Related papers: Non-Convex Multi-species Hopfield models
We study the recognition capabilities of the Hopfield model with auxiliary hidden layers, which emerge naturally upon a Hubbard-Stratonovich transformation. We show that the recognition capabilities of such a model at zero-temperature…
These are lecture notes for a course on machine learning with neural networks for scientists and engineers that I have given at Gothenburg University and Chalmers Technical University in Gothenburg, Sweden. The material is organised into…
The brain is a noisy system subject to energy constraints. These facts are rarely taken into account when modelling artificial neural networks. In this paper, we are interested in demonstrating that those factors can actually lead to the…
A large number of studies have shown the existence of metabolic covalent modifications in different molecular structures, able to store biochemical information that is not encoded by the DNA. Some of these covalent mark patterns can be…
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…
This paper presents a neural network model (associative memory model) for memory and recall of images. In this model, only a single neuron can memorize multi-images and when that neuron is activated, it is possible to recall all the…
In [7] Krotov and Hopfield suggest a generalized version of the well-known Hopfield model of associative memory. In their version they consider a polynomial interaction function and claim that this increases the storage capacity of the…
When do language diffusion models memorize their training data, and how to quantitatively assess their true generative regime? We address these questions by showing that Uniform-based Discrete Diffusion Models (UDDMs) fundamentally behave…
Networks in machine learning offer examples of complex high-dimensional dynamical systems reminiscent of biological systems. Here, we study the learning dynamics of Generalized Hopfield networks, which permit a visualization of internal…
Associative memory models based on Hopfield networks and self-attention based on key-value mechanisms have been popular approaches in the study of memory mechanisms in deep learning. It has been pointed out that the state update rule of the…
Associative memory models, such as Hopfield networks and their modern variants, have garnered renewed interest due to advancements in memory capacity and connections with self-attention in transformers. In this work, we introduce a unified…
We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…
Recently, the original storage prescription for the Hopfield model of neural networks -- as well as for its dense generalizations -- has been turned into a genuine Hebbian learning rule by postulating the expression of its Hamiltonian for…
We extend the framework of Boltzmann machines to a network of complex-valued neurons with variable amplitudes, referred to as Complex Amplitude-Phase Boltzmann machine (CAP-BM). The model is capable of performing unsupervised learning on…
Krotov and Hopfield (2021) proposed a biologically plausible two-layer associative memory network with memory storage capacity exponential in the number of visible neurons. However, the capacity was only linear in the number of hidden…
Based on the standard many-fermion field theory, the authors construct models describing ultracold fermions in a 1D optical lattices by implementing a mode expansion of the fermionic field operator where modes, in addition to space…
Autoassociative networks were proposed in the 80's as simplified models of memory function in the brain, using recurrent connectivity with hebbian plasticity to store patterns of neural activity that can be later recalled. This type of…
This paper presents a multi-point stimulation of a Hebbian neural network with investigation of the interplay between the stimulus waves through the neurons of the network. Equilibrium of the resulting memory is achieved for recall of…
We study a variant of the pseudo-inverse learning rule for Hopfield-like Neural Networks, which allows the network to infer archetypal concepts on the basis of a limited number of examples. The mean-field replica theory for this model…
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…