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Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties. In short, the barycenter task is to take the average of a collection of probability distributions w.r.t. given OT discrepancies. We propose a novel algorithm for approximating the continuous Entropic OT (EOT) barycenter for arbitrary OT cost functions. Our approach is built upon the dual reformulation of the EOT problem based on weak OT, which has recently gained the attention of the ML community. Beyond its novelty, our method enjoys several advantageous properties: (i) we establish quality bounds for the recovered solution; (ii) this approach seemlessly interconnects with the Energy-Based Models (EBMs) learning procedure enabling the use of well-tuned algorithms for the problem of interest; (iii) it provides an intuitive optimization scheme avoiding min-max, reinforce and other intricate technical tricks. For validation, we consider several low-dimensional scenarios and image-space setups, including non-Euclidean cost functions. Furthermore, we investigate the practical task of learning the barycenter on an image manifold generated by a pretrained generative model, opening up new directions for real-world applications.

A confidence sequence (CS) is a sequence of confidence sets that contains a target parameter of an underlying stochastic process at any time step with high probability. This paper proposes a new approach to constructing CSs for means of bounded multivariate stochastic processes using a general gambling framework, extending the recently established coin toss framework for bounded random processes. The proposed gambling framework provides a general recipe for constructing CSs for categorical and probability-vector-valued observations, as well as for general bounded multidimensional observations through a simple reduction. This paper specifically explores the use of the mixture portfolio, akin to Cover's universal portfolio, in the proposed framework and investigates the properties of the resulting CSs. Simulations demonstrate the tightness of these confidence sequences compared to existing methods. When applied to the sampling without-replacement setting for finite categorical data, it is shown that the resulting CS based on a universal gambling strategy is provably tighter than that of the posterior-prior ratio martingale proposed by Waudby-Smith and Ramdas.

The partial Gromov-Wasserstein (PGW) problem facilitates the comparison of measures with unequal masses residing in potentially distinct metric spaces, thereby enabling unbalanced and partial matching across these spaces. In this paper, we demonstrate that the PGW problem can be transformed into a variant of the Gromov-Wasserstein problem, akin to the conversion of the partial optimal transport problem into an optimal transport problem. This transformation leads to two new solvers, mathematically and computationally equivalent, based on the Frank-Wolfe algorithm, that provide efficient solutions to the PGW problem. We further establish that the PGW problem constitutes a metric for metric measure spaces. Finally, we validate the effectiveness of our proposed solvers in terms of computation time and performance on shape-matching and positive-unlabeled learning problems, comparing them against existing baselines.

Modeling complementary relationships greatly helps recommender systems to accurately and promptly recommend the subsequent items when one item is purchased. Unlike traditional similar relationships, items with complementary relationships may be purchased successively (such as iPhone and Airpods Pro), and they not only share relevance but also exhibit dissimilarity. Since the two attributes are opposites, modeling complementary relationships is challenging. Previous attempts to exploit these relationships have either ignored or oversimplified the dissimilarity attribute, resulting in ineffective modeling and an inability to balance the two attributes. Since Graph Neural Networks (GNNs) can capture the relevance and dissimilarity between nodes in the spectral domain, we can leverage spectral-based GNNs to effectively understand and model complementary relationships. In this study, we present a novel approach called Spectral-based Complementary Graph Neural Networks (SComGNN) that utilizes the spectral properties of complementary item graphs. We make the first observation that complementary relationships consist of low-frequency and mid-frequency components, corresponding to the relevance and dissimilarity attributes, respectively. Based on this spectral observation, we design spectral graph convolutional networks with low-pass and mid-pass filters to capture the low-frequency and mid-frequency components. Additionally, we propose a two-stage attention mechanism to adaptively integrate and balance the two attributes. Experimental results on four e-commerce datasets demonstrate the effectiveness of our model, with SComGNN significantly outperforming existing baseline models.

