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Ronen Talmon

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14 papers

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TMLR Journal 2025 Journal Article

Geometric Optimal Transport for Unsupervised Domain Adaptation

Gal Maman
Ronen Talmon

Optimal Transport (OT) is a widely used and powerful approach in domain adaptation. While effective, most existing methods rely on the pairwise squared Euclidean distances for the transportation cost, implicitly assuming a Euclidean space. In this paper, we challenge this assumption by introducing Geometric Optimal Transport (GOT), a new transport cost designed for domain adaptation under the manifold assumption. By utilizing concepts and tools from the field of manifold learning, specifically diffusion geometry, we derive an operator that accounts for the intra-domain geometries, extending beyond the conventional inter-domain distances. This operator, which quantifies the probability of transporting between source and target samples, forms the basis for our cost. We demonstrate how the proposed cost, defined by an anisotropic diffusion process, naturally aligns with the desired properties for domain adaptation. To further enhance performance, we integrate source labels into the operator, thereby guiding the anisotropic diffusion according to the classes. We showcase the effectiveness of GOT through comprehensive experiments, demonstrating its superior performance compared to recent methods across various benchmarks and datasets.

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NeurIPS Conference 2025 Conference Paper

Joint Hierarchical Representation Learning of Samples and Features via Informed Tree-Wasserstein Distance

Ya-Wei Eileen Lin
Ronald Coifman
Gal Mishne
Ronen Talmon

High-dimensional data often exhibit hierarchical structures in both modes: samples and features. Yet, most existing approaches for hierarchical representation learning consider only one mode at a time. In this work, we propose an unsupervised method for jointly learning hierarchical representations of samples and features via Tree-Wasserstein Distance (TWD). Our method alternates between the two data modes. It first constructs a tree for one mode, then computes a TWD for the other mode based on that tree, and finally uses the resulting TWD to build the second mode’s tree. By repeatedly alternating through these steps, the method gradually refines both trees and the corresponding TWDs, capturing meaningful hierarchical representations of the data. We provide a theoretical analysis showing that our method converges. We show that our method can be integrated into hyperbolic graph convolutional networks as a pre-processing technique, improving performance in link prediction and node classification tasks. In addition, our method outperforms baselines in sparse approximation and unsupervised Wasserstein distance learning tasks on word-document and single-cell RNA-sequencing datasets.

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NeurIPS Conference 2025 Conference Paper

Learning Shared Representations from Unpaired Data

Amitai Yacobi
Nir Ben-Ari
Ronen Talmon
Uri Shaham

Learning shared representations is a primary area of multimodal representation learning. The current approaches to achieve a shared embedding space rely heavily on paired samples from each modality, which are significantly harder to obtain than unpaired ones. In this work, we demonstrate that shared representations can be learned almost exclusively from unpaired data. Our arguments are grounded in the spectral embeddings of the random walk matrices constructed independently from each unimodal representation. Empirical results in computer vision and natural language processing domains support its potential, revealing the effectiveness of unpaired data in capturing meaningful cross-modal relations, demonstrating high capabilities in retrieval tasks, generation, arithmetics, zero-shot, and cross-domain classification. This work, to the best of our knowledge, is the first to demonstrate these capabilities almost exclusively from unpaired samples, giving rise to a cross-modal embedding that could be viewed as universal, i. e. , independent of the specific modalities of the data. Our project page: https: //shaham-lab. github. io/SUE_page.

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NeurIPS Conference 2025 Conference Paper

Spectral Graph Coarsening Using Inner Product Preservation and the Grassmann Manifold

Ido Cohen
Ronen Talmon

We propose a novel functorial graph coarsening method that preserves inner products between node features, a property often overlooked by existing approaches focusing primarily on structural fidelity. By treating node features as functions on the graph and preserving their inner products, our method retains both structural and feature relationships, facilitating substantial benefits for downstream tasks. To formalize this, we introduce the Inner Product Error (IPE), which quantifies how the inner products between node features are preserved. Leveraging the underlying geometry of the problem on the Grassmann manifold, we formulate an optimization objective that minimizes the IPE, also for unseen smooth functions. We show that minimizing the IPE improves standard coarsening metrics, and illustrate our method’s properties through visual examples that highlight its clustering ability. Empirical results on benchmarks for graph coarsening and node classification show that our approach outperforms existing state-of-the-art methods.

