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This paper concerns the problem of multi-object tracking based on the min-cost flow (MCF) formulation, which is conventionally studied as an instance of linear program. Given its computationally tractable inference, the success of MCF…

As neural networks are increasingly being applied to real-world applications, mechanisms to address distributional shift and sequential task learning without forgetting are critical. Methods incorporating network expansion have shown…

Normalizing flows have shown great promise for modelling flexible probability distributions in a computationally tractable way. However, whilst data is often naturally described on Riemannian manifolds such as spheres, torii, and hyperbolic…

This paper introduces the unsupervised assignment flow that couples the assignment flow for supervised image labeling with Riemannian gradient flows for label evolution on feature manifolds. The latter component of the approach encompasses…

Deep Metric Learning (DML) methods have been proven relevant for visual similarity learning. However, they sometimes lack generalization properties because they are trained often using an inappropriate sample selection strategy or due to…

Normalizing flows (NFs) provide a powerful tool to construct an expressive distribution by a sequence of trackable transformations of a base distribution and form a probabilistic model of underlying data. Rotation, as an important quantity…

Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…

In this paper, we propose Continuous Graph Flow, a generative continuous flow based method that aims to model complex distributions of graph-structured data. Once learned, the model can be applied to an arbitrary graph, defining a…

Flow Matching has limited ability in achieving one-step generation due to its reliance on learned curved trajectories. Previous studies have attempted to address this limitation by either modifying the coupling distribution to prevent…

Continuous normalizing flows (CNFs) are a generative method for learning probability distributions, which is based on ordinary differential equations. This method has shown remarkable empirical success across various applications, including…

Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…

Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…

Diffusion models have become a leading framework in generative modeling, yet their theoretical understanding -- especially for high-dimensional data concentrated on low-dimensional structures -- remains incomplete. This paper investigates…

We study the problem of estimating a manifold from random samples. In particular, we consider piecewise constant and piecewise linear estimators induced by k-means and k-flats, and analyze their performance. We extend previous results for…

We propose two graph neural network layers for graphs with features in a Riemannian manifold. First, based on a manifold-valued graph diffusion equation, we construct a diffusion layer that can be applied to an arbitrary number of nodes and…

Foundational language models show a remarkable ability to learn new concepts during inference via context data. However, similar work for images lag behind. To address this challenge, we introduce FLoWN, a flow matching model that learns to…

Normalizing Flows (NFs) are a class of generative models distinguished by a mathematically invertible architecture, where the forward pass transforms data into a latent space for density estimation, and the reverse pass generates new…

Function approximation based on data drawn randomly from an unknown distribution is an important problem in machine learning. The manifold hypothesis assumes that the data is sampled from an unknown submanifold of a high dimensional…

The ability of Flow Matching (FM) to model complex conditional distributions has established it as the state-of-the-art for prediction tasks (e.g., robotics, weather forecasting). However, deployment in safety-critical settings is hindered…

The normalization constraint on probability density poses a significant challenge for solving the Fokker-Planck equation. Normalizing Flow, an invertible generative model leverages the change of variables formula to ensure probability…