相关论文: Neural network-based singularity detection and app…

In this work, we develop a novel neural network (NN) approach to solve the discrete inverse conductivity problem of recovering the conductivity profile on network edges from the discrete Dirichlet-to-Neumann map on a square lattice. The…

The weight space of an artificial neural network can be systematically explored using tools from statistical mechanics. We employ a combination of a hybrid Monte Carlo algorithm which performs long exploration steps, a ratchet-based…

Neural networks often operate in the overparameterized regime, in which there are far more parameters than training samples, allowing the training data to be fit perfectly. That is, training the network effectively learns an interpolating…

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very…

A key challenge in scientific machine learning is solving partial differential equations (PDEs) on complex domains, where the curved geometry complicates the approximation of functions and their derivatives required by differential…

To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approach explicitly crafted for solving multiscale elliptic…

This paper introduces a new learning paradigm termed Neural Metamorphosis (NeuMeta), which aims to build self-morphable neural networks. Contrary to crafting separate models for different architectures or sizes, NeuMeta directly learns the…

Parameter-efficient fine-tuning (PEFT) methods such as \lora{} adapt large pretrained models by adding small weight-space updates. While effective, weight deltas are hard to interpret mechanistically, and they do not directly expose…

Neural networks (NNs) whose subnetworks implement reusable functions are expected to offer numerous advantages, including compositionality through efficient recombination of functional building blocks, interpretability, preventing…

Artificial neural networks are functions depending on a finite number of parameters typically encoded as weights and biases. The identification of the parameters of the network from finite samples of input-output pairs is often referred to…

In this paper we approach the problem of unique and stable identifiability of generic deep artificial neural networks with pyramidal shape and smooth activation functions from a finite number of input-output samples. More specifically we…

We propose a custom learning algorithm for shallow over-parameterized neural networks, i.e., networks with single hidden layer having infinite width. The infinite width of the hidden layer serves as an abstraction for the…

We address the structure identification and the uniform approximation of sums of ridge functions $f(x)=\sum_{i=1}^m g_i(a_i\cdot x)$ on ${\mathbb R}^d$, representing a general form of a shallow feed-forward neural network, from a small…

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the…

$\partial\mathbb{B}$ nets are differentiable neural networks that learn discrete boolean-valued functions by gradient descent. $\partial\mathbb{B}$ nets have two semantically equivalent aspects: a differentiable soft-net, with real weights,…

We propose a compression based continual task learning method that can dynamically grow a neural network. Inspired from the recent model compression techniques, we employ compression-aware training and perform low-rank weight approximations…

This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized,…

This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any H\"{o}lder smooth…

Neural networks activated by the rectified linear unit (ReLU) play a central role in the recent development of deep learning. The topic of approximating functions from H\"older spaces by these networks is crucial for understanding the…

The method recently introduced in arXiv:2011.10115 realizes a deep neural network with just a single nonlinear element and delayed feedback. It is applicable for the description of physically implemented neural networks. In this work, we…