Related papers: Geometry-Preserving Neural Architectures on Manifo…

Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. Manifold learning algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through non-linear…

This paper introduces a new probabilistic framework for supervised learning in neural systems. It is designed to model complex, uncertain systems whose random outputs are strongly non-Gaussian given deterministic inputs. The architecture…

Most state-of-the-art deep geometric learning single-view reconstruction approaches rely on encoder-decoder architectures that output either shape parametrizations or implicit representations. However, these representations rarely preserve…

In this paper, we extend the previous convergence results for the generalized alternating projection method applied to subspaces in [arXiv:1703.10547] to hold also for smooth manifolds. We show that the algorithm locally behaves similarly…

Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…

Continual learning systems operating in fixed-dimensional spaces face a fundamental geometric barrier: the flat manifold problem. When experience is represented as a linear trajectory in Euclidean space, the geodesic distance between…

The recent proliferation of 3D content that can be consumed on hand-held devices necessitates efficient tools for transmitting large geometric data, e.g., 3D meshes, over the Internet. Detailed high-resolution assets can pose a challenge to…

We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

To preserve previously learned representations, continual learning systems must strike a balance between plasticity, the ability to acquire new knowledge, and stability. This stability-plasticity dilemma affects how representations can be…

Advances in neural operators have introduced discretization invariant surrogate models for PDEs on general geometries, yet many approaches struggle to encode local geometric structure and variable domains efficiently. We introduce enf2enf,…

Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…

Manifold learning aims to discover and represent low-dimensional structures underlying high-dimensional data while preserving critical topological and geometric properties. Existing methods often fail to capture local details with global…

Knowledge Graph Embeddings (KGEs) have shown promising performance on link prediction tasks by mapping the entities and relations from a knowledge graph into a geometric space (usually a vector space). Ultimately, the plausibility of the…

We study the problem of transfer learning, observing that previous efforts to understand its information-theoretic limits do not fully exploit the geometric structure of the source and target domains. In contrast, our study first…

The fundamental idea of embedding a network in a metric space is rooted in the principle of proximity preservation. Nodes are mapped into points of the space with pairwise distance that reflects their proximity in the network. Popular…

Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…

Deep neural networks learn feature representations via complex geometric transformations of the input data manifold. Despite the models' empirical success across domains, our understanding of neural feature representations is still…