Author name cluster

Théo Uscidda

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5 papers

2 author rows

ICLR Conference 2025 Conference Paper

Disentangled Representation Learning with the Gromov-Monge Gap

Théo Uscidda
Luca Eyring
Karsten Roth
Fabian J. Theis
Zeynep Akata
Marco Cuturi

Learning disentangled representations from unlabelled data is a fundamental challenge in machine learning. Solving it may unlock other problems, such as generalization, interpretability, or fairness. Although remarkably challenging to solve in theory, disentanglement is often achieved in practice through prior matching. Furthermore, recent works have shown that prior matching approaches can be enhanced by leveraging geometrical considerations, e.g., by learning representations that preserve geometric features of the data, such as distances or angles between points. However, matching the prior while preserving geometric features is challenging, as a mapping that *fully* preserves these features while aligning the data distribution with the prior does not exist in general. To address these challenges, we introduce a novel approach to disentangled representation learning based on quadratic optimal transport. We formulate the problem using Gromov-Monge maps that transport one distribution onto another with minimal distortion of predefined geometric features, preserving them *as much as can be achieved*. To compute such maps, we propose the Gromov-Monge-Gap (GMG), a regularizer quantifying whether a map moves a reference distribution with minimal geometry distortion. We demonstrate the effectiveness of our approach for disentanglement across four standard benchmarks, outperforming other methods leveraging geometric considerations.

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NeurIPS Conference 2024 Conference Paper

GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics

Dominik Klein
Théo Uscidda
Fabian Theis
Marco Cuturi

Single-cell genomics has significantly advanced our understanding of cellular behavior, catalyzing innovations in treatments and precision medicine. However, single-cell sequencing technologies are inherently destructive and can only measure a limited array of data modalities simultaneously. This limitation underscoresthe need for new methods capable of realigning cells. Optimal transport (OT)has emerged as a potent solution, but traditional discrete solvers are hampered byscalability, privacy, and out-of-sample estimation issues. These challenges havespurred the development of neural network-based solvers, known as neural OTsolvers, that parameterize OT maps. Yet, these models often lack the flexibilityneeded for broader life science applications. To address these deficiencies, ourapproach learns stochastic maps (i. e. transport plans), allows for any cost function, relaxes mass conservation constraints and integrates quadratic solvers to tackle thecomplex challenges posed by the (Fused) Gromov-Wasserstein problem. Utilizingflow matching as a backbone, our method offers a flexible and effective framework. We demonstrate its versatility and robustness through applications in cell development studies, cellular drug response modeling, and cross-modality cell translation, illustrating significant potential for enhancing therapeutic strategies.

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NeurIPS Conference 2024 Conference Paper

Mirror and Preconditioned Gradient Descent in Wasserstein Space

Clément Bonet
Théo Uscidda
Adam David
Pierre-Cyril Aubin-Frankowski
Anna Korba

As the problem of minimizing functionals on the Wasserstein space encompasses many applications in machine learning, different optimization algorithms on $\mathbb{R}^d$ have received their counterpart analog on the Wasserstein space. We focus here on lifting two explicit algorithms: mirror descent and preconditioned gradient descent. These algorithms have been introduced to better capture the geometry of the function to minimize and are provably convergent under appropriate (namely relative) smoothness and convexity conditions. Adapting these notions to the Wasserstein space, we prove guarantees of convergence of some Wasserstein-gradient-based discrete-time schemes for new pairings of objective functionals and regularizers. The difficulty here is to carefully select along which curves the functionals should be smooth and convex. We illustrate the advantages of adapting the geometry induced by the regularizer on ill conditioned optimization tasks, and showcase the improvement of choosing different discrepancies and geometries in a computational biology task of aligning single-cells.

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ICLR Conference 2024 Conference Paper

Unbalancedness in Neural Monge Maps Improves Unpaired Domain Translation

Luca Eyring
Dominik Klein 0005
Théo Uscidda
Giovanni Palla
Niki Kilbertus
Zeynep Akata
Fabian J. Theis

In optimal transport (OT), a Monge map is known as a mapping that transports a source distribution to a target distribution in the most cost-efficient way. Recently, multiple neural estimators for Monge maps have been developed and applied in diverse unpaired domain translation tasks, e.g. in single-cell biology and computer vision. However, the classic OT framework enforces mass conservation, which makes it prone to outliers and limits its applicability in real-world scenarios. The latter can be particularly harmful in OT domain translation tasks, where the relative position of a sample within a distribution is explicitly taken into account. While unbalanced OT tackles this challenge in the discrete setting, its integration into neural Monge map estimators has received limited attention. We propose a theoretically grounded method to incorporate unbalancedness into any Monge map estimator. We improve existing estimators to model cell trajectories over time and to predict cellular responses to perturbations. Moreover, our approach seamlessly integrates with the OT flow matching (OT-FM) framework. While we show that OT-FM performs competitively in image translation, we further improve performance by incorporating unbalancedness (UOT-FM), which better preserves relevant features. We hence establish UOT-FM as a principled method for unpaired image translation.

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ICML Conference 2023 Conference Paper

The Monge Gap: A Regularizer to Learn All Transport Maps

Théo Uscidda
Marco Cuturi

Optimal transport (OT) theory has been used in machine learning to study and characterize maps that can push-forward efficiently a probability measure onto another. Recent works have drawn inspiration from Brenier’s theorem, which states that when the ground cost is the squared-Euclidean distance, the “best” map to morph a continuous measure in $\mathcal{P}(\mathbb{R}^d)$ into another must be the gradient of a convex function. To exploit that result, Makkuva et. al (2020); Korotin et. al (2020) consider maps $T=\nabla f_\theta$, where $f_\theta$ is an input convex neural network (ICNN), as defined by Amos et. al (2017), and fit $\theta$ with SGD using samples. Despite their mathematical elegance, fitting OT maps with ICNNs raises many challenges, due notably to the many constraints imposed on $\theta$; the need to approximate the conjugate of $f_\theta$; or the limitation that they only work for the squared-Euclidean cost. More generally, we question the relevance of using Brenier’s result, which only applies to densities, to constrain the architecture of candidate maps fitted on samples. Motivated by these limitations, we propose a radically different approach to estimating OT maps: Given a cost $c$ and a reference measure $\rho$, we introduce a regularizer, the Monge gap $\mathcal{M}^c_{\rho}(T)$ of a map $T$. That gap quantifies how far a map $T$ deviates from the ideal properties we expect from a $c$-OT map. In practice, we drop all architecture requirements for $T$ and simply minimize a distance (e. g. , the Sinkhorn divergence) between $T\sharp\mu$ and $\nu$, regularized by $\mathcal{M}^c_\rho(T)$. We study $\mathcal{M}^c_{\rho}$ and show how our simple pipeline significantly outperforms other baselines in practice.

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