Related papers: Visualising energy landscapes through manifold lea…

Many real-world physics and engineering problems arise in geometrically complex domains discretized by meshes for numerical simulations. The nodes of these potentially irregular meshes naturally form point clouds whose limited tractability…

We present a new method GTSNE to visualize high-dimensional data points in the two dimensional map. The technique is a variation of t-SNE that produces better visualizations by capturing both the local neighborhood structure and the macro…

Simplicial map neural networks (SMNNs) are topology-based neural networks with interesting properties such as universal approximation ability and robustness to adversarial examples under appropriate conditions. However, SMNNs present some…

Learning policies for multi-entity systems in 3D environments is far more complicated against single-entity scenarios, due to the exponential expansion of the global state space as the number of entities increases. One potential solution of…

Graph Neural Networks (GNNs) are powerful models for graph-structured data, with broad applications. However, the interplay between GNN parameter optimization, expressivity, and generalization remains poorly understood. We address this by…

We propose a novel efficient architecture for learning long-term evolution in complex multi-scale physical systems which is based on the idea of separation of scales. Structures of various scales that dynamically emerge in the system…

Projections, or dimensionality reduction methods, are techniques of choice for the visual exploration of high-dimensional data. Many such techniques exist, each one of them having a distinct visual signature - i.e., a recognizable way to…

Potential Energy Surfaces (PESs) are an indispensable tool to investigate, characterise and understand chemical and biological systems in the gas and condensed phases. Advances in Machine Learning (ML) methodologies have led to the…

Global optimization of atomistic structure rely on the generation of new candidate structures in order to drive the exploration of the potential energy surface (PES) in search for the global minimum energy (GM) structure. In this work, we…

Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…

Manifold visualisation techniques are commonly used to visualise high-dimensional datasets in physical sciences. In this paper we apply a recently introduced manifold visualisation method, called Slise, on datasets from physics and…

In this paper, we propose GPSP, a novel Graph Partition and Space Projection based approach, to learn the representation of a heterogeneous network that consists of multiple types of nodes and links. Concretely, we first partition the…

Despite their effective use in various fields, many aspects of neural networks are poorly understood. One important way to investigate the characteristics of neural networks is to explore the loss landscape. However, most models produce a…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a…

We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the…

Sparse autoencoders (SAEs) have emerged as a powerful tool for uncovering interpretable features in large language models (LLMs) through the sparse directions they learn. However, the sheer number of extracted directions makes comprehensive…

Over the last two decades, Electron Energy Loss Spectroscopy (EELS) imaging with a scanning transmission electron microscope (STEM) has emerged as a technique of choice for visualizing complex chemical, electronic, plasmonic, and phononic…

Appearance-based gaze estimation frequently relies on deep Convolutional Neural Networks (CNNs). These models are accurate, but computationally expensive and act as "black boxes", offering little interpretability. Geometric methods based on…

Understanding the informative structures of scenes is essential for low-level vision tasks. Unfortunately, it is difficult to obtain a concrete visual definition of the informative structures because influences of visual features are…