Tensor networks in machine learning

Sengupta, Richik; Adhikary, Soumik; Oseledets, Ivan; Biamonte, Jacob

doi:10.4171/mag/101

Cited by 8 publications

(5 citation statements)

References 40 publications

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“…Tensor networks have been used to describe and predict quantum states [49]. It has also been used to study low-energy multibody quantum entanglement of local Hamiltonians [50], and to study ground states dynamics and interactions in quantum chemistry [51], [52].…”

Section: Tensor Networkmentioning

confidence: 99%

Quantum Machine Learning and TensorNetworks as an Aid in the Clinical Diagnosis ofCoronary Artery Disease

Bopardikar,

Montoya,

Decoodt

et al. 2024

Preprint

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Current applications of quantum machine learning are emerging, dueto the potential benefits that quantum technologies could bring in thenear future. One of the most recent developments is tensor network-based architectures, to explore the feasibility of the application of thismethod to healthcare, in this paper tensor networks are applied to theIEEE Heart Disease (COMPREHENSIVE) dataset for supervised clas-sification of coronary artery disease diagnosis. Three quantum machinelearning models were implemented in this study: 3-qubit Q-MPS, 4 qubitQ-MERA and 4-qubit Q-TTN. These were compared to six classical ma-chine learning models: Logistic Regression, Naive Bayes, Support VectorMachines (SVM), Decision Tree, Random Forest, and XGBoost; achiev-ing similar or better results than those of the best classical models. Themodels were evaluated following different strategies to modify the trainingand testing conditions, applying variations to the dataset by isolating theCleveland and Hungary datasets, which are subsets of the former. Addi-tionally, the impact of the input feature space preparation is demonstratedexperimentally, showing that there exist preferred conditions where thegeneralization of the model is maximum.

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Section: Tensor Networkmentioning

confidence: 99%

Quantum Machine Learning and TensorNetworks as an Aid in the Clinical Diagnosis ofCoronary Artery Disease

Bopardikar,

Montoya,

Decoodt

et al. 2024

Preprint

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show abstract

“…Yet, as Ref. [144] mentions, machine learning can aid, in turn, in determining a factorization of a TN approximating a data set. Moreover, TNs are also used to compress the layers of ANN architectures, besides a variety of other uses.…”

Section: Tns As a Generalization Of The Main Model Architectures In MLmentioning

confidence: 99%

Control flow in active inference systems

Fields¹,

Fabrocini²,

Friston³

et al. 2023

Preprint

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Living systems face both environmental complexity and limited access to free-energy resources. Survival under these conditions requires a control system that can activate, or deploy, available perception and action resources in a context specific way. We show here that when systems are described as executing active inference driven by the free-energy principle (and hence can be considered Bayesian prediction-error minimizers), their control flow systems can always be represented as tensor networks (TNs). We show how TNs as control systems can be implmented within the general framework of quantum topological neural networks, and discuss the implications of these results for modeling biological systems at multiple scales.

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“…Yet, as Ref. [52] mentions, machine learning can aid, in turn, in determining a factorization of a TN approximating a data set. Moreover, TNs are also used to compress the layers of ANN architectures, besides a variety of other uses.…”

Section: Tns As a Generalization Of The Main Model Architectures In MLmentioning

confidence: 99%

Control Flow in Active Inference Systems—Part II: Tensor Networks as General Models of Control Flow

Fields

Fabrocini

Friston

et al. 2023

IEEE Trans. Mol. Biol. Multi-Scale Commun.

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Living systems face both environmental complexity and limited access to free-energy resources. Survival under these conditions requires a control system that can activate, or deploy, available perception and action resources in a context specific way. In Part I, we introduced the free-energy principle (FEP) and the idea of active inference as Bayesian prediction-error minimization, and show how the control problem arises in active inference systems. We then review classical and quantum formulations of the FEP, with the former being the classical limit of the latter. In this accompanying Part II, we show that when systems are described as executing active inference driven by the FEP, their control flow systems can always be represented as tensor networks (TNs). We show how TNs as control systems can be implemented within the general framework of quantum topological neural networks, and discuss the implications of these results for modeling biological systems at multiple scales.

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Tensor networks in machine learning

Cited by 8 publications

References 40 publications

Quantum Machine Learning and TensorNetworks as an Aid in the Clinical Diagnosis ofCoronary Artery Disease

Quantum Machine Learning and TensorNetworks as an Aid in the Clinical Diagnosis ofCoronary Artery Disease

Control flow in active inference systems

Control Flow in Active Inference Systems—Part II: Tensor Networks as General Models of Control Flow

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