Denoising diffusion probabilistic models (DDPMs) have recently taken the field of generative modeling by storm, pioneering new state-of-the-art results in disciplines such as computer vision and computational biology for diverse tasks ranging from text-guided image generation to structure-guided protein design. Along this latter line of research, methods have recently been proposed for generating 3D molecules using equivariant graph neural networks (GNNs) within a DDPM framework. However, such methods are unable to learn important geometric and physical properties of 3D molecules during molecular graph generation, as they adopt molecule-agnostic and non-geometric GNNs as their 3D graph denoising networks, which negatively impacts their ability to effectively scale to datasets of large 3D molecules. In this work, we address these gaps by introducing the Geometry-Complete Diffusion Model (GCDM) for 3D molecule generation, which outperforms existing 3D molecular diffusion models by significant margins across conditional and unconditional settings for the QM9 dataset as well as for the larger GEOM-Drugs dataset. Importantly, we demonstrate that the geometry-complete denoising process GCDM learns for 3D molecule generation allows the model to generate realistic and stable large molecules at the scale of GEOM-Drugs, whereas previous methods fail to do so with the features they learn. Additionally, we show that extensions of GCDM can not only effectively design 3D molecules for specific protein pockets but also that GCDM's geometric features can effectively be repurposed to directly optimize the geometry and chemical composition of existing 3D molecules for specific molecular properties, demonstrating new, real-world versatility of molecular diffusion models. Our source code and data are freely available at //github.com/BioinfoMachineLearning/Bio-Diffusion.

Document-level translation models are usually evaluated using general metrics such as BLEU, which are not informative about the benefits of context. Current work on context-aware evaluation, such as contrastive methods, only measure translation accuracy on words that need context for disambiguation. Such measures cannot reveal whether the translation model uses the correct supporting context. We propose to complement accuracy-based evaluation with measures of context utilization. We find that perturbation-based analysis (comparing models' performance when provided with correct versus random context) is an effective measure of overall context utilization. For a finer-grained phenomenon-specific evaluation, we propose to measure how much the supporting context contributes to handling context-dependent discourse phenomena. We show that automatically-annotated supporting context gives similar conclusions to human-annotated context and can be used as alternative for cases where human annotations are not available. Finally, we highlight the importance of using discourse-rich datasets when assessing context utilization.

Despite the recent progress in deep learning, most approaches still go for a silo-like solution, focusing on learning each task in isolation: training a separate neural network for each individual task. Many real-world problems, however, call for a multi-modal approach and, therefore, for multi-tasking models. Multi-task learning (MTL) aims to leverage useful information across tasks to improve the generalization capability of a model. This thesis is concerned with multi-task learning in the context of computer vision. First, we review existing approaches for MTL. Next, we propose several methods that tackle important aspects of multi-task learning. The proposed methods are evaluated on various benchmarks. The results show several advances in the state-of-the-art of multi-task learning. Finally, we discuss several possibilities for future work.

Generative commonsense reasoning which aims to empower machines to generate sentences with the capacity of reasoning over a set of concepts is a critical bottleneck for text generation. Even the state-of-the-art pre-trained language generation models struggle at this task and often produce implausible and anomalous sentences. One reason is that they rarely consider incorporating the knowledge graph which can provide rich relational information among the commonsense concepts. To promote the ability of commonsense reasoning for text generation, we propose a novel knowledge graph augmented pre-trained language generation model KG-BART, which encompasses the complex relations of concepts through the knowledge graph and produces more logical and natural sentences as output. Moreover, KG-BART can leverage the graph attention to aggregate the rich concept semantics that enhances the model generalization on unseen concept sets. Experiments on benchmark CommonGen dataset verify the effectiveness of our proposed approach by comparing with several strong pre-trained language generation models, particularly KG-BART outperforms BART by 5.80, 4.60, in terms of BLEU-3, 4. Moreover, we also show that the generated context by our model can work as background scenarios to benefit downstream commonsense QA tasks.

Representation learning on a knowledge graph (KG) is to embed entities and relations of a KG into low-dimensional continuous vector spaces. Early KG embedding methods only pay attention to structured information encoded in triples, which would cause limited performance due to the structure sparseness of KGs. Some recent attempts consider paths information to expand the structure of KGs but lack explainability in the process of obtaining the path representations. In this paper, we propose a novel Rule and Path-based Joint Embedding (RPJE) scheme, which takes full advantage of the explainability and accuracy of logic rules, the generalization of KG embedding as well as the supplementary semantic structure of paths. Specifically, logic rules of different lengths (the number of relations in rule body) in the form of Horn clauses are first mined from the KG and elaborately encoded for representation learning. Then, the rules of length 2 are applied to compose paths accurately while the rules of length 1 are explicitly employed to create semantic associations among relations and constrain relation embeddings. Besides, the confidence level of each rule is also considered in optimization to guarantee the availability of applying the rule to representation learning. Extensive experimental results illustrate that RPJE outperforms other state-of-the-art baselines on KG completion task, which also demonstrate the superiority of utilizing logic rules as well as paths for improving the accuracy and explainability of representation learning.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.