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We prove that for a broad class of permutation-equivariant learning rules (including SGD, Adam, and others), the training process induces a bi-Lipschitz mapping between neurons and strongly constrains the topology of the neuron distribution…
We present a formal measure-theoretical theory of neural networks (NN) built on probability coupling theory. Our main contributions are summarized as follows. * Built on the formalism of probability coupling theory, we derive an algorithm…
We study associative memory based on temporal coding in which successful retrieval is realized as an entrainment in a network of simple phase oscillators with distributed natural frequencies under the influence of white noise. The memory…
This paper describes a framework for modeling the interface between perception and memory on the algorithmic level of analysis. It is consistent with phenomena associated with many different brain regions. These include view-dependence (and…
The brain can reproduce memories from partial data; this ability is critical for memory recall. The process of memory recall has been studied using auto-associative networks such as the Hopfield model. This kind of model reliably converges…
In this work, we introduce Adapt & Align, a method for continual learning of neural networks by aligning latent representations in generative models. Neural Networks suffer from abrupt loss in performance when retrained with additional…
Spin-glass models of associative memories are a cornerstone between statistical physics and theoretical neuroscience. In these networks, stochastic spin-like units interact through a synaptic matrix shaped by local Hebbian learning. In…
This paper proposes a latent space energy-based prior model for semi-supervised learning. The model stands on a generator network that maps a latent vector to the observed example. The energy term of the prior model couples the latent…
The aim of the present paper is to study the effects of Hebbian learning in random recurrent neural networks with biological connectivity, i.e. sparse connections and separate populations of excitatory and inhibitory neurons. We furthermore…
Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
We study a sequential-learning model featuring a network of naive agents with Gaussian information structures. Agents apply a heuristic rule to aggregate predecessors' actions. They weigh these actions according the strengths of their…
We generalize the approach of arXiv:1805.04138 for the case of the Hopfield neural network in the recall stage on a triangular lattice with isotropic weights. It appears that some properties of this model, in particular the probability 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…
The human brain can be considered as complex networks, composed of various regions that continuously exchange their information with each other, forming the brain network graph, from which nodes and edges are extracted using resting-state…
We use the Higgs mechanism to investigate connections between higher-rank symmetric $U(1)$ gauge theories and gapped fracton phases. We define two classes of rank-2 symmetric $U(1)$ gauge theories: the $(m,n)$ scalar and vector charge…
We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with $N$-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in…
In this review I summarize how machine learning can be used in lattice gauge theory simulations and what ap\-proaches are currently available to improve the sampling of gauge field configurations, with a focus on applications in…
We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant…
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…