Related papers: Learning Topology-Driven Multi-Subspace Fusion for…

Many molecular properties depend on 3D geometry, where non-covalent interactions, stereochemical effects, and medium- to long-range forces are determined by spatial distances and angles that cannot be uniquely captured by a 2D bond graph.…

This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…

Recent deep learning models can efficiently combine inputs from different modalities (e.g., images and text) and learn to align their latent representations, or to translate signals from one domain to another (as in image captioning, or…

We introduce a novel co-learning paradigm for manifolds naturally equipped with a group action, motivated by recent developments on learning a manifold from attached fibre bundle structures. We utilize a representation theoretic mechanism…

This work presents a novel algorithm for progressively adapting neural network architecture along the depth. In particular, we attempt to address the following questions in a mathematically principled way: i) Where to add a new capacity…

Network embedding is an effective technique to learn the low-dimensional representations of nodes in networks. Real-world networks are usually with multiplex or having multi-view representations from different relations. Recently, there has…

As datasets used in scientific applications become more complex, studying the geometry and topology of data has become an increasingly prevalent part of the data analysis process. This can be seen for example with the growing interest in…

The goal of multi-modal learning is to use complimentary information on the relevant task provided by the multiple modalities to achieve reliable and robust performance. Recently, deep learning has led significant improvement in multi-modal…

Many existing learning-based grasping approaches concentrate on a single embodiment, provide limited generalization to higher DoF end-effectors and cannot capture a diverse set of grasp modes. We tackle the problem of grasping using…

We present a novel online depth map fusion approach that learns depth map aggregation in a latent feature space. While previous fusion methods use an explicit scene representation like signed distance functions (SDFs), we propose a learned…

Multiscale topology optimization (TO) of hyperelastic materials remains computationally prohibitive due to the repeated solution of microscale boundary value problems. In this work, we present a concurrent multiscale topology optimization…

Unmanned aerial vehicles (UAVs) are pivotal for future 6G non-terrestrial networks, yet their high mobility creates a complex coupled optimization problem for beamforming and trajectory design. Existing numerical methods suffer from…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Parametrizations of data manifolds in shape spaces can be computed using the rich toolbox of Riemannian geometry. This, however, often comes with high computational costs, which raises the question if one can learn an efficient neural…

Traditional neural networks (multi-layer perceptrons) have become an important tool in data science due to their success across a wide range of tasks. However, their performance is sometimes unsatisfactory, and they often require a large…

The problem of linking functional connectomics to behavior is extremely challenging due to the complex interactions between the two distinct, but related, data domains. We propose a coupled manifold optimization framework which projects…

We introduce a Bayesian model for inferring mixtures of subspaces of different dimensions. The key challenge in such a mixture model is specification of prior distributions over subspaces of different dimensions. We address this challenge…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

In the realm of multimodal data integration, feature alignment plays a pivotal role. This paper introduces an innovative approach to feature alignment that revolutionizes the fusion of multimodal information. Our method employs a novel…

We propose a deep autoencoder with graph topology inference and filtering to achieve compact representations of unorganized 3D point clouds in an unsupervised manner. Many previous works discretize 3D points to voxels and then use…