Related papers: Selecting High-Dimensional Representations of Phys…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
Sampling from learned high-dimensional distributions is a foundational computational problem. We introduce U-turn chains: Markov chains obtained by iterating short forward-backward steps of a diffusion model, in which each step proposes a…
Ptychography is a scanning coherent diffractive imaging technique that enables imaging nanometer-scale features in extended samples. One main challenge is that widely used iterative image reconstruction methods often require significant…
Cross-diffusion systems arise as hydrodynamic limits of lattice multi-species interacting particle models. The objective of this work is to provide a numerical scheme for the simulation of the cross-diffusion system identified in [J.…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
We introduce a novel class of sample-based explanations we term high-dimensional representers, that can be used to explain the predictions of a regularized high-dimensional model in terms of importance weights for each of the training…
Most existing MRI reconstruction methods perform tar-geted reconstruction of the entire MR image without tak-ing specific tissue regions into consideration. This may fail to emphasize the reconstruction accuracy on im-portant tissues for…
Validating safety-critical autonomous systems in high-dimensional domains such as robotics presents a significant challenge. Existing black-box approaches based on Markov chain Monte Carlo may require an enormous number of samples, while…
This article considers the generative modeling of the (mixed) states of quantum systems, and an approach based on denoising diffusion model is proposed. The key contribution is an algorithmic innovation that respects the physical nature of…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…
This work presents a multiscale framework to solve a class of stochastic optimal control problems in the context of robot motion planning and control in a complex environment. In order to handle complications resulting from a large decision…
Interstellar medium widely exists in the universe at multi-scales. In this study, we introduce the {\it Multi-scale Decomposition Reconstruction} method, an equation-based model designed to derive width maps of interstellar medium…
Diffusions are a successful technique to sample from high-dimensional distributions. The target distribution can be either explicitly given or learnt from a collection of samples. They implement a diffusion process whose endpoint is a…
In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
Advances in mobile computing technologies have made it possible to monitor and apply data-driven interventions across complex systems in real time. Markov decision processes (MDPs) are the primary model for sequential decision problems with…
By decomposing the image formation process into a sequential application of denoising autoencoders, diffusion models (DMs) achieve state-of-the-art synthesis results on image data and beyond. Additionally, their formulation allows for a…
Hyperdimensional computing (HDC) is an increasingly popular computing paradigm with immense potential for future intelligent applications. Although the main ideas already took form in the 1990s, HDC recently gained significant attention,…
This paper presents a general and systematic discussion of various symbolic representations of iterated maps through subshifts. We give a unified model for all continuous maps on a metric space, by representing a map through a general…