Estimating the parameters of a probabilistic directed graphical model from incomplete data remains a long-standing challenge. This is because, in the presence of latent variables, both the likelihood function and posterior distribution are intractable without further assumptions about structural dependencies or model classes. While existing learning methods are fundamentally based on likelihood maximization, here we offer a new view of the parameter learning problem through the lens of optimal transport. This perspective licenses a general framework that operates on any directed graphs without making unrealistic assumptions on the posterior over the latent variables or resorting to black-box variational approximations. We develop a theoretical framework and support it with extensive empirical evidence demonstrating the flexibility and versatility of our approach. Across experiments, we show that not only can our method recover the ground-truth parameters but it also performs comparably or better on downstream applications, notably the non-trivial task of discrete representation learning.

Unsupervised domain adaptation (UDA) aims to transfer knowledge from a labeled source domain to an unlabeled target domain. In this paper, we introduce a novel approach called class-aware optimal transport (OT), which measures the OT distance between a distribution over the source class-conditional distributions and a mixture of source and target data distribution. Our class-aware OT leverages a cost function that determines the matching extent between a given data example and a source class-conditional distribution. By optimizing this cost function, we find the optimal matching between target examples and source class-conditional distributions, effectively addressing the data and label shifts that occur between the two domains. To handle the class-aware OT efficiently, we propose an amortization solution that employs deep neural networks to formulate the transportation probabilities and the cost function. Additionally, we propose minimizing class-aware Higher-order Moment Matching (HMM) to align the corresponding class regions on the source and target domains. The class-aware HMM component offers an economical computational approach for accurately evaluating the HMM distance between the two distributions. Extensive experiments on benchmark datasets demonstrate that our proposed method significantly outperforms existing state-of-the-art baselines.

Mitigating catastrophic forgetting is a key hurdle in continual learning. Deep Generative Replay (GR) provides techniques focused on generating samples from prior tasks to enhance the model's memory capabilities. With the progression in generative AI, generative models have advanced from Generative Adversarial Networks (GANs) to the more recent Diffusion Models (DMs). A major issue is the deterioration in the quality of generated data compared to the original, as the generator continuously self-learns from its outputs. This degradation can lead to the potential risk of catastrophic forgetting occurring in the classifier. To address this, we propose the Class-Prototype Conditional Diffusion Model (CPDM), a GR-based approach for continual learning that enhances image quality in generators and thus reduces catastrophic forgetting in classifiers. The cornerstone of CPDM is a learnable class-prototype that captures the core characteristics of images in a given class. This prototype, integrated into the diffusion model's denoising process, ensures the generation of high-quality images. It maintains its effectiveness for old tasks even when new tasks are introduced, preserving image generation quality and reducing the risk of catastrophic forgetting in classifiers. Our empirical studies on diverse datasets demonstrate that our proposed method significantly outperforms existing state-of-the-art models, highlighting its exceptional ability to preserve image quality and enhance the model's memory retention.

Drawing inspiration from prompt tuning techniques applied to Large Language Models, recent methods based on pre-trained ViT networks have achieved remarkable results in the field of Continual Learning. Specifically, these approaches propose to maintain a set of prompts and allocate a subset of them to learn each task using a key-query matching strategy. However, they may encounter limitations when lacking control over the correlations between old task queries and keys of future tasks, the shift of features in the latent space, and the relative separation of latent vectors learned in independent tasks. In this work, we introduce a novel key-query learning strategy based on orthogonal projection, inspired by model-agnostic meta-learning, to enhance prompt matching efficiency and address the challenge of shifting features. Furthermore, we introduce a One-Versus-All (OVA) prototype-based component that enhances the classification head distinction. Experimental results on benchmark datasets demonstrate that our method empowers the model to achieve results surpassing those of current state-of-the-art approaches by a large margin of up to 20%. Our code is available at https://anonymous.4open.science/r/KOPPA/README.md. Continual Learning (CL) is an evolving field in machine learning, aiming to enable models to learn continuously from a sequence of tasks with varying data distributions. A challenging CL scenario is Class Incremental Learning (CIL), where a model sequentially learns new categories and must classify all seen classes without task-ID information, leading to a fundamental issue in CL known as Catastrophic Forgetting (CF) (French, 1999), where performance on earlier tasks degrades due to the absence of old task data and differences in data distributions. In CIL, models are required to classify test samples without prior knowledge of their task IDs.

Contrastive learning (CL) allows us to create meaningful features without any label information. In the first phase, CL approaches learn the features, which are then classified by a linear classifier that has been learned from labeled data. While existing theoretical works have studied the connection between the supervised loss in the second phase and the unsupervised loss in the first phase to explain why the unsupervised loss can support the supervised loss, there has been no theoretical examination of the connection between the unsupervised loss in the first phase and the robust supervised loss in the second phase, which can shed light on how to establish an effective unsupervised loss in the first phase. To fill this gap, our paper develops rigorous theories to identify which components in the supervised loss can aid the robust supervised loss. Finally, we conduct experiments to verify our findings. All code used in this work is available at https://anonymous.4open.science/r/rosa.

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.

Neurons can display highly variable dynamics. While such variability presumably supports the wide range of behaviors generated by the organism, their gene expressions are relatively stable in the adult brain. This suggests that neuronal activity is a combination of its time-invariant identity and the inputs the neuron receives from the rest of the circuit. Here, we propose a self-supervised learning based method to assign time-invariant representations to individual neurons based on permutation-, and population size-invariant summary of population recordings. We fit dynamical models to neuronal activity to learn a representation by considering the activity of both the individual and the neighboring population. Our self-supervised approach and use of implicit representations enable robust inference against imperfections such as partial overlap of neurons across sessions, trial-to-trial variability, and limited availability of molecular (transcriptomic) labels for downstream supervised tasks. We demonstrate our method on a public multimodal dataset of mouse cortical neuronal activity and transcriptomic labels. We report > 35% improvement in predicting the transcriptomic subclass identity and > 20% improvement in predicting class identity with respect to the state-of-the-art.

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.

Multi-Task Learning (MTL) is a widely-used and powerful learning paradigm for training deep neural networks that allows learning more than one objective by a single backbone. Compared to training tasks separately, MTL significantly reduces computational costs, improves data efficiency, and potentially enhances model performance by leveraging knowledge across tasks. Hence, it has been adopted in a variety of applications, ranging from computer vision to natural language processing and speech recognition. Among them, there is an emerging line of work in MTL that focuses on manipulating the task gradient to derive an ultimate gradient descent direction to benefit all tasks. Despite achieving impressive results on many benchmarks, directly applying these approaches without using appropriate regularization techniques might lead to suboptimal solutions on real-world problems. In particular, standard training that minimizes the empirical loss on the training data can easily suffer from overfitting to low-resource tasks or be spoiled by noisy-labeled ones, which can cause negative transfer between tasks and overall performance drop. To alleviate such problems, we propose to leverage a recently introduced training method, named Sharpness-aware Minimization, which can enhance model generalization ability on single-task learning. Accordingly, we present a novel MTL training methodology, encouraging the model to find task-based flat minima for coherently improving its generalization capability on all tasks. Finally, we conduct comprehensive experiments on a variety of applications to demonstrate the merit of our proposed approach to existing gradient-based MTL methods, as suggested by our developed theory.

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}.