Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Fundamental Theorem of Algebra01:30

Fundamental Theorem of Algebra

190
The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as:  with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the...
190
Torque Free Motion01:15

Torque Free Motion

775
The torque-free motion refers to the movement of a rigid body in space when no external torques are acting upon it. This type of motion can be observed in environments where there are no external forces or frictions, like in outer space. For example, a rotation of Mars in space is a torque-free motion. Mars is an axisymmetric object, meaning it has an axis of symmetry along which it rotates, designated as the z-axis. The rotating frame of reference is defined such that the center of mass of...
775
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

18.7K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
18.7K
Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

1.1K
The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
1.1K
Inertia Tensor01:24

Inertia Tensor

1.1K
The concept of the inertia tensor is employed to depict the mass distribution and rotational inertia of a solid or rigid object. This tensor is expressed through a three-by-three matrix. Each component within this matrix corresponds to varying moments of inertia about specific axes.
The diagonal components of the inertia tensor matrix represent the moments of inertia concerning the principal axes of the object. These primary axes are defined as the axes where the object experiences the least...
1.1K
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

2.6K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
2.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Reconfiguration of d-orbital states drives non-radiative energy dissipation in semiconductors.

Materials horizons·2026
Same author

Dynamical freezing for magnetometry in an interacting spin ensemble.

Nature·2026
Same author

Uncertainty-guided model learning for trustworthy medical image segmentation.

Medical & biological engineering & computing·2026
Same author

Editorial Expression of Concern: Should chronic hepatitis B mothers breastfeed? A meta analysis.

BMC public health·2026
Same author

Suppressive Effects of an Inhibitor Composition on Skin Ulceration and Transcriptomic Analysis in the Sea Cucumber <i>Apostichopus japonicus</i> Exposed to No. 0 Diesel Oil.

Biology·2026
Same author

Uptake and effectiveness of a novel seasonal influenza vaccination campaign for school-age children in the 2023/2024 influenza season in Shanghai, China.

Vaccine·2026
Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026
Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026
Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026
Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026
Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026
Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026
See all related articles

Related Experiment Videos

No-Free-Lunch Theorems for Tensor Network Machine Learning Models.

Jing-Chuan Wu1, Qi Ye2,3,4, Dong-Ling Deng2,3,5

  • 1Nankai University, Theoretical Physics Division, Chern Institute of Mathematics and LPMC, Tianjin 300071, China.

Physical Review Letters
|December 12, 2025
PubMed
Summary
This summary is machine-generated.

Tensor network machine learning models face inherent limitations, as proven by the no-free-lunch theorem. This research rigorously analyzes these constraints for matrix product states and projected entangled-pair states.

Related Experiment Videos

Area of Science:

  • Quantum Information Science
  • Machine Learning Theory
  • Computational Physics

Background:

  • Tensor network machine learning models offer versatility for complex data tasks.
  • A thorough understanding of their assumptions and limitations is currently lacking.
  • Formalizing the no-free-lunch theorem for specific tensor network models is challenging.

Purpose of the Study:

  • To rigorously formulate and analyze the no-free-lunch theorem for tensor network machine learning models.
  • To investigate the generalization risks associated with learning from data encoded in tensor network states.
  • To establish intrinsic limitations of these quantum-inspired learning frameworks.

Main Methods:

  • Proving a no-free-lunch theorem for matrix product state (MPS) based machine learning models.
  • Developing a combinatorial method, the "puzzle of polyominoes," to circumvent partition function calculations.
  • Proving the no-free-lunch theorem for 2D projected entangled-pair states (PEPS) using the combinatorial method.

Main Results:

  • A rigorous no-free-lunch theorem is established for MPS-based machine learning.
  • The no-free-lunch theorem is proven for 2D PEPS, overcoming computational challenges.
  • An adversarial theorem is derived as a direct consequence of the no-free-lunch findings.

Conclusions:

  • Tensor network-based learning models possess intrinsic, rigorously defined limitations.
  • The study provides a framework for analyzing the strengths and weaknesses of quantum-inspired machine learning.
  • Future research can explore these analytical avenues for broader machine learning applications.