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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of one, the...
Propagation of Action Potentials01:23

Propagation of Action Potentials

The propagation of an action potential refers to the process by which a nerve impulse, or "action potential," travels along a neuron.
Neurons (nerve cells) have a resting membrane potential, with a slightly negative charge inside compared to outside. This is maintained by ion channels, such as sodium (Na+) and potassium (K+) channels, which control the flow of ions. When a stimulus, like a touch or a signal from another neuron, triggers the neuron, sodium channels open, allowing sodium ions to...
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...
The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
Free Energy Changes for Nonstandard States03:25

Free Energy Changes for Nonstandard States

The free energy change for a process taking place with reactants and products present under nonstandard conditions (pressures other than 1 bar; concentrations other than 1 M) is related to the standard free energy change according to this equation:

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Related Experiment Video

Updated: May 17, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor
10:00

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Double descent: When do neural quantum states generalize?

M Schuyler Moss1,2, Alev Orfi3,4, Christopher Roth3

  • 1University of Waterloo, Department of Physics and Astronomy, Ontario N2L 3G1, Canada.

Physical Review. E
|May 16, 2026
PubMed
Summary
This summary is machine-generated.

Neural quantum states (NQS) show the double descent phenomenon seen in deep learning. However, the practical overparameterized regime for NQS is typically out of reach for current problems.

Related Experiment Videos

Last Updated: May 17, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor
10:00

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

Area of Science:

  • Quantum Many-Body Physics
  • Machine Learning

Background:

  • Neural quantum states (NQS) offer flexible parametrizations for quantum many-body physics.
  • NQS aim to reduce the exponential scaling of Hilbert space with fewer parameters.
  • The relationship between NQS and standard deep learning neural networks is not fully understood.

Purpose of the Study:

  • To investigate if NQS exhibit the double descent phenomenon characteristic of deep learning.
  • To determine the conditions under which NQS display this phenomenon.
  • To understand the implications for NQS architecture design.

Main Methods:

  • A simplified supervised learning setting was used to train NQS.
  • Network size and training data were varied to observe generalization behavior.
  • Comparison of NQS performance with theoretical expectations of double descent.

Main Results:

  • NQS demonstrate the double descent phenomenon in a supervised setting.
  • The second descent (improvement in overparameterized regime) requires network sizes far exceeding practical limits.
  • Typical NQS applications are situated in the underparameterized regime.
  • Optimal network size in the underparameterized regime is influenced by the number of unique training samples.

Conclusions:

  • While double descent is present in NQS, the practical implications favor physics-informed architectures over direct ML heuristics.
  • Symmetry-aware and physics-informed design is crucial for effective NQS.
  • Current NQS applications likely benefit more from understanding the underparameterized regime.