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ICLR Conference 2025 Conference Paper

Supervised and Semi-Supervised Diffusion Maps with Label-Driven Diffusion

Harel Mendelman
Ronen Talmon

In this paper, we introduce Supervised Diffusion Maps (SDM) and Semi-Supervised Diffusion Maps (SSDM), which transform the well-known unsupervised dimensionality reduction algorithm, Diffusion Maps, into supervised and semi-supervised learning tools. The proposed methods, SDM and SSDM, are based on our new approach that treats the labels as a second view of the data. This unique framework allows us to incorporate ideas from multi-view learning. Specifically, we propose constructing two affinity kernels corresponding to the data and the labels. We then propose a multiplicative interpolation scheme of the two kernels, whose purpose is twofold. First, our scheme extracts the common structure underlying the data and the labels by defining a diffusion process driven by the data and the labels. This label-driven diffusion produces an embedding that emphasizes the properties relevant to the label-related task. Second, the proposed interpolation scheme balances the influence of the two kernels. We show on multiple benchmark datasets that the embedding learned by SDM and SSDM is more effective in downstream regression and classification tasks than existing unsupervised, supervised, and semi-supervised nonlinear dimension reduction methods.

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ICLR Conference 2025 Conference Paper

Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchy

Ya-Wei Eileen Lin
Ronald R. Coifman
Gal Mishne
Ronen Talmon

Finding meaningful distances between high-dimensional data samples is an important scientific task. To this end, we propose a new tree-Wasserstein distance (TWD) for high-dimensional data with two key aspects. First, our TWD is specifically designed for data with a latent feature hierarchy, i.e., the features lie in a hierarchical space, in contrast to the usual focus on embedding samples in hyperbolic space. Second, while the conventional use of TWD is to speed up the computation of the Wasserstein distance, we use its inherent tree as a means to learn the latent feature hierarchy. The key idea of our method is to embed the features into a multi-scale hyperbolic space using diffusion geometry and then present a new tree decoding method by establishing analogies between the hyperbolic embedding and trees. We show that our TWD computed based on data observations provably recovers the TWD defined with the latent feature hierarchy and that its computation is efficient and scalable. We showcase the usefulness of the proposed TWD in applications to word-document and single-cell RNA-sequencing datasets, demonstrating its advantages over existing TWDs and methods based on pre-trained models.

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NeurIPS Conference 2024 Conference Paper

Equivariant Machine Learning on Graphs with Nonlinear Spectral Filters

Ya-Wei Eileen Lin
Ronen Talmon
Ron Levie

Equivariant machine learning is an approach for designing deep learning models that respect the symmetries of the problem, with the aim of reducing model complexity and improving generalization. In this paper, we focus on an extension of shift equivariance, which is the basis of convolution networks on images, to general graphs. Unlike images, graphs do not have a natural notion of domain translation. Therefore, we consider the graph functional shifts as the symmetry group: the unitary operators that commute with the graph shift operator. Notably, such symmetries operate in the signal space rather than directly in the spatial space. We remark that each linear filter layer of a standard spectral graph neural network (GNN) commutes with graph functional shifts, but the activation function breaks this symmetry. Instead, we propose nonlinear spectral filters (NLSFs) that are fully equivariant to graph functional shifts and show that they have universal approximation properties. The proposed NLSFs are based on a new form of spectral domain that is transferable between graphs. We demonstrate the superior performance of NLSFs over existing spectral GNNs in node and graph classification benchmarks.

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TMLR Journal 2024 Journal Article

Supervised Domain Adaptation Based on Marginal and Conditional Distributions Alignment

Ori Katz
Ronen Talmon
Uri Shaham

Supervised domain adaptation (SDA) is an area of machine learning, where the goal is to achieve good generalization performance on data from a target domain, given a small corpus of labeled training data from the target domain and a large corpus of labeled data from a related source domain. In this work, based on a generalization of a well-known theoretical result of \citet{ben2010theory}, we propose an SDA approach, in which the adaptation is performed by aligning the marginal and conditional components of the input-label joint distributions. In addition to being theoretically grounded, we demonstrate that the proposed approach has two advantages over existing SDA approaches. First, it applies to a broad collection of learning tasks, such as regression, classification, multi-label classification, and few-shot learning. Second, it takes into account the geometric structure of the input and label spaces. Experimentally, despite its generality, our approach demonstrates on-par or superior results compared with recent state-of-the-art task-specific methods.

