Introducing Fractional Classification Loss for Robust Learning with Noisy Labels

Robust loss functions are crucial for training deep neural networks in the presence of label noise, yet existing approaches require extensive, dataset-specific hyperparameter tuning. In this work, we introduce Fractional Classification Loss (FCL), an adaptive robust loss that automatically calibrates its robustness to label noise during training. Built within the active-passive loss framework, FCL employs the fractional derivative of the Cross-Entropy (CE) loss as its active component and the Mean Absolute Error (MAE) as its passive loss component. With this formulation, we demonstrate that the fractional derivative order $\mu$ spans a family of loss functions that interpolate between MAE-like robustness and CE-like fast convergence. Furthermore, we integrate $\mu$ into the gradient-based optimization as a learnable parameter and automatically adjust it to optimize the trade-off between robustness and convergence speed. We reveal that FCL's unique property establishes a critical trade-off that enables the stable learning of $\mu$: lower log penalties on difficult or mislabeled examples improve robustness but impose higher penalties on easy or clean data, reducing model confidence in them. Consequently, FCL can dynamically reshape its loss landscape to achieve effective classification performance under label noise. Extensive experiments on benchmark datasets show that FCL achieves state-of-the-art results without the need for manual hyperparameter tuning.

Redefining Clustered Federated Learning for System Identification: The Path of ClusterCraft

This paper addresses the System Identification (SYSID) problem within the framework of federated learning. We introduce a novel algorithm, Incremental Clustering-based federated learning method for SYSID (IC-SYSID), designed to tackle SYSID challenges across multiple data sources without prior knowledge. IC-SYSID utilizes an incremental clustering method, ClusterCraft (CC), to eliminate the dependency on the prior knowledge of the dataset. CC starts with a single cluster model and assigns similar local workers to the same clusters by dynamically increasing the number of clusters. To reduce the number of clusters generated by CC, we introduce ClusterMerge, where similar cluster models are merged. We also introduce enhanced ClusterCraft to reduce the generation of similar cluster models during the training. Moreover, IC-SYSID addresses cluster model instability by integrating a regularization term into the loss function and initializing cluster models with scaled Glorot initialization. It also utilizes a mini-batch deep learning approach to manage large SYSID datasets during local training. Through the experiments conducted on a real-world representing SYSID problem, where a fleet of vehicles collaboratively learns vehicle dynamics, we show that IC-SYSID achieves a high SYSID performance while preventing the learning of unstable clusters.

A State Alignment-Centric Approach to Federated System Identification: The FedAlign Framework

This paper presents FedAlign, a Federated Learning (FL) framework particularly designed for System Identification (SYSID) tasks by aligning state representations. Local workers can learn State-Space Models (SSMs) with equivalent representations but different dynamics. We demonstrate that directly aggregating these local SSMs via FedAvg results in a global model with altered system dynamics. FedAlign overcomes this problem by employing similarity transformation matrices to align state representations of local SSMs, thereby establishing a common parameter basin that retains the dynamics of local SSMs. FedAlign computes similarity transformation matrices via two distinct approaches: FedAlign-A and FedAlign-O. In FedAlign-A, we represent the global SSM in controllable canonical form (CCF). We apply control theory to analytically derive similarity transformation matrices that convert each local SSM into this form. Yet, establishing global SSM in CCF brings additional alignment challenges in multi input - multi output SYSID as CCF representation is not unique, unlike in single input - single output SYSID. In FedAlign-O, we address these alignment challenges by reformulating the local parameter basin alignment problem as an optimization task. We determine the parameter basin of a local worker as the common parameter basin and solve least square problems to obtain similarity transformation matrices needed to align the remaining local SSMs. Through the experiments conducted on synthetic and real-world datasets, we show that FedAlign outperforms FedAvg, converges faster, and provides improved stability of the global SSM thanks to the efficient alignment of local parameter basins.