Three-body renormalization group limit cycles based on unsupervised feature learning

• URL: http://arxiv.org/abs/2111.07820v1
• Date: Mon, 15 Nov 2021 15:04:24 GMT
• Title: Three-body renormalization group limit cycles based on unsupervised feature learning
• Authors: Bastian Kaspschak and Ulf-G. Mei{\ss}ner
• Abstract summary: We address the question which two-body interactions lead to limit cycles in the three-body system at low energies. We apply an elitist genetic algorithm to a population of synthetic potentials that minimizes a specially defined limit-cycle-loss. The resulting fittest individuals suggest that the inverse square potential is the only two-body potential that minimizes this limit cycle loss independent of the hyperangle.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Both the three-body system and the inverse square potential carry a special significance in the study of renormalization group limit cycles. In this work, we pursue an exploratory approach and address the question which two-body interactions lead to limit cycles in the three-body system at low energies, without imposing any restrictions upon the scattering length. For this, we train a boosted ensemble of variational autoencoders, that not only provide a severe dimensionality reduction, but also allow to generate further synthetic potentials, which is an important prerequisite in order to efficiently search for limit cycles in low-dimensional latent space. We do so by applying an elitist genetic algorithm to a population of synthetic potentials that minimizes a specially defined limit-cycle-loss. The resulting fittest individuals suggest that the inverse square potential is the only two-body potential that minimizes this limit cycle loss independent of the hyperangle.

Related papers

• Zero-Shot Cyclic Peptide Design via Composable Geometric Constraints [65.77915791312634]
  We propose CP-Composer, a novel generative framework that enables zero-shot cyclic peptide generation.<n>Our approach decomposes complex cyclization patterns into unit constraints, which are incorporated into a diffusion model.<n>Our model, despite trained with linear peptides, is capable of generating diverse target-binding cyclic peptides, reaching success rates from 38% to 84%.
  arXiv  Detail & Related papers  (2025-07-06T03:30:45Z)
• Finite-Time Information-Theoretic Bounds in Queueing Control [54.11376591632282]
  We derive new policies that achieve them-for the total queue length in scheduling problems over processing networks with both adversarial and arrivals.<n>These findings reveal a fundamental limitation on "drift-only" methods and point the way toward principled, non-asymptotic optimality in queueing control.
  arXiv  Detail & Related papers  (2025-06-23T04:14:40Z)
• The horocycle regulator: exact cutoff-independence in AdS/CFT [1.124958340749622]
  We investigate a holographic regularization scheme defined in three-dimensional anti-de Sitter space constructed from textithorocycles We describe a broad class of such information measures, and describe how the field theory dual to the horocycle regulator is inherently non-local.
  arXiv  Detail & Related papers  (2024-10-01T18:00:00Z)
• Tripod: Three Complementary Inductive Biases for Disentangled Representation Learning [52.70210390424605]
  In this work, we consider endowing a neural network autoencoder with three select inductive biases from the literature. In practice, however, naively combining existing techniques instantiating these inductive biases fails to yield significant benefits. We propose adaptations to the three techniques that simplify the learning problem, equip key regularization terms with stabilizing invariances, and quash degenerate incentives. The resulting model, Tripod, achieves state-of-the-art results on a suite of four image disentanglement benchmarks.
  arXiv  Detail & Related papers  (2024-04-16T04:52:41Z)
• Universal tetramer limit-cycle at the unitarity limit [0.0]
  A four-boson limit-cycle independent of the Efimov one appears in Hamiltonian systems at the unitary limit. This is a universal manifestation of an independent four-boson scale associated with a cycle beyond the Efimov one.
  arXiv  Detail & Related papers  (2023-03-27T07:33:00Z)
• Autonomous coherence protection of a two-level system in a fluctuating environment [68.8204255655161]
  We re-examine a scheme originally intended to remove the effects of static Doppler broadening from an ensemble of non-interacting two-level systems (qubits) We demonstrate that this scheme is far more powerful and can also protect a single (or even an ensemble) qubit's energy levels from noise which depends on both time and space.
  arXiv  Detail & Related papers  (2023-02-08T01:44:30Z)
• Orbit quantization in a retarded harmonic oscillator [0.0]
  We analytically predict the value of the first Hopf bifurcation, unleashing a self-oscillatory motion. When the system is driven very far from equilibrium, a multiscale strange attractor displaying intrinsic and robust intermittency is uncovered.
  arXiv  Detail & Related papers  (2023-01-25T04:47:06Z)
• A Functional-Space Mean-Field Theory of Partially-Trained Three-Layer Neural Networks [49.870593940818715]
  We study the infinite-width limit of a type of three-layer NN model whose first layer is random and fixed. Our theory accommodates different scaling choices of the model, resulting in two regimes of the MF limit that demonstrate distinctive behaviors.
  arXiv  Detail & Related papers  (2022-10-28T17:26:27Z)
• Beyond the Edge of Stability via Two-step Gradient Updates [49.03389279816152]
  Gradient Descent (GD) is a powerful workhorse of modern machine learning. GD's ability to find local minimisers is only guaranteed for losses with Lipschitz gradients. This work focuses on simple, yet representative, learning problems via analysis of two-step gradient updates.
  arXiv  Detail & Related papers  (2022-06-08T21:32:50Z)
• New insights into four-boson renormalization group limit cycles [0.0]
  We generate populations of synthetic singular potentials within the latent space of a boosted ensemble of variational autoencoders. We prove to generate limit cycles for four bosons and which is already known to produce limit cycles in the three-boson system. This also indicates that a four-body term does not enter low-energy observables at leading order, since we do not observe any additional scale to emerge.
  arXiv  Detail & Related papers  (2022-03-28T09:15:36Z)
• The Power of Sampling: Dimension-free Risk Bounds in Private ERM [25.676350220943274]
  We show that our algorithm can achieve rank-dependent risk bounds for non-smooth convex objectives using only zeroth order oracles. This highlights the power of sampling in differential privacy.
  arXiv  Detail & Related papers  (2021-05-28T07:28:24Z)
• On Lower Bounds for Standard and Robust Gaussian Process Bandit Optimization [55.937424268654645]
  We consider algorithm-independent lower bounds for the problem of black-box optimization of functions having a bounded norm. We provide a novel proof technique for deriving lower bounds on the regret, with benefits including simplicity, versatility, and an improved dependence on the error probability.
  arXiv  Detail & Related papers  (2020-08-20T03:48:14Z)
• Competitive Mirror Descent [67.31015611281225]
  Constrained competitive optimization involves multiple agents trying to minimize conflicting objectives, subject to constraints. We propose competitive mirror descent (CMD): a general method for solving such problems based on first order information. As a special case we obtain a novel competitive multiplicative weights algorithm for problems on the positive cone.
  arXiv  Detail & Related papers  (2020-06-17T22:11:35Z)

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.