme; however, in domains with highly entangled causal and spurious factors, the separation may be less effective\. Future work could explore more efficient architectures, alternative reliability estimation methods that do not require validation data, and theoretical analysis of the conditions under which the causal\-spurious decomposition is well\-defined\.

## 8Conclusion

This work addresses the critical challenge of dynamic feature drift in federated learning, a prevalent issue in real\-world applications such as financial technology with non\-stationary data streams\. To tackle this problem, we proposedFedCausal\-Dyn, a novel framework based on a causal\-dynamic paradigm\. It incorporates three core innovations: explicit Causal\-Domain Feature Separation to disentangle invariant predictive features from spurious domain\-specific variations, Reliable and Dynamic Prototype Aggregation which weights local knowledge by its estimated quality, and Causal\-Feature Guided Collaborative Regularization to align local features with robust global prototypes while enforcing domain invariance\.

Extensive evaluations on three federated domain generalization benchmarks \(Office\-10,Digits, andPACS\) demonstrate the superior performance of FedCausal\-Dyn\. Our method achieves state\-of\-the\-art average accuracy across all datasets \(68\.95%, 89\.34%, and 61\.26%, respectively\), consistently outperforming a comprehensive suite of strong baselines\. Moreover, it exhibits the most stable performance, as evidenced by the lowest average standard deviation \(1\.15\) in all trials\.

Ablation studies confirm the contribution of each component\. The Causal\-Feature Guided Collaborative Regularization is identified as the most critical, while explicit feature separation is essential to prevent performance degradation\. Both the reliability\-aware aggregation and the privacy\-enhanced mixup provide complementary benefits, underscoring the synergistic design\. Supplementary analyses, including training curves and feature visualizations, further support the framework’s robust optimization dynamics and its ability to learn well\-separated, domain\-invariant causal representations\.

FedCausal\-Dyn offers a robust and principled solution for federated learning in dynamic, heterogeneous environments\. Future work may explore its application to other non\-stationary learning scenarios and investigate adaptive mechanisms for reliability weight estimation\.

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