We propose a framework grounded in gradient flow theory and informed by geometric structure that provides multiple diverse solutions for a given task, ensuring collaborative results that enhance performance and adaptability across different tasks. This framework enables flexibility, allowing for efficient task-specific fine-tuning while preserving the knowledge of the pre-trained foundation models. Extensive experiments across transfer learning, few-shot learning, and domain generalization show that our proposed approach consistently outperforms existing Bayesian methods, delivering strong performance with affordable computational overhead and offering a practical solution by updating only a small subset of parameters.

Knowledge distillation is an attractive approach for learning compact deep neural networks, which learns a lightweight student model by distilling knowledge from a complex teacher model. Attention-based knowledge distillation is a specific form of intermediate feature-based knowledge distillation that uses attention mechanisms to encourage the student to better mimic the teacher. However, most of the previous attention-based distillation approaches perform attention in the spatial domain, which primarily affects local regions in the input image. This may not be sufficient when we need to capture the broader context or global information necessary for effective knowledge transfer. In frequency domain, since each frequency is determined from all pixels of the image in spatial domain, it can contain global information about the image. Inspired by the benefits of the frequency domain, we propose a novel module that functions as an attention mechanism in the frequency domain. The module consists of a learnable global filter that can adjust the frequencies of student’s features under the guidance of the teacher’s features, which encourages the student’s features to have patterns similar to the teacher’s features. We then propose an enhanced knowledge review-based distillation model by leveraging the proposed frequency attention module. The extensive experiments with various teacher and student architectures on image classification and object detection benchmark datasets show that the proposed approach outperforms other knowledge distillation methods.

Distributional robustness is a promising framework for training deep learning models that are less vulnerable to adversarial examples and data distribution shifts. Previous works have mainly focused on exploiting distributional robustness in the data space. In this work, we explore an optimal transport-based distributional robustness framework in model spaces. Specifically, we examine a model distribution within a Wasserstein ball centered on a given model distribution that maximizes the loss. We have developed theories that enable us to learn the optimal robust center model distribution. Interestingly, our developed theories allow us to flexibly incorporate the concept of sharpness awareness into training, whether it's a single model, ensemble models, or Bayesian Neural Networks, by considering specific forms of the center model distribution. These forms include a Dirac delta distribution over a single model, a uniform distribution over several models, and a general Bayesian Neural Network. Furthermore, we demonstrate that Sharpness-Aware Minimization (SAM) is a specific case of our framework when using a Dirac delta distribution over a single model, while our framework can be seen as a probabilistic extension of SAM. To validate the effectiveness of our framework in the aforementioned settings, we conducted extensive experiments, and the results reveal remarkable improvements compared to the baselines.

Bayesian Neural Networks (BNNs) provide a probabilistic interpretation for deep learning models by imposing a prior distribution over model parameters and inferring a posterior distribution based on observed data. The model sampled from the posterior distribution can be used for providing ensemble predictions and quantifying prediction uncertainty. It is well-known that deep learning models with lower sharpness have better generalization ability. However, existing posterior inferences are not aware of sharpness/flatness in terms of formulation, possibly leading to high sharpness for the models sampled from them. In this paper, we develop theories, the Bayesian setting, and the variational inference approach for the sharpness-aware posterior. Specifically, the models sampled from our sharpness-aware posterior, and the optimal approximate posterior estimating this sharpness-aware posterior, have better flatness, hence possibly possessing higher generalization ability. We conduct experiments by leveraging the sharpness-aware posterior with state-of-the-art Bayesian Neural Networks, showing that the flat-seeking counterparts outperform their baselines in all metrics of interest.

Multi-source Domain Adaptation (MSDA) is more practical but challenging than the conventional unsupervised domain adaptation due to the involvement of diverse multiple data sources. Two fundamental challenges of MSDA are: (i) how to deal with the diversity in the multiple source domains and (ii) how to cope with the data shift between the target domain and the source domains. In this paper, to address the first challenge, we propose a theoretical-guaranteed approach to combine domain experts locally trained on its own source domain to achieve a combined multi-source teacher that globally predicts well on the mixture of source domains. To address the second challenge, we propose to bridge the gap between the target domain and the mixture of source domains in the latent space via a generator or feature extractor. Together with bridging the gap in the latent space, we train a student to mimic the predictions of the teacher expert on both source and target examples. In addition, our approach is guaranteed with rigorous theory offered insightful justifications of how each component influences the transferring performance. Extensive experiments conducted on three benchmark datasets show that our proposed method achieves state-of-the-art performances to the best of our knowledge.