Related papers: Geometric Neural Operators via Lie Group-Constrain…

We present a new class of stochastic, geometrically-driven optimization algorithms on the orthogonal group $O(d)$ and naturally reductive homogeneous manifolds obtained from the action of the rotation group $SO(d)$. We theoretically and…

Quantum graphical models (QGMs) extend the classical framework for reasoning about uncertainty by incorporating the quantum mechanical view of probability. Prior work on QGMs has focused on hidden quantum Markov models (HQMMs), which can be…

Machine unlearning (MU) has emerged to enhance the privacy and trustworthiness of deep neural networks. Approximate MU is a practical method for large-scale models. Our investigation into approximate MU starts with identifying the steepest…

We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). These systems are typically…

We explore the use of a topological manifold, represented as a collection of charts, as the target space of neural network based representation learning tasks. This is achieved by a simple adjustment to the output of an encoder's network…

Geometric deep learning has gained much attention in recent years due to more available data acquired from non-Euclidean domains. Some examples include point clouds for 3D models and wireless sensor networks in communications. Graphs are…

Handling orientations of robots and objects is a crucial aspect of many applications. Yet, ever so often, there is a lack of mathematical correctness when dealing with orientations, especially in learning pipelines involving, for example,…

Norm-constrained linear minimization oracle (LMO)-based optimizers such as spectral gradient descent and Muon are attractive in large-scale learning, but extending them to manifold-constrained problems is nontrivial and often leads to…

This study aims to predict the spatio-temporal evolution of physical quantities observed in multi-layered display panels subjected to the drop impact of a ball. To model these complex interactions, graph neural networks have emerged as…

Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…

Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we…

Leveraging nonlinear parametrizations for model reduction can overcome the Kolmogorov barrier that affects transport-dominated problems. In this work, we build on the reduced dynamics given by Neural Galerkin schemes and propose to…

Gradient-based Meta-RL (GMRL) refers to methods that maintain two-level optimisation procedures wherein the outer-loop meta-learner guides the inner-loop gradient-based reinforcement learner to achieve fast adaptations. In this paper, we…

In this paper we propose and study a technique to impose structural constraints on the output of a neural network, which can reduce amount of computation and number of parameters besides improving prediction accuracy when the output is…

Enabling low precision implementations of deep learning models, without considerable performance degradation, is necessary in resource and latency constrained settings. Moreover, exploiting the differences in sensitivity to quantization…

Symmetric positive definite (SPD) matrices used as feature descriptors in image recognition are usually high dimensional. Traditional manifold learning is only applicable for reducing the dimension of high-dimensional vector-form data. For…

In multi-task learning (MTL), we improve the performance of key machine learning algorithms by training various tasks jointly. When the number of tasks is large, modeling task structure can further refine the task relationship model. For…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Tracking non-stationary covariance matrices is fundamental to vision yet hindered by existing estimators that either neglect manifold constraints or rely on first-order updates, incurring inevitable phase lag during rapid evolution. We…

Purpose: To develop a deep learning method on a nonlinear manifold to explore the temporal redundancy of dynamic signals to reconstruct cardiac MRI data from highly undersampled measurements. Methods: Cardiac MR image reconstruction is…