3IA PhD/Postdoc Seminar #52

Flash presentation | A quick overview of Optimal Transport in Machine Learning

Abstract: This presentation will be an overview of the use of Optimal Transport (OT) in Machine Learning. Optimal Transport is an old topic in applied mathematics, first introduced by Gaspard Monge in his \textit{Mémoire sur la théorie des déblais et des remblais} in 1781, and then studied by Kantorovitch who introduced a continuous relaxation of the original Monge problem. We will cover the mathematical formulation of OT problem, numerical methods to solve it and the use of OT in machine learning for structured data, domain adaptation and generative modeling. The goal of my PhD is to investigate the use of OT in Domain Adaptation.

Task Singular Vectors: Reducing Task Interference in Model Merging

Abstract: Task Arithmetic has emerged as a simple yet effective method to merge models without additional training. However, by treating entire networks as flat parameter vectors, it overlooks key structural information and is susceptible to task interference. In this paper, we study task vectors at the layer level, focusing on task layer matrices and their singular value decomposition. In particular, we concentrate on the resulting singular vectors, which we refer to as Task Singular Vectors (TSV). Recognizing that layer task matrices are often low-rank, we propose TSV-Compress (TSV-C), a simple procedure that compresses them to 10% of their original size while retaining 99% of accuracy. We further leverage this low-rank space to define a new measure of task interference based on the interaction of singular vectors from different tasks. Building on these findings, we introduce TSV-Merge (TSV-M), a novel model merging approach that combines compression with interference reduction, significantly outperforming existing methods.
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