Quantum field-theoretic machine learning

• URL: http://arxiv.org/abs/2102.09449v1
• Date: Thu, 18 Feb 2021 16:12:51 GMT
• Title: Quantum field-theoretic machine learning
• Authors: Dimitrios Bachtis, Gert Aarts, Biagio Lucini
• Abstract summary: We recast the $phi4$ scalar field theory as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. Neural networks are additionally derived from the $phi4$ theory which can be viewed as generalizations of conventional neural networks.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We derive machine learning algorithms from discretized Euclidean field theories, making inference and learning possible within dynamics described by quantum field theory. Specifically, we demonstrate that the $\phi^{4}$ scalar field theory satisfies the Hammersley-Clifford theorem, therefore recasting it as a machine learning algorithm within the mathematically rigorous framework of Markov random fields. We illustrate the concepts by minimizing an asymmetric distance between the probability distribution of the $\phi^{4}$ theory and that of target distributions, by quantifying the overlap of statistical ensembles between probability distributions and through reweighting to complex-valued actions with longer-range interactions. Neural networks architectures are additionally derived from the $\phi^{4}$ theory which can be viewed as generalizations of conventional neural networks and applications are presented. We conclude by discussing how the proposal opens up a new research avenue, that of developing a mathematical and computational framework of machine learning within quantum field theory.

Related papers

• Fourier Neural Differential Equations for learning Quantum Field Theories [57.11316818360655]
  A Quantum Field Theory is defined by its interaction Hamiltonian, and linked to experimental data by the scattering matrix. In this paper, NDE models are used to learn theory, Scalar-Yukawa theory and Scalar Quantum Electrodynamics. The interaction Hamiltonian of a theory can be extracted from network parameters.
  arXiv  Detail & Related papers  (2023-11-28T22:11:15Z)
• Neural Network Field Theories: Non-Gaussianity, Actions, and Locality [0.0]
  Both the path integral measure in field theory and ensembles of neural networks describe distributions over functions. An expansion in $1/N$ corresponds to interactions in the field theory, but others, such as in a small breaking of the statistical independence of network parameters, can also lead to interacting theories.
  arXiv  Detail & Related papers  (2023-07-06T18:00:01Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Unified Field Theory for Deep and Recurrent Neural Networks [56.735884560668985]
  We present a unified and systematic derivation of the mean-field theory for both recurrent and deep networks. We find that convergence towards the mean-field theory is typically slower for recurrent networks than for deep networks. Our method exposes that Gaussian processes are but the lowest order of a systematic expansion in $1/n$.
  arXiv  Detail & Related papers  (2021-12-10T15:06:11Z)
• Quantum field theories, Markov random fields and machine learning [0.0]
  We will discuss how discretized Euclidean field theories can be recast within the mathematical framework of Markov random fields. Specifically, we will demonstrate that the $phi4$ scalar field theory on a square lattice satisfies the Hammersley-Clifford theorem. We will then discuss applications pertinent to the minimization of an asymmetric distance between the probability distribution of the $phi4$ machine learning algorithms and that of target probability distributions.
  arXiv  Detail & Related papers  (2021-10-21T06:50:33Z)
• Quantum Simulation of Conformal Field Theory [77.34726150561087]
  We describe a quantum algorithm to simulate the dynamics of conformal field theories. A full analysis of the approximation errors suggests near-term applicability.
  arXiv  Detail & Related papers  (2021-09-29T06:44:33Z)
• Machine learning with quantum field theories [0.0]
  We will show that the $phi4$ scalar field theory on a square lattice satisfies the local Markov property and can therefore be recast as a Markov random field. We will then derive from the $phi4$ theory machine learning algorithms and neural networks which can be viewed as generalizations of conventional neural network architectures.
  arXiv  Detail & Related papers  (2021-09-16T05:42:01Z)
• Computation in a general physical setting [0.0]
  This paper reviews and extends some results on the computational ability of quantum theory. It provides a refined version of the conjecture that a quantum computer can simulate the computation in any theory. It ends by describing an important relation between this conjecture and delegated computation, similar to the relation between quantum non-locality and device-independent cryptography.
  arXiv  Detail & Related papers  (2021-08-25T20:00:20Z)
• A Chain Graph Interpretation of Real-World Neural Networks [58.78692706974121]
  We propose an alternative interpretation that identifies NNs as chain graphs (CGs) and feed-forward as an approximate inference procedure. The CG interpretation specifies the nature of each NN component within the rich theoretical framework of probabilistic graphical models. We demonstrate with concrete examples that the CG interpretation can provide novel theoretical support and insights for various NN techniques.
  arXiv  Detail & Related papers  (2020-06-30T14:46:08Z)
• Simple heuristics for efficient parallel tensor contraction and quantum circuit simulation [1.4416132811087747]
  We propose a parallel algorithm for the contraction of tensor networks using probabilistic models. We apply the resulting algorithm to the simulation of random quantum circuits.
  arXiv  Detail & Related papers  (2020-04-22T23:00:42Z)
• Stochastic Flows and Geometric Optimization on the Orthogonal Group [52.50121190744979]
  We present a new class of geometrically-driven optimization algorithms on the orthogonal group $O(d)$. We show that our methods can be applied in various fields of machine learning including deep, convolutional and recurrent neural networks, reinforcement learning, flows and metric learning.
  arXiv  Detail & Related papers  (2020-03-30T15:37:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.