Related papers: Basis-to-Basis Operator Learning Using Function En…

Neural operator learning as a means of mapping between complex function spaces has garnered significant attention in the field of computational science and engineering (CS&E). In this paper, we apply Neural operator learning to the…

End-to-end autonomous driving has made impressive progress in recent years. Existing methods usually adopt the decoupled encoder-decoder paradigm, where the encoder extracts hidden features from raw sensor data, and the decoder outputs the…

We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…

This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…

Recent studies on Learning to Optimize (L2O) suggest a promising path to automating and accelerating the optimization procedure for complicated tasks. Existing L2O models parameterize optimization rules by neural networks, and learn those…

There has been great progress in unifying various table-to-text tasks using a single encoder-decoder model trained via multi-task learning (Xie et al., 2022). However, existing methods typically encode task information with a simple dataset…

The convolution operator is the fundamental building block of modern convolutional neural networks (CNNs), owing to its simplicity, translational equivariance, and efficient implementation. However, its structure as a fixed, linear,…

This expository article presents the approach to statistical machine learning based on reproducing kernel Hilbert spaces. The basic framework is introduced for scalar-valued learning and then extended to operator learning. Finally, learning…

Image-based table recognition is a challenging task due to the diversity of table styles and the complexity of table structures. Most of the previous methods focus on a non-end-to-end approach which divides the problem into two separate…

Recent metric-based meta-learning approaches, which learn a metric space that generalizes well over combinatorial number of different classification tasks sampled from a task distribution, have been shown to be effective for few-shot…

Outside of transfer learning settings, reinforcement learning agents start their learning process from a clean slate. As a result, such agents have to go through a slow process to learn even the most obvious skills required to solve a…

Self-evolving scientific agents capable of conquering the hard tail of formal mathematics require Compositional Learning Behaviours (CLBs) -- the capacity to ground and recombine novel symbolic structures in context, beyond mere…

Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel…

The ability to learn robust policies while generalizing over large discrete action spaces is an open challenge for intelligent systems, especially in noisy environments that face the curse of dimensionality. In this paper, we present a…

We develop fast and memory efficient numerical methods for learning functions of many variables that admit sparse representations in terms of general bounded orthonormal tensor product bases. Such functions appear in many applications…

Many classical Computer Vision problems, such as essential matrix computation and pose estimation from 3D to 2D correspondences, can be tackled by solving a linear least-square problem, which can be done by finding the eigenvector…

On-line and batch learning of a perceptron in a discrete weight space, where each weight can take $2 L+1$ different values, are examined analytically and numerically. The learning algorithm is based on the training of the continuous…

Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…

End-to-end training of deep learning-based models allows for implicit learning of intermediate representations based on the final task loss. However, the end-to-end approach ignores the useful domain knowledge encoded in explicit…

This paper investigates the possibility of approximating multiple mathematical operations in latent space for expression derivation. To this end, we introduce different multi-operational representation paradigms, modelling mathematical…