Related papers: Modeling Quantum Mechanical Observers via Neural-G…
This paper presents adaptive observers for online state and parameter estimation of a class of nonlinear systems motivated by biophysical models of neuronal circuits. We first present a linear-in-the-parameters design that solves a…
Building on our recent work on {\em neuromimetic control theory}, new results on resilience and neuro-inspired quantization are reported. The term neuromimetic refers to the models having features that are characteristic of the neurobiology…
The problem of the observer in quantum mechanics is getting new human content. The paradox of Wigner's friend and its extended versions have observers who not only observe quantum phenomena, but communicate, have memories and even…
Quantum neural networks generalize classical artificial neural networks into the quantum domain. They are formulated as parameterized quantum circuits which are optimized by measuring and minimizing a suitably chosen loss function. The core…
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…
We show how a Hopfield network with modifiable recurrent connections undergoing slow Hebbian learning can extract the underlying geometry of an input space. First, we use a slow/fast analysis to derive an averaged system whose dynamics…
It is shown that a Hopfield recurrent neural network exhibits a scaling regime, whose specific exponents depend on the number of parcels used and the decay length of the coupling strength. This scaling regime recovers the picture introduced…
Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the…
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…
The Hamiltonian formalism plays a central role in classical and quantum physics. Hamiltonians are the main tool for modelling the continuous time evolution of systems with conserved quantities, and they come equipped with many useful…
The state space of a conventional Hopfield network typically exhibits many different attractors of which only a small subset satisfy constraints between neurons in a globally optimal fashion. It has recently been demonstrated that combining…
We study the asymptotic behaviour for asymmetric neuronal dynamics in a network of Hopfield neurons. The randomness in the network is modelled by random couplings which are centered Gaussian correlated random variables. We prove that the…
We reflect on the information paradigm in quantum and gravitational physics and on how it may assist us in approaching quantum gravity. We begin by arguing, using a reconstruction of its formalism, that quantum theory can be regarded as a…
Hopfield models, originally developed to study memory retrieval in neural networks, have become versatile tools for modeling diverse biological systems in which function emerges from collective dynamics. In this review, we provide a…
An adaptive observer is designed for online estimation of Hilbert-Schmidt operators from online measurement of the state for some class of nonlinear infinite-dimensional dynamical systems. Convergence is ensured under detectability and…
Understanding the dynamic reorganization of brain networks is critical for predicting cognitive decline, neurological progression, and individual variability in clinical outcomes. This work proposes a multimodal graph neural network…
In this work, we propose a distributed adaptive observer for a class of nonlinear networked systems inspired by biophysical neural network models. Neural systems learn by adjusting intrinsic and synaptic weights in a distributed fashion,…
We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule…
Quantum dissipation arises from the unavoidable coupling between a quantum system and its surrounding environment, which is known as a major obstacle in the quantum processing of information. Apart from its existence, how to trace the…
Motivated by Heisenberg's assertion that electron trajectories do not exist until they are observed, we present a new approach to quantum mechanics in which the concept of observer independent system under observation is eliminated.…