Related papers: Multi-Operational Mathematical Derivations in Late…
This work explores the application of deep operator learning principles to a problem in statistical physics. Specifically, we consider the linear kinetic equation, consisting of a differential advection operator and an integral collision…
The Active Subspace (AS) method is a widely used technique for identifying the most influential directions in high-dimensional input spaces that affect the output of a computational model. The standard AS algorithm requires a sufficient…
We propose an operadic framework suitable for describing algebraic structures with operations being multilinear differential operators of varying orders or, more generally, formal series of such operators. The framework is built upon the…
Accurately solving partial differential equations (PDEs) is essential across many scientific disciplines. However, high-fidelity solvers can be computationally prohibitive, motivating the development of reduced-order models (ROMs).…
Learning dynamical systems through operator-theoretic representations provides a powerful framework for analyzing complex dynamics, as spectral quantities such as eigenvalues and invariant structures encode characteristic time scales and…
Given a set of matrices, modeled as samples of a matrix-valued function, we suggest a method to approximate the underline function using a product approximation operator. This operator extends known approximation methods by exploiting the…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
We assume some standard choices for the branch cuts of a group of functions and consider the problem of then calculating the branch cuts of expressions involving those functions. Typical examples include the addition formulae for inverse…
State-space exploration is an essential step in many modeling and analysis problems. Its goal is to find the states reachable from the initial state of a discrete-state model described. The state space can used to answer important…
We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…
Decoder-only language models have the ability to dynamically switch between various computational tasks based on input prompts. Despite many successful applications of prompting, there is very limited understanding of the internal mechanism…
Different encodings of datapoints in the latent space of latent-vector generative models may result in more or less effective and disentangled characterizations of the different explanatory factors of variation behind the data. Many works…
Manifold learning seeks a low dimensional representation that faithfully captures the essence of data. Current methods can successfully learn such representations, but do not provide a meaningful set of operations that are associated with…
We present a multi-task learning formulation for Deep Gaussian processes (DGPs), through non-linear mixtures of latent processes. The latent space is composed of private processes that capture within-task information and shared processes…
We introduce a scalable approach for object pose estimation trained on simulated RGB views of multiple 3D models together. We learn an encoding of object views that does not only describe an implicit orientation of all objects seen during…
Offline handwritten mathematical expression recognition is a challenging task, because handwritten mathematical expressions mainly have two problems in the process of recognition. On one hand, it is how to correctly recognize different…
The manipulator workspace mapping is an important problem in robotics and has attracted significant attention in the community. However, most of the pre-existing algorithms have expensive time complexity due to the reliance on sophisticated…
Teleoperation is a valuable tool for robotic manipulators in highly unstructured environments. However, finding an intuitive mapping between a human hand and a non-anthropomorphic robot hand can be difficult, due to the hands' dissimilar…
Recent advances of image-to-image translation focus on learning the one-to-many mapping from two aspects: multi-modal translation and multi-domain translation. However, the existing methods only consider one of the two perspectives, which…
Humans inherently possess generalizable visual representations that empower them to efficiently explore and interact with the environments in manipulation tasks. We advocate that such a representation automatically arises from…