Related papers: Selecting High-Dimensional Representations of Phys…

Machine-learning generative methods for material design are constructed by representing a given chemical structure, either a solid or a molecule, over appropriate atomic features, generally called structural descriptors. These must be fully…

Markov State Models (MSM) are widely used to elucidate dynamic properties of molecular systems from unbiased Molecular Dynamics (MD). However, the implementation of reweighting schemes for MSMs to analyze biased simulations, for example…

This chapter discusses the way in which dimensionality reduction algorithms such as diffusion maps and sketch-map can be used to analyze molecular dynamics trajectories. The first part discusses how these various algorithms function, as…

Diffusion Maps framework is a kernel based method for manifold learning and data analysis that defines diffusion similarities by imposing a Markovian process on the given dataset. Analysis by this process uncovers the intrinsic geometric…

Deep neural networks can learn powerful prior probability models for images, as evidenced by the high-quality generations obtained with recent score-based diffusion methods. But the means by which these networks capture complex global…

This work introduces the Grassmannian Diffusion Maps, a novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the…

This paper addresses the problem of mapping high-dimensional data to a low-dimensional space, in the presence of other known features. This problem is ubiquitous in science and engineering as there are often controllable/measurable features…

We present a new object representation, called Dense RepPoints, that utilizes a large set of points to describe an object at multiple levels, including both box level and pixel level. Techniques are proposed to efficiently process these…

Detail features of magnetic resonance images play a cru-cial role in accurate medical diagnosis and treatment, as they capture subtle changes that pose challenges for doc-tors when performing precise judgments. However, the widely utilized…

Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining high-dimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to…

This work presents an unsupervised deep learning scheme that exploiting high-dimensional assisted score-based generative model for color image restoration tasks. Considering that the sample number and internal dimension in score-based…

Advances in deep learning models have revolutionized the study of biomolecule systems and their mechanisms. Graph representation learning, in particular, is important for accurately capturing the geometric information of biomolecules at…

Diffusion probabilistic models (DPMs) have achieved remarkable quality in image generation that rivals GANs'. But unlike GANs, DPMs use a set of latent variables that lack semantic meaning and cannot serve as a useful representation for…

Magnetic Resonance Imaging (MRI) is a powerful imaging technique widely used for visualizing structures within the human body and in other fields such as plant sciences. However, there is a demand to develop fast 3D-MRI reconstruction…

Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…

In this paper, we introduce a denoising diffusion algorithm to discover microstructures with nonlinear fine-tuned properties. Denoising diffusion probabilistic models are generative models that use diffusion-based dynamics to gradually…

Accurate dose distribution prediction is crucial in the radiotherapy planning. Although previous methods based on convolutional neural network have shown promising performance, they have the problem of over-smoothing, leading to prediction…

Faithfully representing chemical environments is essential for describing materials and molecules with machine learning approaches. Here, we present a systematic classification of these representations and then investigate: (i) the…

Diffusion Probabilistic Models (DPMs) have recently demonstrated impressive results on various generative tasks.Despite its promises, the learned representations of pre-trained DPMs, however, have not been fully understood. In this paper,…

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…