# Greedy Shallow Networks: An Approach for Constructing and Training Neural Networks

## TL;DR

This paper introduces a greedy algorithm for constructing shallow neural networks with ReLU activation, using integral representations to efficiently select network parameters, potentially reducing reliance on backpropagation training.

## Contribution

The paper proposes a novel greedy approach utilizing the ridgelet transform to efficiently build and initialize shallow neural networks, offering an alternative to traditional training methods.

## Key findings

- The method effectively constructs neural networks with competitive performance.
- It provides improved initializations that can sometimes replace full training.
- Numerical experiments validate the approach's advantages over conventional techniques.

## Abstract

We present a greedy-based approach to construct an efficient single hidden layer neural network with the ReLU activation that approximates a target function. In our approach we obtain a shallow network by utilizing a greedy algorithm with the prescribed dictionary provided by the available training data and a set of possible inner weights. To facilitate the greedy selection process we employ an integral representation of the network, based on the ridgelet transform, that significantly reduces the cardinality of the dictionary and hence promotes feasibility of the greedy selection. Our approach allows for the construction of efficient architectures which can be treated either as improved initializations to be used in place of random-based alternatives, or as fully-trained networks in certain cases, thus potentially nullifying the need for backpropagation training. Numerical experiments demonstrate the tenability of the proposed concept and its advantages compared to the conventional techniques for selecting architectures and initializations for neural networks.