Optimal transport (OT) has been gaining in recent years an increasing attention in the machine learning community, mainly due to its capacity to exploit the geometric property of the samples.

Enzymes are crucial catalysts that enable a wide range of biochemical reactions. Efficiently identifying specific enzymes from vast protein libraries is essential for advancing biocatalysis. Traditional computational methods for enzyme screening and retrieval are time-consuming and resource-intensive. Recently, deep learning approaches have shown promise. However, these methods focus solely on the interaction between enzymes and reactions, overlooking the inherent hierarchical relationships within each domain. To address these limitations, we introduce FGW-CLIP, a novel contrastive learning framework based on optimizing the fused Gromov-Wasserstein distance. FGW-CLIP incorporates multiple alignments, including inter-domain alignment between reactions and enzymes and intra-domain alignment within enzymes and reactions. By introducing a tailored regularization term, our method minimizes the Gromov-Wasserstein distance between enzyme and reaction spaces, which enhances information integration across these domains. Extensive evaluations demonstrate the superiority of FGW-CLIP in challenging enzyme-reaction tasks. On the widely-used EnzymeMap benchmark, FGW-CLIP achieves state-of-the-art performance in enzyme virtual screening, as measured by BEDROC and EF metrics. Moreover, FGW-CLIP consistently outperforms across all three splits of ReactZyme, the largest enzyme-reaction benchmark, demonstrating robust generalization to novel enzymes and reactions. These results position FGW-CLIP as a promising framework for enzyme discovery in complex biochemical settings, with strong adaptability across diverse screening scenarios.

In this work, we present LOTUS (Learning to Learn with Optimal Transport for Unsupervised Scenarios), a simple yet effective method to perform model selection for multiple unsupervised machine learning(ML) tasks such as outlier detection and clustering. Our intuition behind this work is that a machine learning pipeline will perform well in a new dataset if it previously worked well on datasets with a similar underlying data distribution. We use Optimal Transport distances to find this similarity between unlabeled tabular datasets and recommend machine learning pipelines with one unified single method on two downstream unsupervised tasks: outlier detection and clustering. We present the effectiveness of our approach with experiments against strong baselines and show that LOTUS is a very promising first step toward model selection for multiple unsupervised ML tasks.

In this paper, we address the partial Wasserstein and Gromov-Wasserstein problems and propose exact algorithms to solve them.

The Gromov-Wasserstein (GW) variant of optimal transport, designed to compare probability densities defined over distinct metric spaces, has emerged as an important tool for the analysis of data with complex structure, such as ensembles of point clouds or networks. To overcome certain limitations, such as the restriction to comparisons of measures of equal mass and sensitivity to outliers, several unbalanced or partial transport relaxations of the GW distance have been introduced in the recent literature. This paper is concerned with the Conic Gromov-Wasserstein (CGW) distance introduced by S ejourn e, Vialard, and Peyr e [35]. We provide a novel formulation in terms of semi-couplings, and extend the framework beyond the metric measure space setting, to compare more general network and hypernetwork structures. With this new formulation, we establish several fundamental properties of the CGW metric, including its scaling behavior under dilation, variational convergence in the limit of volume growth constraints, and comparison bounds with established optimal transport metrics. We further derive quantitative bounds that characterize the robustness of the CGW metric to perturbations in the underlying measures. The hypernetwork formulation of CGW admits a simple and provably convergent block coordinate ascent algorithm for its estimation, and we demonstrate the computational tractability and scalability of our approach through experiments on synthetic and real-world high-dimensional and structured datasets.

Recent advances have discussed cell complexes as ideal learning representations. However, there is a lack of available machine learning methods suitable for learning on CW complexes. In this paper, we derive an explicit expression for the Wasserstein distance between cell complex signal distributions in terms of a Hodge-Laplacian matrix. This leads to a structurally meaningful measure to compare CW complexes and define the optimal transportation map. In order to simultaneously include both feature and structure information, we extend the Fused Gromov-Wasserstein distance to CW complexes. Finally, we introduce novel kernels over the space of probability measures on CW complexes based on the dual formulation of optimal transport.

Graph Representation Learning (GRL) is a fundamental task in machine learning, aiming to encode high-dimensional graph-structured data into low-dimensional vectors. Self-Supervised Learning (SSL) methods are widely used in GRL because they can avoid expensive human annotation. In this work, we propose a novel Subgraph Gaussian Embedding Contrast (SubGEC) method. Our approach introduces a sub-graph Gaussian embedding module, which adaptively maps subgraphs to a structured Gaussian space, ensuring the preservation of input sub-graph characteristics while generating subgraphs with a controlled distribution. We then employ optimal transport distances, more precisely the Wasserstein and Gromov-Wasserstein distances, to effectively measure the similarity between subgraphs, enhancing the robustness of the contrastive learning process. Extensive experiments across multiple benchmarks demonstrate that SubGEC outperforms or presents competitive performance against state-of-the-art approaches. Our findings provide insights into the design of SSL methods for GRL, emphasizing the importance of the distribution of the generated contrastive pairs.

The Gromov-Wasserstein (GW) distance is an extension of the optimal transport problem that allows one to match objects between incomparable spaces. At its core, the GW distance is specified as the solution of a non-convex quadratic program and is not known to be tractable to solve. In particular, existing solvers for the GW distance are only able to find locally optimal solutions. In this work, we propose a semi-definite programming (SDP) relaxation of the GW distance. The relaxation can be viewed as the Lagrangian dual of the GW distance augmented with constraints that relate to the linear and quadratic terms of transportation plans.