相关论文: The Kolmogorov-Arnold representation theorem revis…

Deep Reinforcement Learning (RL) powered by neural net approximation of the Q function has had enormous empirical success. While the theory of RL has traditionally focused on linear function approximation (or eluder dimension) approaches,…

Convolutional Neural Networks (CNNs) have achieved comparable error rates to well-trained human on ILSVRC2014 image classification task. To achieve better performance, the complexity of CNNs is continually increasing with deeper and bigger…

Comparing different neural network representations and determining how representations evolve over time remain challenging open questions in our understanding of the function of neural networks. Comparing representations in neural networks…

Recently, Kolmogorov-Arnold Networks (KANs) have been proposed as an alternative to multilayer perceptrons, suggesting advantages in performance and interpretability. We study a typical binary event classification task in high-energy…

Kolmogorov-Arnold Networks (KAN) \cite{liu2024kan} were very recently proposed as a potential alternative to the prevalent architectural backbone of many deep learning models, the multi-layer perceptron (MLP). KANs have seen success in…

Although neural networks traditionally are typically used to approximate functions defined over $\mathbb{R}^n$, the successes of graph neural networks, point-cloud neural networks, and manifold deep learning among other methods have…

In comparison to classical shallow representation learning techniques, deep neural networks have achieved superior performance in nearly every application benchmark. But despite their clear empirical advantages, it is still not well…

The ability of neural networks to represent more features than neurons makes interpreting them challenging. This phenomenon, known as superposition, has spurred efforts to find architectures that are more interpretable than standard…

Multilayer Perceptrons (MLPs) have long been a cornerstone in deep learning, known for their capacity to model complex relationships. Recently, Kolmogorov-Arnold Networks (KANs) have emerged as a compelling alternative, utilizing highly…

The efficiency of recurrent neural networks (RNNs) in dealing with sequential data has long been established. However, unlike deep, and convolution networks where we can attribute the recognition of a certain feature to every layer, it is…

Symbolic neural networks, such as Kolmogorov-Arnold Networks (KAN), offer a promising approach for integrating prior knowledge with data-driven methods, making them valuable for addressing inverse problems in scientific and engineering…

A new Kolmogorov-Arnold network (KAN) is proposed to approximate potentially irregular functions in high dimensions. We provide error bounds for this approximation, assuming that the Kolmogorov-Arnold expansion functions are sufficiently…

Kolmogorov-Arnold networks (KANs) as an alternative to multi-layer perceptrons (MLPs) are a recent development demonstrating strong potential for data-driven modeling. This work applies KANs as the backbone of a neural ordinary differential…

This paper aims to interpret the mechanism of feedforward ReLU networks by exploring their solutions for piecewise linear functions, through the deduction from basic rules. The constructed solution should be universal enough to explain some…

We introduce a novel deep learning algorithm for computing convex conjugates of differentiable convex functions, a fundamental operation in convex analysis with various applications in different fields such as optimization, control theory,…

Deep learning methods have been widely used as an end-to-end modeling strategy of electrical energy systems because of their conveniency and powerful pattern recognition capability. However, due to the "closed-box" nature, deep learning…

Consider a feedforward neural network $\psi: \mathbb{R}^d\rightarrow \mathbb{R}^d$ such that $\psi\approx \nabla f$, where $f:\mathbb{R}^d \rightarrow \mathbb{R}$ is a smooth function, therefore $\psi$ must satisfy $\partial_j \psi_i =…

In this paper, we study the problem of optimizing a two-layer artificial neural network that best fits a training dataset. We look at this problem in the setting where the number of parameters is greater than the number of sampled points.…

We provide a refined characterization of the super-Turing computational power of analog, evolving, and stochastic neural networks based on the Kolmogorov complexity of their real weights, evolving weights, and real probabilities,…

We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors $\boldsymbol x \in \mathbb R^d$, $r$ hidden units with weights $\{\boldsymbol w_i\}_{1\le…