Related papers: Geometry-Preserving Neural Architectures on Manifo…
Neural models learn representations of high-dimensional data on low-dimensional manifolds. Multiple factors, including stochasticities in the training process, model architectures, and additional inductive biases, may induce different…
In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Common datadriven and learning-based methods such as neural…
We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries. To this end, we…
Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…
We integrate two powerful ideas, geometry and deep visual representation learning, into recurrent network architectures for mobile visual scene understanding. The proposed networks learn to "lift" and integrate 2D visual features over time…
Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…
Learning unknown dynamics under environmental (or external) constraints is fundamental to many fields (e.g., modern robotics), particularly challenging when constraint information is only locally available and uncertain. Existing approaches…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…
Diffusion-based manifold learning methods have proven useful in representation learning and dimensionality reduction of modern high dimensional, high throughput, noisy datasets. Such datasets are especially present in fields like biology…
This paper investigates the challenge of learning image manifolds, specifically pose manifolds, of 3D objects using limited training data. It proposes a DNN approach to manifold learning and for predicting images of objects for novel,…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
Continual learning methods usually preserve old behavior by regularizing parameters, matching old outputs, or replaying previous examples. These strategies can reduce forgetting, but they do not directly specify how the latent…
Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…
Deep Generative Models are frequently used to learn continuous representations of complex data distributions using a finite number of samples. For any generative model, including pre-trained foundation models with Diffusion or Transformer…
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…
How can we design neural networks that allow for stable universal approximation of maps between topologically interesting manifolds? The answer is with a coordinate projection. Neural networks based on topological data analysis (TDA) use…
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…
We present recurrent geometry-aware neural networks that integrate visual information across multiple views of a scene into 3D latent feature tensors, while maintaining an one-to-one mapping between 3D physical locations in the world scene…
Despite the promise of scientific machine learning (SciML) in combining data-driven techniques with mechanistic modeling, existing approaches for incorporating hard constraints in neural differential equations (NDEs) face significant…