Jingwen Fu

Haoran Zhang, Shuanghao Bai, Wanqi Zhou et al.

Source-free domain generalization (SFDG) tackles the challenge of adapting models to unseen target domains without access to source domain data. To deal with this challenging task, recent advances in SFDG have primarily focused on leveraging the text modality of vision-language models such as CLIP. These methods involve developing a transferable linear classifier based on diverse style features extracted from the text and learned prompts or deriving domain-unified text representations from domain banks. However, both style features and domain banks have limitations in capturing comprehensive domain knowledge. In this work, we propose Prompt-Driven Text Adapter (PromptTA) method, which is designed to better capture the distribution of style features and employ resampling to ensure thorough coverage of domain knowledge. To further leverage this rich domain information, we introduce a text adapter that learns from these style features for efficient domain information storage. Extensive experiments conducted on four benchmark datasets demonstrate that PromptTA achieves state-of-the-art performance. The code is available at https://github.com/zhanghr2001/PromptTA.

Bohan Wang, Jingwen Fu, Huishuai Zhang et al.

Recently, Arjevani et al. [1] established a lower bound of iteration complexity for the first-order optimization under an $L$-smooth condition and a bounded noise variance assumption. However, a thorough review of existing literature on Adam's convergence reveals a noticeable gap: none of them meet the above lower bound. In this paper, we close the gap by deriving a new convergence guarantee of Adam, with only an $L$-smooth condition and a bounded noise variance assumption. Our results remain valid across a broad spectrum of hyperparameters. Especially with properly chosen hyperparameters, we derive an upper bound of the iteration complexity of Adam and show that it meets the lower bound for first-order optimizers. To the best of our knowledge, this is the first to establish such a tight upper bound for Adam's convergence. Our proof utilizes novel techniques to handle the entanglement between momentum and adaptive learning rate and to convert the first-order term in the Descent Lemma to the gradient norm, which may be of independent interest.

Jingwen Fu, Bohan Wang, Huishuai Zhang et al.

Momentum has become a crucial component in deep learning optimizers, necessitating a comprehensive understanding of when and why it accelerates stochastic gradient descent (SGD). To address the question of ''when'', we establish a meaningful comparison framework that examines the performance of SGD with Momentum (SGDM) under the \emph{effective learning rates} $η_{ef}$, a notion unifying the influence of momentum coefficient $μ$ and batch size $b$ over learning rate $η$. In the comparison of SGDM and SGD with the same effective learning rate and the same batch size, we observe a consistent pattern: when $η_{ef}$ is small, SGDM and SGD experience almost the same empirical training losses; when $η_{ef}$ surpasses a certain threshold, SGDM begins to perform better than SGD. Furthermore, we observe that the advantage of SGDM over SGD becomes more pronounced with a larger batch size. For the question of ``why'', we find that the momentum acceleration is closely related to \emph{abrupt sharpening} which is to describe a sudden jump of the directional Hessian along the update direction. Specifically, the misalignment between SGD and SGDM happens at the same moment that SGD experiences abrupt sharpening and converges slower. Momentum improves the performance of SGDM by preventing or deferring the occurrence of abrupt sharpening. Together, this study unveils the interplay between momentum, learning rates, and batch sizes, thus improving our understanding of momentum acceleration.

Jingwen Fu, Zhizheng Zhang, Dacheng Yin et al.

This paper explores the connection between learning trajectories of Deep Neural Networks (DNNs) and their generalization capabilities when optimized using (stochastic) gradient descent algorithms. Instead of concentrating solely on the generalization error of the DNN post-training, we present a novel perspective for analyzing generalization error by investigating the contribution of each update step to the change in generalization error. This perspective allows for a more direct comprehension of how the learning trajectory influences generalization error. Building upon this analysis, we propose a new generalization bound that incorporates more extensive trajectory information. Our proposed generalization bound depends on the complexity of learning trajectory and the ratio between the bias and diversity of training set. Experimental findings reveal that our method effectively captures the generalization error throughout the training process. Furthermore, our approach can also track changes in generalization error when adjustments are made to learning rates and label noise levels. These results demonstrate that learning trajectory information is a valuable indicator of a model's generalization capabilities.

Jingwen Fu, Nanning Zheng

This paper explores the generalization characteristics of iterative learning algorithms with bounded updates for non-convex loss functions, employing information-theoretic techniques. Our key contribution is a novel bound for the generalization error of these algorithms with bounded updates. Our approach introduces two main novelties: 1) we reformulate the mutual information as the uncertainty of updates, providing a new perspective, and 2) instead of using the chaining rule of mutual information, we employ a variance decomposition technique to decompose information across iterations, allowing for a simpler surrogate process. We analyze our generalization bound under various settings and demonstrate improved bounds. To bridge the gap between theory and practice, we also examine the previously observed scaling behavior in large language models. Ultimately, our work takes a further step for developing practical generalization theories.

Jingwen Fu, Zhizheng Zhang, Yan Lu et al.

Compositional Generalization (CG) embodies the ability to comprehend novel combinations of familiar concepts, representing a significant cognitive leap in human intellectual advancement. Despite its critical importance, the deep neural network (DNN) faces challenges in addressing the compositional generalization problem, prompting considerable research interest. However, existing theories often rely on task-specific assumptions, constraining the comprehensive understanding of CG. This study aims to explore compositional generalization from a task-agnostic perspective, offering a complementary viewpoint to task-specific analyses. The primary challenge is to define CG without overly restricting its scope, a feat achieved by identifying its fundamental characteristics and basing the definition on them. Using this definition, we seek to answer the question "what does the ultimate solution to CG look like?" through the following theoretical findings: 1) the first No Free Lunch theorem in CG, indicating the absence of general solutions; 2) a novel generalization bound applicable to any CG problem, specifying the conditions for an effective CG solution; and 3) the introduction of the generative effect to enhance understanding of CG problems and their solutions. This paper's significance lies in providing a general theory for CG problems, which, when combined with prior theorems under task-specific scenarios, can lead to a comprehensive understanding of CG.