Related papers: Modeling Quantum Mechanical Observers via Neural-G…
We revisit the problem of characterising the mean-field limit of a network of Hopfield-like neurons. Building on the previous works of Ben Arous and Guionnet we establish for a large class of networks of Hopfield-like neurons, i.e. rate…
The control of neuronal networks, whether biological or neuromorphic, relies on tools for estimating parameters in the presence of model uncertainty. In this work, we explore the robustness of adaptive observers for neuronal estimation.…
We describe a model element able to perform universal stochastic approximations of continuous multivariable functions in both neuron-like and quantum form. The implementation of this model in the form of a multi-barrier, multiple-slit…
In this work we analyze the emergence of phase transitions in a quantum brain model inspired by the Lipkin-Meshkov-Glick framework, where biologically motivated synaptic feedback modulates the collective interaction in a nonlinear and…
Artificial neural networks have been proposed as potential algorithms that could benefit from being implemented and run on quantum computers. In particular, they hold promise to greatly enhance Artificial Intelligence tasks, such as image…
Recent research has demonstrated the usefulness of neural networks as variational ansatz functions for quantum many-body states. However, high-dimensional sampling spaces and transient autocorrelations confront these approaches with a…
Human learning is a complex phenomenon that requires adaptive processes across a range of temporal and spacial scales. While our understanding of those processes at single scales has increased exponentially over the last few years, a…
Fully connected Blume-Emery-Griffiths neural networks performing pattern recognition and associative memory have been heuristically studied in the past (mainly via the replica trick and under the replica symmetric assumption) as…
Visual attention is a mechanism closely intertwined with vision and memory. Top-down information influences visual processing through attention. We designed a neural network model inspired by aspects of human visual attention. This model…
We introduce a Hopfield-type associative memory in which effective connectivity is multiplicatively modulated by astrocytic gains evolving under an entropy-regularized replicator equation. The coupled neuron-astrocyte dynamics admit a…
Based on an observation that the basic mode of a common microwave waveguide is a solution to the Klein-Gordon equation, quantum mechanics is modeled as the wave-function propagated inside a waveguide. The guide width is determined by the…
Interpretations of quantum theory have traditionally assumed a "Galilean" observer, a bare "point of view" implemented physically by a quantum system. This paper investigates the consequences of replacing such an…
Nonlinear time-dependent partial differential equations are essential in modeling complex phenomena across diverse fields, yet they pose significant challenges due to their computational complexity, especially in higher dimensions. This…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the…
We consider that a network is an observation, and a collection of observed networks forms a sample. In this setting, we provide methods to test whether all observations in a network sample are drawn from a specified model. We achieve this…
Due to their immense representative power, neural network quantum states (NQS) have gained significant interest in current research. In recent advances in the field of NQS, it has been demonstrated that this approach can compete with…
The structure of continuous Hopfield networks is revisited from a system-theoretic point of view. After adopting a novel electrical network interpretation involving nonlinear capacitors, it is shown that Hopfield networks admit a…
We propose a new model of neural network. It consists of spin variables to describe the state of neurons as in the Hopfield model and new gauge variables to describe the state of synapses. The model possesses local gauge symmetry and…
We start with a discussion of the use of mathematics to model the real world then justify the role of Hilbert space formalism for such modelling in the general context of quantum logic. Following this, the incompleteness of the…