相关论文: On the capacity of neural networks

This paper examines the memory capacity of generalized neural networks. Hopfield networks trained with a variety of learning techniques are investigated for their capacity both for binary and non-binary alphabets. It is shown that the…

Quantum neural networks form one pillar of the emergent field of quantum machine learning. Here, quantum generalisations of classical networks realizing associative memories - capable of retrieving patterns, or memories, from corrupted…

Understanding the theoretical foundations of how memories are encoded and retrieved in neural populations is a central challenge in neuroscience. A popular theoretical scenario for modeling memory function is the attractor neural network…

Recent developments in Quantum Machine Learning have seen the introduction of several models to generalize the classical perceptron to the quantum regime. The capabilities of these quantum models need to be determined precisely in order to…

The standard Hopfield model for associative neural networks accounts for biological Hebbian learning and acts as the harmonic oscillator for pattern recognition, however its maximal storage capacity is $\alpha \sim 0.14$, far from the…

Understanding the memory capacity of neural networks remains a challenging problem in implementing artificial intelligence systems. In this paper, we address the notion of capacity with respect to Hopfield networks and propose a dynamic…

The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological…

We consider two models of Hopfield-like associative memory with $q$-valued neurons: Potts-glass neural network (PGNN) and parametrical neural network (PNN). In these models neurons can be in more than two different states. The models have…

The performance of large neural networks can be judged not only by their storage capacity but also by the time required for learning. A polynomial learning algorithm with learning time $\sim N^2$ in a network with $N$ units might be…

We derive the calculation of two critical numbers predicting the behavior of perceptron networks. First, we derive the calculation of what we call the lossless memory (LM) dimension. The LM dimension is a generalization of the…

This paper combines quantum computation with classical neural network theory to produce a quantum computational learning algorithm. Quantum computation uses microscopic quantum level effects to perform computational tasks and has produced…

The storage capacity of the Hopfield model is about 15% of the network size. It can be increased significantly in the Potts-glass model of the associative memory only. In this model neurons can be in more than two different states. We show…

In \cite{Hop82}, Hopfield introduced a \emph{Hebbian} learning rule based neural network model and suggested how it can efficiently operate as an associative memory. Studying random binary patterns, he also uncovered that, if a small…

A key open question in quantum computation is what advantages quantum neural networks (QNNs) may have over classical neural networks (NNs), and in what situations these advantages may transpire. Here we address this question by studying the…

Quantum computing allows for the potential of significant advancements in both the speed and the capacity of widely used machine learning techniques. Here we employ quantum algorithms for the Hopfield network, which can be used for pattern…

We analyze the storage capacity of the Hopfield models on classes of random graphs. While such a setup has been analyzed for the case that the underlying random graph model is an Erd\"{o}s-Renyi graph, other architectures, including those…

In this paper we revisit one of the classical perceptron problems from the neural networks and statistical physics. In \cite{Gar88} Gardner presented a neat statistical physics type of approach for analyzing what is now typically referred…

A long standing open problem in the theory of neural networks is the development of quantitative methods to estimate and compare the capabilities of different architectures. Here we define the capacity of an architecture by the binary…

We consider the problem of training a neural network to store a set of patterns with maximal noise robustness. A solution, in terms of optimal weights and state update rules, is derived by training each individual neuron to perform either…

Artificial networks have been studied through the prism of statistical mechanics as disordered systems since the 80s, starting from the simple models of Hopfield's associative memory and the single-neuron perceptron classifier. Assuming…