Related papers: Neural networks with high order connections
Hopfield networks are an attractive choice for solving many types of computational problems because they provide a biologically plausible mechanism. The Self-Optimization (SO) model adds to the Hopfield network by using a biologically…
Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible…
A recurrent neural network model storing multiple spatial maps, or ``charts'', is analyzed. A network of this type has been suggested as a model for the origin of place cells in the hippocampus of rodents. The extremely diluted and fully…
The thermodynamic and retrieval properties of the Blume-Emery-Griffiths neural network with synchronous updating and variable dilution are studied using replica mean-field theory. Several forms of dilution are allowed by pruning the…
We describe a class of systems theory based neural networks called "Network Of Recurrent neural networks" (NOR), which introduces a new structure level to RNN related models. In NOR, RNNs are viewed as the high-level neurons and are used to…
The spherical version of the Hopfield model for pattern recognition is considered in the static limit. Structures inside the patterns are modeled by Gaussian random variables that reward correlation between pairs of spins in a given…
In this paper we introduce and investigate the statistical mechanics of hierarchical neural networks: First, we approach these systems \`a la Mattis, by thinking at the Dyson model as a single-pattern hierarchical neural network and we…
Spiking neural networks play an important role in brain-like neuromorphic computations and in studying working mechanisms of neural circuits. One drawback of training a large scale spiking neural network is that updating all weights is…
Associative memory models such as the Hopfield network and its dense generalizations with higher-order interactions exhibit a "blackout catastrophe" -- a discontinuous transition where stable memory states abruptly vanish when the number of…
In the present paper, an effort has been made for storing and recalling images with Hopfield Neural Network Model of auto-associative memory. Images are stored by calculating a corresponding weight matrix. Thereafter, starting from an…
In Hopfield-type associative memory models, memories are stored in the connectivity matrix and can be retrieved subsequently thanks to the collective dynamics of the network. In these models, the retrieval of a particular memory can be…
Traditional functional connectivity based on functional magnetic resonance imaging (fMRI) can only capture pairwise interactions between brain regions. Hypergraphs, which reveal high-order relationships among multiple brain regions, have…
A set of fixed points of the Hopfield type neural network was under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…
Increasing the size of a Transformer does not always lead to enhanced performance. This phenomenon cannot be explained by the empirical scaling laws. Furthermore, the model's enhanced performance is closely associated with its memorization…
We develop a statistical mechanical approach based on the replica method to study the design space of deep and wide neural networks constrained to meet a large number of training data. Specifically, we analyze the configuration space of the…
Hebbian learning limits Hopfield network storage capacity (pattern-to-neuron ratio around 0.14). We propose Kernel Logistic Regression (KLR) learning. Unlike linear methods, KLR uses kernels to implicitly map patterns to high-dimensional…
Classical Hopfield networks are limited to static patterns due to symmetric weights, whereas asymmetric networks can encode temporal sequences via limit-cycle attractors. Achieving high-capacity storage of long sequences in classical…
A recent dynamic mean-field theory for sequence processing in fully connected neural networks of Hopfield-type (During, Coolen and Sherrington, 1998) is extended and analized here for a symmetrically diluted network with finite connectivity…
Introduction. Neural network models of autoassociative, distributed memory allow storage and retrieval of many items (vectors) where the number of stored items can exceed the vector dimension (the number of neurons in the network). This…
Spin glass models, such as the Sherrington-Kirkpatrick, Hopfield and Ising models, are all well-studied members of the exponential family of discrete distributions, and have been influential in a number of application domains where they are…