Related papers: Partition of unity networks: deep hp-approximation

Unstructured pruning has the limitation of dealing with the sparse and irregular weights. By contrast, structured pruning can help eliminate this drawback but it requires complex criterion to determine which components to be pruned. To this…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of dimensionality. Specifically, we introduce a concept which we…

Recent advances in solving ordinary differential equations (ODEs) with neural networks have been remarkable. Neural networks excel at serving as trial functions and approximating solutions within functional spaces, aided by gradient…

Graph similarity computation aims to predict a similarity score between one pair of graphs to facilitate downstream applications, such as finding the most similar chemical compounds similar to a query compound or Fewshot 3D Action…

The universal approximation theorem establishes that neural networks can approximate any continuous function on a compact set. Later works in approximation theory provide quantitative approximation rates for ReLU networks on the class of…

Field-programmable gate arrays (FPGAs) are widely used to implement deep learning inference. Standard deep neural network inference involves the computation of interleaved linear maps and nonlinear activation functions. Prior work for…

We propose a method for approximating the contraction of a tensor network by partitioning the network into a sum of computationally cheaper networks. This method, which we call a partitioned network expansion (PNE), builds upon recent work…

Deep neural networks (DNNs) and Kolmogorov-Arnold networks (KANs) are popular methods for function approximation due to their flexibility and expressivity. However, they typically require a large number of trainable parameters to produce a…

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

Deploying deep neural networks (DNNs) on resource-constrained edge devices such as FPGAs requires a careful balance among latency, power, and hardware resource usage, while maintaining high accuracy. Existing Lookup Table (LUT)-based DNNs…

Privacy-Preserving Neural Networks (PPNN) are advanced to perform inference without breaching user privacy, which can serve as an essential tool for medical diagnosis to simultaneously achieve big data utility and privacy protection. As one…

We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…

In this work we introduce Lean Point Networks (LPNs) to train deeper and more accurate point processing networks by relying on three novel point processing blocks that improve memory consumption, inference time, and accuracy: a…

FPGAs have distinct advantages as a technology for deploying deep neural networks (DNNs) at the edge. Lookup Table (LUT) based networks, where neurons are directly modeled using LUTs, help maximize this promise of offering ultra-low latency…

This paper establishes an approximation theorem for randomized neural networks (RaNNs) whose hidden-layer parameters are uniformly sampled from a prescribed bounded domain. Our analysis shows that, for RaNNs of the form $\mathop{\sum}_i W_i…

In addition to being extremely non-linear, modern problems require millions if not billions of parameters to solve or at least to get a good approximation of the solution, and neural networks are known to assimilate that complexity by…

This paper presents Discriminative Part Network (DP-Net), a deep architecture with strong interpretation capabilities, which exploits a pretrained Convolutional Neural Network (CNN) combined with a part-based recognition module. This system…

Depth separation results propose a possible theoretical explanation for the benefits of deep neural networks over shallower architectures, establishing that the former possess superior approximation capabilities. However, there are no known…

Objective: To develop a robust and compact deep learning model for automated knee cartilage segmentation on point-of-care ultrasound (POCUS) devices. Methods: We propose MonoUNet, a novel, highly compact segmentation model consisting of (i)…