Despite a strong theoretical foundation, empirical experiments reveal that existing domain generalization (DG) algorithms often fail to consistently outperform the ERM baseline. We argue that this issue arises because most DG studies focus on establishing theoretical guarantees for generalization under unrealistic assumptions, such as the availability of sufficient, diverse (or even infinite) domains or access to target domain knowledge. As a result, the extent to which domain generalization is achievable in scenarios with limited domains remains largely unexplored. This paper seeks to address this gap by examining generalization through the lens of the conditions necessary for its existence and learnability. Specifically, we systematically establish a set of necessary and sufficient conditions for generalization. Our analysis highlights that existing DG methods primarily act as regularization mechanisms focused on satisfying sufficient conditions, while often neglecting necessary ones. However, sufficient conditions cannot be verified in settings with limited training domains. In such cases, regularization targeting sufficient conditions aims to maximize the likelihood of generalization, whereas regularization targeting necessary conditions ensures its existence. Using this analysis, we reveal the shortcomings of existing DG algorithms by showing that, while they promote sufficient conditions, they inadvertently violate necessary conditions. To validate our theoretical insights, we propose a practical method that promotes the sufficient condition while maintaining the necessary conditions through a novel subspace representation alignment strategy. This approach highlights the advantages of preserving the necessary conditions on well-established DG benchmarks.

Sharpness-Aware Minimization (SAM) has attracted significant attention for its effectiveness in improving generalization across various tasks. However, its underlying principles remain poorly understood. In this work, we analyze SAM's training dynamics using the maximum eigenvalue of the Hessian as a measure of sharpness, and propose a third-order stochastic differential equation (SDE), which reveals that the dynamics are driven by a complex mixture of second- and third-order terms. We show that alignment between the perturbation vector and the top eigenvector is crucial for SAM's effectiveness in regularizing sharpness, but find that this alignment is often inadequate in practice, limiting SAM's efficiency. Building on these insights, we introduce Eigen-SAM, an algorithm that explicitly aims to regularize the top Hessian eigenvalue by aligning the perturbation vector with the leading eigenvector. We validate the effectiveness of our theory and the practical advantages of our proposed approach through comprehensive experiments. Code is available at https://github.com/RitianLuo/EigenSAM.

Federated Class-Incremental Learning (FCIL) is an underexplored yet pivotal issue, involving the dynamic addition of new classes in the context of federated learning. In this field, Data-Free Knowledge Transfer (DFKT) plays a crucial role in addressing catastrophic forgetting and data privacy problems. However, prior approaches lack the crucial synergy between DFKT and the model training phases, causing DFKT to encounter difficulties in generating high-quality data from a non-anchored latent space of the old task model. In this paper, we introduce LANDER (Label Text Centered Data-Free Knowledge Transfer) to address this issue by utilizing label text embeddings (LTE) produced by pretrained language models. Specifically, during the model training phase, our approach treats LTE as anchor points and constrains the feature embeddings of corresponding training samples around them, enriching the surrounding area with more meaningful information. In the DFKT phase, by using these LTE anchors, LANDER can synthesize more meaningful samples, thereby effectively addressing the forgetting problem. Additionally, instead of tightly constraining embeddings toward the anchor, the Bounding Loss is introduced to encourage sample embeddings to remain flexible within a defined radius. This approach preserves the natural differences in sample embeddings and mitigates the embedding overlap caused by heterogeneous federated settings. Extensive experiments conducted on CIFAR100, Tiny-ImageNet, and ImageNet demonstrate that LANDER significantly outperforms previous methods and achieves state-of-the-art performance in FCIL. The code is available at https://github.com/tmtuan1307/lander.

Machine unlearning has become a pivotal task to erase the influence of data from a trained model. It adheres to recent data regulation standards and enhances the privacy and security of machine learning applications. Most existing machine unlearning methods perform well, however, they typically necessitate access to the entirety of the remaining data, which might not be feasible in certain scenarios. In this work, we present a new machine unlearning approach Scissorhands, which operates effectively with only a subset of the training data. Initially, Scissorhands identifies the most pertinent parameters in the given model relative to the forgetting data via connection sensitivity. This process involves reinitializing the most influential top-$k$ percent of these parameters, resulting in a trimmed model for erasing the influence of the forgetting data. Subsequently, Scissorhands retrains the trimmed model through a min-max optimization process, seeking parameters that preserve information on the remaining data while discarding information related to the forgetting data. Our experimental results, conducted across five distinct datasets and utilizing both CNN and ViT, demonstrate that Scissorhands, despite utilizing only a limited portion of the training data, showcases competitive performance when compared to existing methods.

We introduce a language-grounded visual prompting method to adapt the visual encoder of vision-language models for downstream tasks. By capitalizing on language integration, we devise a parameter-efficient strategy to adjust the input of the visual encoder, eliminating the need to modify or add to the model's parameters. Due to this design choice, our algorithm can operate even in black-box scenarios, showcasing adaptability in situations where access to the model's parameters is constrained. We will empirically demonstrate that, compared to prior art, grounding visual prompts with language enhances both the accuracy and speed of adaptation. Moreover, our algorithm excels in base-to-novel class generalization, overcoming limitations of visual prompting and exhibiting the capacity to generalize beyond seen classes. We thoroughly assess and evaluate our method across a variety of image recognition datasets, such as EuroSAT, UCF101, DTD, and CLEVR, spanning different learning situations, including few-shot learning, base-to-novel class generalization, and transfer learning.

