Related papers: Minimum Description Length Hopfield Networks
The Dense Associative Memory generalizes the Hopfield network by allowing for sharper interaction functions. This increases the capacity of the network as an autoassociative memory as nearby learned attractors will not interfere with one…
Storing memory for molecular recognition is an efficient strategy for responding to external stimuli. Biological processes use different strategies to store memory. In the olfactory cortex, synaptic connections form when stimulated by an…
This paper studies the memorization capacity of deep neural networks with ReLU activation. Specifically, we investigate the minimal size of such networks to memorize any $N$ data points in the unit ball with pairwise separation distance…
We investigate a new method to augment recurrent neural networks with extra memory without increasing the number of network parameters. The system has an associative memory based on complex-valued vectors and is closely related to…
We introduce Graph Hopfield Networks, whose energy function couples associative memory retrieval with graph Laplacian smoothing for node classification. Gradient descent on this joint energy yields an iterative update interleaving Hopfield…
The organizational principles behind the connectivity of a complex network are known to influence its behavior. In this work we investigate, using the Hopfield model, the influence of the network architecture on the performance for…
In this work we propose an energy functional along the lines of Modern Hopfield Networks (MNH), the stationary points of which correspond to the attention due to Vaswani et al. [12], thus unifying both frameworks. The minima of this…
Generative models, including diffusion models, are increasingly used as foundation models and adapted through sequential fine-tuning, making continual learning an essential problem setting. However, continual learning in such generative…
A ternary/binary data coding algorithm and conditions under which Hopfield networks implement optimal convolutional or Hamming decoding algorithms has been described. Using the coding/decoding approach (an optimal Binary Signal Detection…
The aim of this thesis is to compare the capacity of different models of neural networks. We start by analysing the problem solving capacity of a single perceptron using a simple combinatorial argument. After some observations on the…
Continuous-Time Recurrent Neural Networks (CTRNNs) have been widely used for their capacity to model complex temporal behaviour. However, their internal dynamics often remain difficult to interpret. In this paper, we propose a new class 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…
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…
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…
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…
Layer-wise capacity in large language models is highly non-uniform: some layers contribute disproportionately to loss reduction while others are near-redundant. Existing methods for exploiting this non-uniformity, such as…
Modern Hopfield Networks (MHNs) have emerged as powerful components in deep learning, serving as effective replacements for pooling layers, LSTMs, and attention mechanisms. While recent advancements have significantly improved their storage…
Recent vision and multimodal foundation backbones, such as Transformer families and state-space models like Mamba, have achieved remarkable progress, enabling unified modeling across images, text, and beyond. Despite their empirical…
Federated learning enables collaborative training without sharing raw data, but struggles under client heterogeneity and streaming distribution shifts, where drift and novel data can impair convergence and cause forgetting. We propose a…
The Hopfield network (HN) is a classical model of associative memory whose dynamics are closely related to the Ising spin system with 2-body interactions. Stored patterns are encoded as minima of an energy function shaped by a Hebbian…