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AAAI Conference 2024 Conference Paper

The Expected Loss of Preconditioned Langevin Dynamics Reveals the Hessian Rank

Amitay Bar
Rotem Mulayoff
Tomer Michaeli
Ronen Talmon

Langevin dynamics (LD) is widely used for sampling from distributions and for optimization. In this work, we derive a closed-form expression for the expected loss of preconditioned LD near stationary points of the objective function. We use the fact that at the vicinity of such points, LD reduces to an Ornstein–Uhlenbeck process, which is amenable to convenient mathematical treatment. Our analysis reveals that when the preconditioning matrix satisfies a particular relation with respect to the noise covariance, LD's expected loss becomes proportional to the rank of the objective's Hessian. We illustrate the applicability of this result in the context of neural networks, where the Hessian rank has been shown to capture the complexity of the predictor function but is usually computationally hard to probe. Finally, we use our analysis to compare SGD-like and Adam-like preconditioners and identify the regimes under which each of them leads to a lower expected loss.

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ICML Conference 2023 Conference Paper

Few-Sample Feature Selection via Feature Manifold Learning

David Cohen
Tal Shnitzer
Yuval Kluger
Ronen Talmon

In this paper, we present a new method for few-sample supervised feature selection (FS). Our method first learns the manifold of the feature space of each class using kernels capturing multi-feature associations. Then, based on Riemannian geometry, a composite kernel is computed, extracting the differences between the learned feature associations. Finally, a FS score based on spectral analysis is proposed. Considering multi-feature associations makes our method multivariate by design. This in turn allows for the extraction of the hidden manifold underlying the features and avoids overfitting, facilitating few-sample FS. We showcase the efficacy of our method on illustrative examples and several benchmarks, where our method demonstrates higher accuracy in selecting the informative features compared to competing methods. In addition, we show that our FS leads to improved classification and better generalization when applied to test data.

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ICML Conference 2023 Conference Paper

Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning

Ya-Wei Eileen Lin
Ronald R. Coifman
Gal Mishne
Ronen Talmon

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

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NeurIPS Conference 2022 Conference Paper

Discovery of Single Independent Latent Variable

Uri Shaham
Jonathan Svirsky
Ori Katz
Ronen Talmon

Latent variable discovery is a central problem in data analysis with a broad range of applications in applied science. In this work, we consider data given as an invertible mixture of two statistically independent components, and assume that one of the components is observed while the other is hidden. Our goal is to recover the hidden component. For this purpose, we propose an autoencoder equipped with a discriminator. Unlike the standard nonlinear ICA problem, which was shown to be non-identifiable, in the special case of ICA we consider here, we show that our approach can recover the component of interest up to entropy-preserving transformation. We demonstrate the performance of the proposed approach in several tasks, including image synthesis, voice cloning, and fetal ECG extraction.

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NeurIPS Conference 2021 Conference Paper

Hyperbolic Procrustes Analysis Using Riemannian Geometry

Ya-Wei Eileen Lin
Yuval Kluger
Ronen Talmon

Label-free alignment between datasets collected at different times, locations, or by different instruments is a fundamental scientific task. Hyperbolic spaces have recently provided a fruitful foundation for the development of informative representations of hierarchical data. Here, we take a purely geometric approach for label-free alignment of hierarchical datasets and introduce hyperbolic Procrustes analysis (HPA). HPA consists of new implementations of the three prototypical Procrustes analysis components: translation, scaling, and rotation, based on the Riemannian geometry of the Lorentz model of hyperbolic space. We analyze the proposed components, highlighting their useful properties for alignment. The efficacy of HPA, its theoretical properties, stability and computational efficiency are demonstrated in simulations. In addition, we showcase its performance on three batch correction tasks involving gene expression and mass cytometry data. Specifically, we demonstrate high-quality unsupervised batch effect removal from data acquired at different sites and with different technologies that outperforms recent methods for label-free alignment in hyperbolic spaces.

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ICML Conference 2020 Conference Paper

Option Discovery in the Absence of Rewards with Manifold Analysis

Amitay Bar
Ronen Talmon
Ron Meir

Options have been shown to be an effective tool in reinforcement learning, facilitating improved exploration and learning. In this paper, we present an approach based on spectral graph theory and derive an algorithm that systematically discovers options without access to a specific reward or task assignment. As opposed to the common practice used in previous methods, our algorithm makes full use of the spectrum of the graph Laplacian. Incorporating modes associated with higher graph frequencies unravels domain subtleties, which are shown to be useful for option discovery. Using geometric and manifold-based analysis, we present a theoretical justification for the algorithm. In addition, we showcase its performance in several domains, demonstrating clear improvements compared to competing methods.

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