Federated Learning (FL) is a distributed learning paradigm that enhances users privacy by eliminating the need for clients to share raw, private data with the server. Despite the success, recent studies expose the vulnerability of FL to model inversion attacks, where adversaries reconstruct users private data via eavesdropping on the shared gradient information. We hypothesize that a key factor in the success of such attacks is the low entanglement among gradients per data within the batch during stochastic optimization. This creates a vulnerability that an adversary can exploit to reconstruct the sensitive data. Building upon this insight, we present a simple, yet effective defense strategy that obfuscates the gradients of the sensitive data with concealed samples. To achieve this, we propose synthesizing concealed samples to mimic the sensitive data at the gradient level while ensuring their visual dissimilarity from the actual sensitive data. Compared to the previous art, our empirical evaluations suggest that the proposed technique provides the strongest protection while simultaneously maintaining the FL performance.

Nowadays, understanding the geometry of the loss landscape shows promise in enhancing a model's generalization ability. In this work, we draw upon prior works that apply geometric principles to optimization and present a novel approach to improve robustness and generalization ability for constrained optimization problems. Indeed, this paper aims to generalize the Sharpness-Aware Minimization (SAM) optimizer to Riemannian manifolds. In doing so, we first extend the concept of sharpness and introduce a novel notion of sharpness on manifolds. To support this notion of sharpness, we present a theoretical analysis characterizing generalization capabilities with respect to manifold sharpness, which demonstrates a tighter bound on the generalization gap, a result not known before. Motivated by this analysis, we introduce our algorithm, Riemannian Sharpness-Aware Minimization (RSAM). To demonstrate RSAM's ability to enhance generalization ability, we evaluate and contrast our algorithm on a broad set of problems, such as image classification and contrastive learning across different datasets, including CIFAR100, CIFAR10, and FGVCAircraft. Our code is publicly available at \url{https://t.ly/RiemannianSAM}.

The performance of a lifelong learning (L3) model degrades when it is trained on a series of tasks, as the geometrical formation of the embedding space changes while learning novel concepts sequentially. The majority of existing L3 approaches operate on a fixed-curvature (e.g., zero-curvature Euclidean) space that is not necessarily suitable for modeling the complex geometric structure of data. Furthermore, the distillation strategies apply constraints directly on low-dimensional embeddings, discouraging the L3 model from learning new concepts by making the model highly stable. To address the problem, we propose a distillation strategy named L3DMC that operates on mixed-curvature spaces to preserve the already-learned knowledge by modeling and maintaining complex geometrical structures. We propose to embed the projected low dimensional embedding of fixed-curvature spaces (Euclidean and hyperbolic) to higher-dimensional Reproducing Kernel Hilbert Space (RKHS) using a positive-definite kernel function to attain rich representation. Afterward, we optimize the L3 model by minimizing the discrepancies between the new sample representation and the subspace constructed using the old representation in RKHS. L3DMC is capable of adapting new knowledge better without forgetting old knowledge as it combines the representation power of multiple fixed-curvature spaces and is performed on higher-dimensional RKHS. Thorough experiments on three benchmarks demonstrate the effectiveness of our proposed distillation strategy for medical image classification in L3 settings. Our code implementation is publicly available at https://github.com/csiro-robotics/L3DMC.

An ultimate objective in continual learning is to preserve knowledge learned in preceding tasks while learning new tasks. To mitigate forgetting prior knowledge, we propose a novel knowledge distillation technique that takes into the account the manifold structure of the latent/output space of a neural network in learning novel tasks. To achieve this, we propose to approximate the data manifold up-to its first order, hence benefiting from linear subspaces to model the structure and maintain the knowledge of a neural network while learning novel concepts. We demonstrate that the modeling with subspaces provides several intriguing properties, including robustness to noise and therefore effective for mitigating Catastrophic Forgetting in continual learning. We also discuss and show how our proposed method can be adopted to address both classification and segmentation problems. Empirically, we observe that our proposed method outperforms various continual learning methods on several challenging datasets including Pascal VOC, and Tiny-Imagenet. Furthermore, we show how the proposed method can be seamlessly combined with existing learning approaches to improve their performances. The codes of this article will be available at https://github.com/csiro-robotics/SDCL.

Learning deep discrete latent presentations offers a promise of better symbolic and summarized abstractions that are more useful to subsequent downstream tasks. Inspired by the seminal Vector Quantized Variational Auto-Encoder (VQ-VAE), most of work in learning deep discrete representations has mainly focused on improving the original VQ-VAE form and none of them has studied learning deep discrete representations from the generative viewpoint. In this work, we study learning deep discrete representations from the generative viewpoint. Specifically, we endow discrete distributions over sequences of codewords and learn a deterministic decoder that transports the distribution over the sequences of codewords to the data distribution via minimizing a WS distance between them. We develop further theories to connect it with the clustering viewpoint of WS distance, allowing us to have a better and more controllable clustering solution. Finally, we empirically evaluate our method on several well-known benchmarks, where it achieves better qualitative and quantitative performances than the other VQ-VAE variants in terms of the codebook utilization and image reconstruction/generation.