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Dense Associative Memory (DAM) generalizes Hopfield networks through higher-order interactions and achieves storage capacity that scales as $O(N^{n-1})$ under suitable pattern separation conditions. Existing dynamical analyses primarily…
Modern Hopfield Neural Networks (HNNs), also known as Dense Associative Memories (DAMs), enhance the performance of simple recurrent neural networks by leveraging the nonlinearities in their energy functions. They have broad applications in…
Sequential learning involves learning tasks in a sequence, and proves challenging for most neural networks. Biological neural networks regularly conquer the sequential learning challenge and are even capable of transferring knowledge both…
Deep neural networks (DNN) trained in a supervised way suffer from two known problems. First, the minima of the objective function used in learning correspond to data points (also known as rubbish examples or fooling images) that lack…
Dense associative memories (DAM), are widespread models in artificial intelligence used for pattern recognition tasks; computationally, they have been proven to be robust against adversarial input and theoretically, leveraging their analogy…
We introduce the Dreaming $L$-directional Associative Memory (DLAM), a multi-layer Hebbian architecture in which off-line dreaming and supervised heteroassociative coupling coexist within a single energy function, placing our approach…
We introduce in-context denoising, a task that refines the connection between attention-based architectures and dense associative memory (DAM) networks, also known as modern Hopfield networks. Using a Bayesian framework, we show…
Dense Associative Memories or modern Hopfield networks permit storage and reliable retrieval of an exponentially large (in the dimension of feature space) number of memories. At the same time, their naive implementation is non-biological,…
Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require…
Dense Associative Memories or Modern Hopfield Networks have many appealing properties of associative memory. They can do pattern completion, store a large number of memories, and can be described using a recurrent neural network with a…
Recent generalizations of the Hopfield model of associative memories are able to store a number $P$ of random patterns that grows exponentially with the number $N$ of neurons, $P=\exp(\alpha N)$. Besides the huge storage capacity, another…
It has been shown that a neural network model recently proposed to describe basic memory performance is based on a ternary/binary coding/decoding algorithm which leads to a new neural network assembly memory model (NNAMM) providing…
Dense associative memory, a fundamental instance of modern Hopfield networks, can store a large number of memory patterns as equilibrium states of recurrent networks. While the stationary-state storage capacity has been investigated, its…
Dense Associative Memory (DAM) models have been attracting renewed attention since they were shown to be robust to adversarial examples and closely related to cutting edge machine learning paradigms, such as the attention mechanism and…
The Hopfield model describes a neural network that stores memories using all-to-all-coupled spins. Memory patterns are recalled under equilibrium dynamics. Storing too many patterns breaks the associative recall process because frustration…
A model of associative memory is studied, which stores and reliably retrieves many more patterns than the number of neurons in the network. We propose a simple duality between this dense associative memory and neural networks commonly used…
Restricted Boltzmann Machines are key tools in Machine Learning and are described by the energy function of bipartite spin-glasses. From a statistical mechanical perspective, they share the same Gibbs measure of Hopfield networks for…
I introduce a novel associative memory model named Correlated Dense Associative Memory (CDAM), which integrates both auto- and hetero-association in a unified framework for continuous-valued memory patterns. Employing an arbitrary graph…
We investigate dense higher-order associative memories in the high storage regime when the stored patterns are biased, namely when the entries of the patterns are not symmetrically distributed around zero. In this setting, the standard…
We present a Hopfield-like autoassociative network for memories representing examples of concepts. Each memory is encoded by two activity patterns with complementary properties. The first is dense and correlated across examples within…