Di Fang

Run He, Kai Tong, Di Fang et al.

In this paper, we introduce analytic federated learning (AFL), a new training paradigm that brings analytical (i.e., closed-form) solutions to the federated learning (FL) with pre-trained models. Our AFL draws inspiration from analytic learning -- a gradient-free technique that trains neural networks with analytical solutions in one epoch. In the local client training stage, the AFL facilitates a one-epoch training, eliminating the necessity for multi-epoch updates. In the aggregation stage, we derive an absolute aggregation (AA) law. This AA law allows a single-round aggregation, reducing heavy communication overhead and achieving fast convergence by removing the need for multiple aggregation rounds. More importantly, the AFL exhibits a property that \textit{invariance to data partitioning}, meaning that regardless of how the full dataset is distributed among clients, the aggregated result remains identical. This could spawn various potentials, such as data heterogeneity invariance and client-number invariance. We conduct experiments across various FL settings including extremely non-IID ones, and scenarios with a large number of clients (e.g., $\ge 1000$). In all these settings, our AFL constantly performs competitively while existing FL techniques encounter various obstacles. Our codes are available at https://github.com/ZHUANGHP/Analytic-federated-learning.

Hsin-Yuan Huang, Yu Tong, Di Fang et al.

Learning a many-body Hamiltonian from its dynamics is a fundamental problem in physics. In this work, we propose the first algorithm to achieve the Heisenberg limit for learning an interacting $N$-qubit local Hamiltonian. After a total evolution time of $\mathcal{O}(ε^{-1})$, the proposed algorithm can efficiently estimate any parameter in the $N$-qubit Hamiltonian to $ε$-error with high probability. The proposed algorithm is robust against state preparation and measurement error, does not require eigenstates or thermal states, and only uses $\mathrm{polylog}(ε^{-1})$ experiments. In contrast, the best previous algorithms, such as recent works using gradient-based optimization or polynomial interpolation, require a total evolution time of $\mathcal{O}(ε^{-2})$ and $\mathcal{O}(ε^{-2})$ experiments. Our algorithm uses ideas from quantum simulation to decouple the unknown $N$-qubit Hamiltonian $H$ into noninteracting patches, and learns $H$ using a quantum-enhanced divide-and-conquer approach. We prove a matching lower bound to establish the asymptotic optimality of our algorithm.

Huiping Zhuang, Yizhu Chen, Di Fang et al.

Class incremental learning (CIL) trains a network on sequential tasks with separated categories in each task but suffers from catastrophic forgetting, where models quickly lose previously learned knowledge when acquiring new tasks. The generalized CIL (GCIL) aims to address the CIL problem in a more real-world scenario, where incoming data have mixed data categories and unknown sample size distribution. Existing attempts for the GCIL either have poor performance or invade data privacy by saving exemplars. In this paper, we propose a new exemplar-free GCIL technique named generalized analytic continual learning (GACL). The GACL adopts analytic learning (a gradient-free training technique) and delivers an analytical (i.e., closed-form) solution to the GCIL scenario. This solution is derived via decomposing the incoming data into exposed and unexposed classes, thereby attaining a weight-invariant property, a rare yet valuable property supporting an equivalence between incremental learning and its joint training. Such an equivalence is crucial in GCIL settings as data distributions among different tasks no longer pose challenges to adopting our GACL. Theoretically, this equivalence property is validated through matrix analysis tools. Empirically, we conduct extensive experiments where, compared with existing GCIL methods, our GACL exhibits a consistently leading performance across various datasets and GCIL settings. Source code is available at https://github.com/CHEN-YIZHU/GACL.

Xiang Zhang, Run He, Jiao Chen et al.

Class-incremental learning (CIL) enables models to learn new classes continually without forgetting previously acquired knowledge. Multi-label CIL (MLCIL) extends CIL to a real-world scenario where each sample may belong to multiple classes, introducing several challenges: label absence, which leads to incomplete historical information due to missing labels, and class imbalance, which results in the model bias toward majority classes. To address these challenges, we propose Label-Augmented Analytic Adaptation (L3A), an exemplar-free approach without storing past samples. L3A integrates two key modules. The pseudo-label (PL) module implements label augmentation by generating pseudo-labels for current phase samples, addressing the label absence problem. The weighted analytic classifier (WAC) derives a closed-form solution for neural networks. It introduces sample-specific weights to adaptively balance the class contribution and mitigate class imbalance. Experiments on MS-COCO and PASCAL VOC datasets demonstrate that L3A outperforms existing methods in MLCIL tasks. Our code is available at https://github.com/scut-zx/L3A.

Run He, Di Fang, Yizhu Chen et al.

Exemplar-free class-incremental learning (EFCIL) aims to mitigate catastrophic forgetting in class-incremental learning (CIL) without available historical training samples as exemplars. Compared with its exemplar-based CIL counterpart that stores exemplars, EFCIL suffers more from forgetting issues. Recently, a new EFCIL branch named Analytic Continual Learning (ACL) introduces a gradient-free paradigm via Recursive Least-Square, achieving a forgetting-resistant classifier training with a frozen backbone during CIL. However, existing ACL suffers from ineffective representations and insufficient utilization of backbone knowledge. In this paper, we propose a representation-enhanced analytic learning (REAL) to address these problems. To enhance the representation, REAL constructs a dual-stream base pretraining followed by representation enhancing distillation process. The dual-stream base pretraining combines self-supervised contrastive learning for general features and supervised learning for class-specific knowledge, followed by the representation enhancing distillation to merge both streams, enhancing representations for subsequent CIL paradigm. To utilize more knowledge from the backbone, REAL presents a feature fusion buffer to multi-layer backbone features, providing informative features for the subsequent classifier training. Our method can be incorporated into existing ACL techniques and provides more competitive performance. Empirical results demonstrate that, REAL achieves state-of-the-art performance on CIFAR-100, ImageNet-100 and ImageNet-1k benchmarks, outperforming exemplar-free methods and rivaling exemplar-based approaches.