Related papers: A Feedforward Unitary Equivariant Neural Network
Equivariant networks are specifically designed to ensure consistent behavior with respect to a set of input transformations, leading to higher sample efficiency and more accurate and robust predictions. However, redesigning each component…
We propose a novel learning method for multilayered neural networks which uses feedforward supervisory signal and associates classification of a new input with that of pre-trained input. The proposed method effectively uses rich input…
Feed-forward neural networks are a novel class of variational wave functions for correlated many-body quantum systems. Here, we propose a specific neural network ansatz suitable for systems with real-valued wave functions. Its…
Ever-increasing throughput specifications in semiconductor manufacturing require operating high-precision mechatronics, such as linear motors, at higher accelerations. In turn this creates higher nonlinear parasitic forces that cannot be…
Many learning tasks, including learning potential energy surfaces from ab initio calculations, involve global spatial symmetries and permutational symmetry between atoms or general particles. Equivariant graph neural networks are a standard…
Polynomial functions have plenty of useful analytical properties, but they are rarely used as learning models because their function class is considered to be restricted. This work shows that when trained properly polynomial functions can…
Many machine learning tasks involve learning functions that are known to be invariant or equivariant to certain symmetries of the input data. However, it is often challenging to design neural network architectures that respect these…
In this paper, we show that feedforward and recurrent neural networks exhibit an outer product derivative structure but that convolutional neural networks do not. This structure makes it possible to use higher-order information without…
Group equivariant neural networks have proven effective in modelling a wide range of tasks where the data lives in a classical geometric space and exhibits well-defined group symmetries. However, these networks are not suitable for learning…
We present an efficient block-diagonal ap- proximation to the Gauss-Newton matrix for feedforward neural networks. Our result- ing algorithm is competitive against state- of-the-art first order optimisation methods, with sometimes…
According to conventional neural network theories, the feature of single-hidden-layer feedforward neural networks(SLFNs) resorts to parameters of the weighted connections and hidden nodes. SLFNs are universal approximators when at least the…
We describe a novel family of models of multi- layer feedforward neural networks in which the activation functions are encoded via penalties in the training problem. Our approach is based on representing a non-decreasing activation function…
A feed-forward neural network has a remarkable property which allows the network itself to be a universal approximator for any functions.Here we present a universal, machine-learning based solver for multi-variable partial differential…
State-of-the-art deep learning systems often require large amounts of data and computation. For this reason, leveraging known or unknown structure of the data is paramount. Convolutional neural networks (CNNs) are successful examples of…
Informed by the basic geometry underlying feed forward neural networks, we initialize the weights of the first layer of a neural network using the linear discriminants which best distinguish individual classes. Networks initialized in this…
We propose a quantum generalisation of a classical neural network. The classical neurons are firstly rendered reversible by adding ancillary bits. Then they are generalised to being quantum reversible, i.e.\ unitary. (The classical networks…
Single layer feedforward networks with random weights are known for their non-iterative and fast training algorithms and are successful in a variety of classification and regression problems. A major drawback of these networks is that they…
Recurrent and convolutional neural networks are the most common architectures used for time series forecasting in deep learning literature. These networks use parameter sharing by repeating a set of fixed architectures with fixed parameters…
Rotation equivariance is a desirable property in many practical applications such as motion forecasting and 3D perception, where it can offer benefits like sample efficiency, better generalization, and robustness to input perturbations.…
Employing equivariance in neural networks leads to greater parameter efficiency and improved generalization performance through the encoding of domain knowledge in the architecture; however, the majority of existing approaches require an a…