Related papers: Neural Operator-Grounded Continuous Tensor Functio…

We analyze the performance of encoder-decoder neural models and compare them with well-known established methods. The latter represent different classes of traditional approaches that are applied to the monotone sequence-to-sequence tasks…

The linear transform-based tensor nuclear norm (TNN) methods have recently obtained promising results for tensor completion. The main idea of this type of methods is exploiting the low-rank structure of frontal slices of the targeted tensor…

The Monte Carlo-type Neural Operator (MCNO) introduces a lightweight architecture for learning solution operators for parametric PDEs by directly approximating the kernel integral using a Monte Carlo approach. Unlike Fourier Neural…

Good pre-trained visual representations could enable robots to learn visuomotor policy efficiently. Still, existing representations take a one-size-fits-all-tasks approach that comes with two important drawbacks: (1) Being completely…

Implicit Neural Representations (INRs) are widely used to encode data as continuous functions, enabling the visualization of large-scale multivariate scientific simulation data with reduced memory usage. However, existing INR-based methods…

Performing machine learning on structured data is complicated by the fact that such data does not have vectorial form. Therefore, multiple approaches have emerged to construct vectorial representations of structured data, from kernel and…

Neural Operators (NOs) have emerged as powerful tools for learning mappings between function spaces. Among them, the kernel integral operator has been widely used in universally approximating architectures. Following the original…

Tucker decomposition is one of the most popular models for analyzing and compressing large-scale tensorial data. Existing Tucker decomposition algorithms usually rely on a single solver to compute the factor matrices and core tensor, and…

The recent rise of generative artificial intelligence (AI), powered by Transformer networks, has achieved remarkable success in natural language processing, computer vision, and graphics. However, the application of Transformers in…

Generating formal-language programs represented by relational tuples, such as Lisp programs or mathematical operations, to solve problems stated in natural language is a challenging task because it requires explicitly capturing discrete…

We introduce simple group-theoretic techniques for classifying conformally-invariant tensor-structures. With them, we classify tensor structures of general n-point functions of non-conserved operators, and $n\geq 4$-point functions of…

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…

As repositories of large scale data in earth observation (EO) have grown, so have transfer and storage costs for model training and inference, expending significant resources. We introduce Neural Embedding Compression (NEC), based on the…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…

Tensor networks are a compressed format for multi-dimensional data. One-dimensional tensor networks -- often referred to as tensor trains (TT) or matrix product states (MPS) -- are increasingly being used as a numerical ansatz for continuum…

Operator learning is a variant of machine learning that is designed to approximate maps between function spaces from data. The Fourier Neural Operator (FNO) is one of the main model architectures used for operator learning. The FNO combines…

We review a class of methods that can be collected under the name nonlinear transform coding (NTC), which over the past few years have become competitive with the best linear transform codecs for images, and have superseded them in terms of…

A long-standing goal in scene understanding is to obtain interpretable and editable representations that can be directly constructed from a raw monocular RGB-D video, without requiring specialized hardware setup or priors. The problem is…

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations. However, in time-dependent problems, standard training strategies such as teacher forcing introduce a mismatch between…