Related papers: Neural Flow Operators can Approximate any Operator…

A key challenge in modern deep learning theory is to explain the remarkable success of gradient-based optimization methods when training large-scale, complex deep neural networks. Though linear convergence of such methods has been proved…

Neural operator methods have emerged as powerful tools for learning mappings between infinite-dimensional function spaces, yet their potential in optimal control remains largely unexplored. We focus on multi-task control problems, whose…

We develop a theoretical analysis for special neural network architectures, termed operator recurrent neural networks, for approximating nonlinear functions whose inputs are linear operators. Such functions commonly arise in solution…

Large language models (LLMs) have shown strong potential in automating the design of agentic workflows. However, existing methods still rely heavily on manually predefined operators, limiting generalization and scalability. To address this…

Operator learning refers to the application of ideas from machine learning to approximate (typically nonlinear) operators mapping between Banach spaces of functions. Such operators often arise from physical models expressed in terms of…

We present a framework to use recently introduced Capsule Networks for solving the problem of Optical Flow, one of the fundamental computer vision tasks. Most of the existing state of the art deep architectures either uses a correlation…

Neural network width and depth are fundamental aspects of network topology. Universal approximation theorems provide that with increasing width or depth, there exists a neural network that approximates a function arbitrarily well. These…

Neural networks are becoming a popular tool for solving many real-world problems such as object recognition and machine translation, thanks to its exceptional performance as an end-to-end solution. However, neural networks are complex…

Deep learning architectures are highly diverse. To prove their universal approximation properties, existing works typically rely on model-specific proofs. Generally, they construct a dedicated mathematical formulation for each architecture…

Concept-based interpretability for Convolutional Neural Networks (CNNs) aims to align internal model representations with high-level semantic concepts, but existing approaches largely overlook the semantic roles of individual filters and…

We consider a family of deep neural networks consisting of two groups of convolutional layers, a downsampling operator, and a fully connected layer. The network structure depends on two structural parameters which determine the numbers of…

Many dynamical processes of complex systems can be understood as the dynamics of a group of nodes interacting on a given network structure. However, finding such interaction structure and node dynamics from time series of node behaviours is…

Classical neural network approximation results take the form: for every function $f$ and every error tolerance $\epsilon > 0$, one constructs a neural network whose architecture and weights depend on $\epsilon$. This paper introduces a…

Several non-linear operators in stochastic analysis, such as solution maps to stochastic differential equations, depend on a temporal structure which is not leveraged by contemporary neural operators designed to approximate general maps…

Function fitting/approximation plays a fundamental role in computer graphics and other engineering applications. While recent advances have explored neural networks to address this task, these methods often rely on architectures with many…

We generalize the fractional packing framework of Garg and Koenemann to the case of linear fractional packing problems over polyhedral cones. More precisely, we provide approximation algorithms for problems of the form $\max\{c^T x : Ax…

Normalizing flows have grown more popular over the last few years; however, they continue to be computationally expensive, making them difficult to be accepted into the broader machine learning community. In this paper, we introduce a…

Traditionally, most complex intelligence architectures are extremely non-convex, which could not be well performed by convex optimization. However, this paper decomposes complex structures into three types of nodes: operators, algorithms…

We introduce graph normalizing flows: a new, reversible graph neural network model for prediction and generation. On supervised tasks, graph normalizing flows perform similarly to message passing neural networks, but at a significantly…

Neural Operators that directly learn mappings between function spaces, such as Deep Operator Networks (DONs) and Fourier Neural Operators (FNOs), have received considerable attention. Despite the universal approximation guarantees for DONs…