Related papers: Coupling quantum-like cognition with the neuronal …
While neural networks have been remarkably successful in a wide array of applications, implementing them in resource-constrained hardware remains an area of intense research. By replacing the weights of a neural network with quantized…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
We discuss a quantum version of an artificial deep neural network where the role of neurons is taken over by qubits and the role of weights is played by unitaries. The role of the non-linear activation function is taken over by subsequently…
We propose a framework for constructing combinatorial complexes (CCs) from fMRI time series data that captures both pairwise and higher-order neural interactions through information-theoretic measures, bridging topological deep learning and…
The use of advanced quantum neuron models for pattern recognition applications requires fault tolerance. Therefore, it is not yet possible to test such models on a large scale in currently available quantum processors. As an alternative, we…
The aim of this review is to highlight the possibility to apply the mathematical formalism and methodology of quantum theory to model behaviour of complex biosystems, from genomes and proteins to animals, humans, ecological and social…
Quantum systems interacting with an unknown environment are notoriously difficult to model, especially in presence of non-Markovian and non-perturbative effects. Here we introduce a neural network based approach, which has the mathematical…
Knowledge representation learning has been commonly adopted to incorporate knowledge graph (KG) into various online services. Although existing knowledge representation learning methods have achieved considerable performance improvement,…
Graph neural networks (GNNs) excel at predictive tasks on graph-structured data but often lack the ability to incorporate symbolic domain knowledge and perform general reasoning. Relational Bayesian Networks (RBNs), in contrast, enable…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
Artificial neural networks bridge input data into output results by approximately encoding the function that relates them. This is achieved after training the network with a collection of known inputs and results leading to an adjustment of…
Deep neural networks are a powerful tool for the characterization of quantum states. Existing networks are typically trained with experimental data gathered from the specific quantum state that needs to be characterized. But is it possible…
This chapter, dedicated to the memory of Mino Freund, summarizes the Quantum Decision Theory (QDT) that we have developed in a series of publications since 2008. We formulate a general mathematical scheme of how decisions are taken, using…
Quantum decision theory (QDT) is a recently developed theory of decision making based on the mathematics of Hilbert spaces, a framework known in physics for its application to quantum mechanics. This framework formalizes the concept of…
Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose…
We develop a uniform theoretical approach towards the analysis of various neural network connectivity architectures by introducing the notion of a quiver neural network. Inspired by quiver representation theory in mathematics, this approach…
We propose a new framework to understand how quantum effects may impact on the dynamics of neural networks. We implement the dynamics of neural networks in terms of Markovian open quantum systems, which allows us to treat thermal and…
Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but…
Quantum probability provides a novel framework for formulating machine-learning (ML) problems in Hilbert space. We introduce a prototype-based learning scheme where class representatives are encoded as generative matrix product states…
In this paper we discuss the existence of joint probability distributions for quantum-like response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral…