Related papers: Set Representation Learning with Generalized Slice…
Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions. Here we consider an alternative, which embeds data as discrete…
Sliced Wasserstein (SW) distances offer an efficient method for comparing high-dimensional probability measures by projecting them onto multiple 1-dimensional probability distributions. However, identifying informative slicing directions…
We present the Fourier Sliced-Wasserstein (FSW) embedding - a novel method to embed multisets and measures over R^d into Euclidean space. Our proposed embedding approximately preserves the sliced Wasserstein distance on distributions,…
We present the Fourier Sliced-Wasserstein (FSW) embedding - a novel method to embed multisets and measures over $\mathbb{R}^d$ into Euclidean space. Our proposed embedding approximately preserves the sliced Wasserstein distance on…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
Multi-view data analysis seeks to integrate multiple representations of the same samples in order to recover a coherent low-dimensional structure. Classical approaches often rely on feature concatenation or explicit alignment assumptions,…
Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…
We propose a novel approach for comparing distributions whose supports do not necessarily lie on the same metric space. Unlike Gromov-Wasserstein (GW) distance which compares pairwise distances of elements from each distribution, we…
A well-designed vectorized representation is crucial for the learning systems natively based on 3D Gaussian Splatting. While 3DGS enables efficient and explicit 3D reconstruction, its parameter-based representation remains hard to learn as…
Representations of sets are challenging to learn because operations on sets should be permutation-invariant. To this end, we propose a Permutation-Optimisation module that learns how to permute a set end-to-end. The permuted set can be…
Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated…
The Wasserstein distance and its variations, e.g., the sliced-Wasserstein (SW) distance, have recently drawn attention from the machine learning community. The SW distance, specifically, was shown to have similar properties to the…
It has been shown beneficial for many types of data which present an underlying hierarchical structure to be embedded in hyperbolic spaces. Consequently, many tools of machine learning were extended to such spaces, but only few…
Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing…
The ability to model relational information using machine learning has driven advancements across various domains, from medicine to social science. While graph representation learning has become mainstream over the past decade, representing…
In this paper, we study the problem of learning compact (low-dimensional) representations for sequential data that captures its implicit spatio-temporal cues. To maximize extraction of such informative cues from the data, we set the problem…
Invariance (defined in a general sense) has been one of the most effective priors for representation learning. Direct factorization of parametric models is feasible only for a small range of invariances, while regularization approaches,…
In this paper we study generative modeling via autoencoders while using the elegant geometric properties of the optimal transport (OT) problem and the Wasserstein distances. We introduce Sliced-Wasserstein Autoencoders (SWAE), which are…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
Self-supervised learning is one of the most promising approaches to acquiring knowledge from limited labeled data. Despite the substantial advancements made in recent years, self-supervised models have posed a challenge to practitioners, as…