Related papers: Geometric Constraints in Probabilistic Manifolds: …
The distribution of galaxies and clusters of galaxies on the mega-parsec scale of the Universe follows an intricate pattern now famously known as the Large-Scale Structure or the Cosmic Web. To study the environments of this network,…
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…
Real-world physical systems are inherently complex, often involving the coupling of multiple physics, making their simulation both highly valuable and challenging. Many mainstream approaches face challenges when dealing with decoupled data.…
Partitioning a set of elements into subsets of a priori unknown sizes is essential in many applications. These subset sizes are rarely explicitly learned - be it the cluster sizes in clustering applications or the number of shared versus…
Purpose: We propose a general framework for quantifying predictive uncertainties of dose-related quantities and leveraging this information in a dose mimicking problem in the context of automated radiation therapy treatment planning.…
Given a set of data points sampled from some underlying space, there are two important challenges in geometric and topological data analysis when dealing with sampled data: reconstruction -- how to assemble discrete samples into global…
Diffusion maps are a commonly used kernel-based method for manifold learning, which can reveal intrinsic structures in data and embed them in low dimensions. However, as with most kernel methods, its implementation requires a heavy…
A probabilistic framework is proposed for the optimization of efficient switched control strategies for physical systems dominated by stochastic excitation. In this framework, the equation for the state trajectory is replaced with an…
We study the problem of learning a neural sampler to generate samples from discrete state spaces where the target probability mass function $\pi\propto\mathrm{e}^{-U}$ is known up to a normalizing constant, which is an important task in…
Representation learning is a fundamental task in machine learning, aiming at uncovering structures from data to facilitate subsequent tasks. However, what is a good representation for planning and reasoning in a stochastic world remains an…
In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric…
We present a characterization of states in generalized probabilistic models by appealing to a non-commutative version of geometric probability theory based on algebraic geometry techniques. Our theoretical framework allows for incorporation…
We present a novel particle management method using the Characteristic Mapping framework. In the context of explicit evolution of parametrized curves and surfaces, the surface distribution of marker points created from sampling the…
Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems…
We explore the problem of generating minority samples using diffusion models. The minority samples are instances that lie on low-density regions of a data manifold. Generating a sufficient number of such minority instances is important,…
Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…
We study regularization in the context of small sample-size learning with over-parameterized neural networks. Specifically, we shift focus from architectural properties, such as norms on the network weights, to properties of the internal…
Learning physical properties of high-dimensional states is crucial for developing quantum technologies but usually consumes an exceedingly large number of samples which are difficult to afford in practice. In this Letter, we use the…
This paper presents mathematical results in support of the methodology of the probabilistic learning on manifolds (PLoM) recently introduced by the authors, which has been used with success for analyzing complex engineering systems. The…
Correcting for detector effects in experimental data, particularly through unfolding, is critical for enabling precision measurements in high-energy physics. However, traditional unfolding methods face challenges in scalability,…