发表机构
Sapienza University of Rome（罗马第一大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对异构联邦系统的表示学习挑战，提出Sheaf-FRL框架，通过层束限制映射实现相邻潜在表示对齐，在协作分类任务中优于基线方法且鲁棒性更强。
AI 中文摘要
异构联邦系统中，智能体需在数据分布、感知模态、模型架构、潜在维度及局部学习目标存在差异的情况下学习并交换有效表示。为应对这一挑战，我们提出基于层束的联邦表示学习（Sheaf-based Federated Representation Learning，SFRL），这是一个通用框架，它结合了局部目标与基于可学习层束限制映射的流形约束几何对齐正则项进行联合优化。与多数现有方法不同，SFRL不假设存在共享的全局潜在空间，相反，全局一致性通过正交变换和等距嵌入实现的相邻潜在表示对齐而自然产生。这种对齐由层束拉普拉斯算子诱导的二次粘合正则项强制执行，其可学习限制映射会根据观测数据调整几何结构。该惩罚项在一小部分共享试点样本上进行评估，确保了可扩展性和通信效率。我们开发了用于求解SFRL的去中心化算法，命名为Sheaf-FRL，该算法在局部模型的梯度更新与边级限制映射的闭式Procrustes更新之间交替进行。我们进一步证明了Sheaf-FRL在确定性和随机设定下均能收敛到一阶平稳点。作为应用，我们考虑语义通信场景下模型与数据异构性条件下的协作分类任务，结果表明，在不同程度的局部分布偏移下，Sheaf-FRL在局部和通信后分类准确率方面均优于基线方法，且对潜在空间维度压缩表现出更强的鲁棒性。
英文摘要
Heterogeneous federated systems require agents to learn and exchange informative representations despite differences in data distributions, sensing modalities, model architectures, latent dimensionalities, and local learning objectives. To address this challenge, we propose Sheaf-based Federated Representation Learning (SFRL), a general framework that jointly optimizes local objectives with a manifold-constrained geometric alignment regularizer based on learnable sheaf restriction maps. Unlike most existing approaches, SFRL does not assume a shared global latent space. Instead, global consistency emerges from the alignment of neighboring latent representations through orthogonal transformations and isometric embeddings. This alignment is enforced by a quadratic gluing regularizer induced by the sheaf Laplacian, whose learnable restriction maps adapt the geometry to the observed data. The penalty is evaluated on a small set of shared pilot samples, ensuring scalability and communication efficiency. We develop a decentralized algorithm for solving SFRL, termed Sheaf-FRL, which alternates between gradient updates of the local models and closed-form Procrustes updates of the edge-wise restriction maps. We further establish convergence of Sheaf-FRL to first-order stationary points in both deterministic and stochastic settings. As an application, we consider a cooperative classification task in the context of semantic communication, under model and data heterogeneity. Our results show that Sheaf-FRL outperforms baseline approaches in terms of local and post-communication classification accuracy across different levels of local distribution shift and exhibits greater robustness to latent-space dimensionality compression.
