相关论文: Neural Network Symmetrisation in Concrete Settings

We consider the problem of symmetrising a neural network along a group homomorphism: given a homomorphism $\varphi : H \to G$, we would like a procedure that converts $H$-equivariant neural networks to $G$-equivariant ones. We formulate…

Symmetries (transformations by group actions) are present in many datasets, and leveraging them holds considerable promise for improving predictions in machine learning. In this work, we aim to understand when and how deep networks -- with…

Deep neural networks have been widely used as universal approximators for functions with inherent physical structures, including permutation symmetry. In this paper, we construct symmetric deep neural networks to approximate symmetric…

Deep neural networks (NN) have achieved great success in many applications. However, why do deep neural networks obtain good generalization at an over-parameterization regime is still unclear. To better understand deep NN, we establish the…

Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…

This work provides an additional step in the theoretical understanding of neural networks. We consider neural networks with one hidden layer and show that when learning symmetric functions, one can choose initial conditions so that standard…

Reliable generalization lies at the heart of safe ML and AI. However, understanding when and how neural networks generalize remains one of the most important unsolved problems in the field. In this work, we conduct an extensive empirical…

For certain infinitely-wide neural networks, the neural tangent kernel (NTK) theory fully characterizes generalization, but for the networks used in practice, the empirical NTK only provides a rough first-order approximation. Still, a…

In this paper, we focus on the topic Synchronization and consensus of Complex Networks and their relationships. It is revealed that two topics are closely relating to each other and all results given in \cite{Li1,Li2} and many other papers…

For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to `train' or `learn' the network are faced with a very large number (in…

In this paper, we focus on the topic Synchronization and consensus of Complex Networks and their relationships. It is revealed that two topics are closely relating to each other and all results given in \cite{Li} can be obtained by the…

Modern deep learning models are highly overparameterized, resulting in large sets of parameter configurations that yield the same outputs. A significant portion of this redundancy is explained by symmetries in the parameter…

Generalization is essential for deep learning. In contrast to previous works claiming that Deep Neural Networks (DNNs) have an implicit regularization implemented by the stochastic gradient descent, we demonstrate explicitly Bayesian…

At this work we introduce horizontally symmetric convolutional kernels for CNNs which make the network output invariant to horizontal flips of the image. We also study other types of symmetric kernels which lead to vertical flip invariance,…

We consider Convolutional Neural Networks (CNNs) with 2D structured features that are symmetric in the spatial dimensions. Such networks arise in modeling pairwise relationships for a sequential recommendation problem, as well as secondary…

We present a general framework for symmetrizing an arbitrary neural-network architecture and making it equivariant with respect to a given group. We build upon the proposals of Kim et al. (2023); Kaba et al. (2023) for symmetrization, and…

We propose a novel class of neural network-like parametrized functions, i.e., general transformation neural networks (GTNNs), for high-dimensional approximation. Conventional deep neural networks sometimes perform less accurately on…

A unified framework for analyzing generalized synchronization in coupled chaotic systems from data is proposed. The key of the proposed approach is the use of the kernel methods recently developed in the field of machine learning. Several…

Despite huge successes on a wide range of tasks, neural networks are known to sometimes struggle to generalise to unseen data. Many approaches have been proposed over the years to promote the generalisation ability of neural networks,…

Humans represent scenes and objects in rich feature spaces, carrying information that allows us to generalise about category memberships and abstract functions with few examples. What determines whether a neural network model generalises…