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Neuroscience and Artificial Intelligence (AI) have progressed in tandem, each contributing to our understanding of the brain, and inspiring recent developments in biologically-plausible neural networks (NNs) and learning rules. Predictive…
We present results for two different kinds of high order connections between neurons acting as corrections to the Hopfield model. Equilibrium properties are analyzed using the replica mean-field theory and compared with numerical…
We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule including passive forgetting and different time scales for neuronal activity and learning…
Many models used in artificial intelligence and cognitive science rely on multi-element patterns stored in "slots" - dedicated storage locations - in a digital computer. As biological brains likely lack slots, we consider how they might…
Understanding how neural networks generalize on unseen data is crucial for designing more robust and reliable models. In this paper, we study the generalization gap of neural networks using methods from topological data analysis. For this…
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…
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…
Energy-based probabilistic models learned by maximizing the likelihood of the data are limited by the intractability of the partition function. A widely used workaround is to maximize the pseudo-likelihood, which replaces the global…
Continual Learning aims to bring machine learning into a more realistic scenario, where tasks are learned sequentially and the i.i.d. assumption is not preserved. Although this setting is natural for biological systems, it proves very…
We consider continuous time Hopfield-like recurrent networks as dynamical models for gene regulation and neural networks. We are interested in networks that contain n high-degree nodes preferably connected to a large number of Ns weakly…
In this paper, we investigate the associative memory in recurrent neural networks, based on the model of evolving neural networks proposed by Nolfi, Miglino and Parisi. Experimentally developed network has highly asymmetric synaptic weights…
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…
In this paper we study, via equilibrium statistical mechanics, the properties of the internal energy of an Hopfield neural network whose patterns are stored continuously (Gaussian distributed). The model is shown to be equivalent to a…
Associative memories in the brain receive and store patterns of activity registered by the sensory neurons, and are able to retrieve them when necessary. Due to their importance in human intelligence, computational models of associative…
We introduce a three-dimensional vectorial extension of the Hopfield associative-memory model in which each neuron is a unit vector on $S^2$ and synaptic couplings are $3\times 3$ blocks generated through a vectorial Hebbian rule. The…
Associative memory, traditionally modeled by Hopfield networks, enables the retrieval of previously stored patterns from partial or noisy cues. Yet, the local computational principles which are required to enable this function remain…
Artificial neural networks (ANNs) show limited performance with scarce or imbalanced training data and face challenges with continuous learning, such as forgetting previously learned data after new tasks training. In contrast, the human…
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…
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…
As a mathematical model of associative memories, the Hopfield model was now well-established and a lot of studies to reveal the pattern-recalling process have been done from various different approaches. As well-known, a single neuron is…