Related papers: Using Self-Organising Mappings to Learn the Struct…

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable…

Many scientific areas are faced with the challenge of extracting information from large, complex, and highly structured data sets. A great deal of modern statistical work focuses on developing tools for handling such data. This paper…

Living organisms rely on molecular networks, such as gene circuits and signaling pathways, for information processing and robust decision-making in crowded, noisy environments. Recent advances show that interacting biomolecules…

In artificial intelligence (AI), especially deep learning, data diversity and volume play a pivotal role in model development. However, training a robust deep learning model often faces challenges due to data privacy, regulations, and the…

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…

Dynamics of protein self-assembly on the inorganic surface and the resultant geometric patterns are visualized using high-speed atomic force microscopy. The time dynamics of the classical macroscopic descriptors such as 2D Fast Fourier…

It is a challenge to manage complex systems efficiently without confronting NP-hard problems. To address the situation we suggest to use self-organization processes of prime integer relations for information processing. Self-organization…

In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches)…

Data preparation, i.e. the process of transforming raw data into a format that can be used for training effective machine learning models, is a tedious and time-consuming task. For image data, preprocessing typically involves a sequence of…

Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…

Big data often has emergent structure that exists at multiple levels of abstraction, which are useful for characterizing complex interactions and dynamics of the observations. Here, we consider multiple levels of abstraction via a…

The paper demonstrates that invariant foliations are accurate, data-efficient and practical tools for data-driven modelling of physical systems. Invariant foliations can be fitted to data that either fill the phase space or cluster about an…

Federated learning is an emerging distributed machine learning framework aiming at protecting data privacy. Data heterogeneity is one of the core challenges in federated learning, which could severely degrade the convergence rate and…

Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to…

We propose a compact and effective framework to fuse multimodal features at multiple layers in a single network. The framework consists of two innovative fusion schemes. Firstly, unlike existing multimodal methods that necessitate…

Detecting structure in data is the first step to arrive at meaningful representations for systems. This is particularly challenging for dislocation networks evolving as a consequence of plastic deformation of crystalline systems. Our study…

Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…

In recent years, deep learning networks have made remarkable strides in the domain of multi-exposure image fusion. Nonetheless, prevailing approaches often involve directly feeding over-exposed and under-exposed images into the network,…

An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or…

Modern information processing relies on the axiom that high-dimensional data lie near low-dimensional geometric structures. This paper revisits the problem of data-driven learning of these geometric structures and puts forth two new…