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

Hilbert order is widely applied in many areas. However, most of the algorithms are confined to low dimensional cases. In this paper, algorithms for encoding and decoding arbitrary dimensional Hilbert order are presented. Eight algorithms…

Modern retrieval system often requires recomputing the representation of every piece of data in the gallery when updating to a better representation model. This process is known as backfilling and can be especially costly in the real world…

The B-operators (abbreviation for Brownian-type operators) are upper triangular 2x2 block matrix operators that satisfy certain algebraic constraints. The purpose of this paper is to characterize the weak, the strongand the uniform…

As an emerging paradigm in scientific machine learning, neural operators aim to learn operators, via neural networks, that map between infinite-dimensional function spaces. Several neural operators have been recently developed. However, all…

This paper presents a framework for computing random operator-valued feature maps for operator-valued positive definite kernels. This is a generalization of the random Fourier features for scalar-valued kernels to the operator-valued case.…

Computer vision is difficult, partly because the desired mathematical function connecting input and output data is often complex, fuzzy and thus hard to learn. Coarse-to-fine (C2F) learning is a promising direction, but it remains unclear…

We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…

Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…

The core challenge of high-dimensional and expensive black-box optimization (BBO) is how to obtain better performance faster with little function evaluation cost. The essence of the problem is how to design an efficient optimization…

Bi-linear feature learning models, like the gated autoencoder, were proposed as a way to model relationships between frames in a video. By minimizing reconstruction error of one frame, given the previous frame, these models learn "mapping…

Many successful deep learning architectures are equivariant to certain transformations in order to conserve parameters and improve generalization: most famously, convolution layers are equivariant to shifts of the input. This approach only…

Results in interpretability suggest that large vision and language models learn implicit linear encodings when models are biased by in-context prompting. However, the existence of similar linear representations in more general adaptation…

We present a new framework for computing fine-scale solutions of multiscale Partial Differential Equations (PDEs) using operator learning tools. Obtaining fine-scale solutions of multiscale PDEs can be challenging, but there are many…

Hyperdimensional Computing (HDC) is a computation framework based on properties of high-dimensional random spaces. It is particularly useful for machine learning in resource-constrained environments, such as embedded systems and IoT, as it…

Unlearning in large foundation models (e.g., LLMs) is essential for enabling dynamic knowledge updates, enforcing data deletion rights, and correcting model behavior. However, existing unlearning methods often require full-model fine-tuning…

The use of high-dimensional features has become a normal practice in many computer vision applications. The large dimension of these features is a limiting factor upon the number of data points which may be effectively stored and processed,…

Adversarial training provides a principled approach for training robust neural networks. From an optimization perspective, adversarial training is essentially solving a bilevel optimization problem. The leader problem is trying to learn a…

Recent advancements in imitation learning have led to transformer-based behavior foundation models (BFMs) that enable multi-modal, human-like control for humanoid agents. While excelling at zero-shot generation of robust behaviors, BFMs…

Learning to optimize (L2O) has recently emerged as a promising approach to solving optimization problems by exploiting the strong prediction power of neural networks and offering lower runtime complexity than conventional solvers. While L2O…

Vision-language foundation models like CLIP have revolutionized the field of artificial intelligence. Nevertheless, VLM models supporting multi-language, e.g., in both Chinese and English, have lagged due to the relative scarcity of…