Machine Learning Calabi-Yau Hypersurfaces

• URL: http://arxiv.org/abs/2112.06350v1
• Date: Sun, 12 Dec 2021 23:17:31 GMT
• Title: Machine Learning Calabi-Yau Hypersurfaces
• Authors: David S. Berman, Yang-Hui He, Edward Hirst
• Abstract summary: We revisit the classic database of weighted-P4s which admit Calabi-Yau 3-fold hypersurfaces. Unsupervised techniques identify an unanticipated almost linear dependence of the topological data on the weights. Supervised techniques are successful in predicting the topological parameters of the hypersurface from its weights with an accuracy of R2 > 95%.
• Score: 0.0
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: We revisit the classic database of weighted-P4s which admit Calabi-Yau 3-fold hypersurfaces equipped with a diverse set of tools from the machine-learning toolbox. Unsupervised techniques identify an unanticipated almost linear dependence of the topological data on the weights. This then allows us to identify a previously unnoticed clustering in the Calabi-Yau data. Supervised techniques are successful in predicting the topological parameters of the hypersurface from its weights with an accuracy of R^2 > 95%. Supervised learning also allows us to identify weighted-P4s which admit Calabi-Yau hypersurfaces to 100% accuracy by making use of partitioning supported by the clustering behaviour.

Related papers

• Enhanced Hamiltonian Learning Precision with Multi-Stage Neural Networks [10.285214278728528]
  We propose a multi-stage neural network framework that enhances Hamiltonian learning precision. Our approach utilizes time-series data from single-qubit Pauli measurements of random initial states. We demonstrate the framework on two-qubit systems, achieving orders-of-magnitude improvement in parameter accuracy.
  arXiv  Detail & Related papers  (2025-03-10T14:10:59Z)
• Data-freeWeight Compress and Denoise for Large Language Models [101.53420111286952]
  We propose a novel approach termed Data-free Joint Rank-k Approximation for compressing the parameter matrices. We achieve a model pruning of 80% parameters while retaining 93.43% of the original performance without any calibration data.
  arXiv  Detail & Related papers  (2024-02-26T05:51:47Z)
• Improving Parameter Training for VQEs by Sequential Hamiltonian Assembly [4.646930308096446]
  A central challenge in quantum machine learning is the design and training of parameterized quantum circuits (PQCs) We propose a Sequential Hamiltonian Assembly, which iteratively approximates the loss function using local components. Our approach outperforms conventional parameter training by 29.99% and the empirical state of the art, Layerwise Learning, by 5.12% in the mean accuracy.
  arXiv  Detail & Related papers  (2023-12-09T11:47:32Z)
• Calabi-Yau Four/Five/Six-folds as $\mathbb{P}^n_\textbf{w}$ Hypersurfaces: Machine Learning, Approximation, and Generation [0.0]
  In this work, neural networks were implemented to learn the Calabi-Yau Hodge numbers from the weight systems. The approximation always provides a tight lower bound, is shown to be dramatically quicker to compute, and gives remarkably accurate results for systems with large weights.
  arXiv  Detail & Related papers  (2023-11-28T19:00:00Z)
• Deep learning complete intersection Calabi-Yau manifolds [0.0]
  We review advancements in deep learning techniques for complete intersection Calabi-Yau (CICY) 3- and 4-folds. We first discuss methodological aspects and data analysis, before describing neural networks architectures. We include new results on extrapolating predictions from low to high Hodge numbers, and conversely.
  arXiv  Detail & Related papers  (2023-11-20T15:37:39Z)
• HSurf-Net: Normal Estimation for 3D Point Clouds by Learning Hyper Surfaces [54.77683371400133]
  We propose a novel normal estimation method called HSurf-Net, which can accurately predict normals from point clouds with noise and density variations. Experimental results show that our HSurf-Net achieves the state-of-the-art performance on the synthetic shape dataset.
  arXiv  Detail & Related papers  (2022-10-13T16:39:53Z)
• Automating DBSCAN via Deep Reinforcement Learning [73.82740568765279]
  We propose a novel Deep Reinforcement Learning guided automatic DBSCAN parameters search framework, namely DRL-DBSCAN. The framework models the process of adjusting the parameter search direction by perceiving the clustering environment as a Markov decision process. The framework consistently improves DBSCAN clustering accuracy by up to 26% and 25% respectively.
  arXiv  Detail & Related papers  (2022-08-09T04:40:11Z)
• Direct parameter estimations from machine-learning enhanced quantum state tomography [3.459382629188014]
  Machine-learning enhanced quantum state tomography (QST) has demonstrated its advantages in extracting complete information about the quantum states. We develop a high-performance, lightweight, and easy-to-install supervised characteristic model by generating the target parameters directly. Such a characteristic model-based ML-QST can avoid the problem of dealing with large Hilbert space, but keep feature extractions with high precision.
  arXiv  Detail & Related papers  (2022-03-30T15:16:02Z)
• Calabi-Yau Metrics, Energy Functionals and Machine-Learning [0.0]
  We show that machine learning is able to predict the K"ahler potential of a Calabi-Yau metric having seen only a small sample of training data.
  arXiv  Detail & Related papers  (2021-12-20T21:30:06Z)
• Beyond Fully-Connected Layers with Quaternions: Parameterization of Hypercomplex Multiplications with $1/n$ Parameters [71.09633069060342]
  We propose parameterizing hypercomplex multiplications, allowing models to learn multiplication rules from data regardless of whether such rules are predefined. Our method not only subsumes the Hamilton product, but also learns to operate on any arbitrary nD hypercomplex space.
  arXiv  Detail & Related papers  (2021-02-17T06:16:58Z)
• Surface Warping Incorporating Machine Learning Assisted Domain Likelihood Estimation: A New Paradigm in Mine Geology Modelling and Automation [68.8204255655161]
  A Bayesian warping technique has been proposed to reshape modeled surfaces based on geochemical and spatial constraints imposed by newly acquired blasthole data. This paper focuses on incorporating machine learning in this warping framework to make the likelihood generalizable. Its foundation is laid by a Bayesian computation in which the geological domain likelihood given the chemistry, p(g|c) plays a similar role to p(y(c)|g.
  arXiv  Detail & Related papers  (2021-02-15T10:37:52Z)
• Nearest Centroid Classification on a Trapped Ion Quantum Computer [57.5195654107363]
  We design a quantum Nearest Centroid classifier, using techniques for efficiently loading classical data into quantum states and performing distance estimations. We experimentally demonstrate it on a 11-qubit trapped-ion quantum machine, matching the accuracy of classical nearest centroid classifiers for the MNIST handwritten digits dataset and achieving up to 100% accuracy for 8-dimensional synthetic data.
  arXiv  Detail & Related papers  (2020-12-08T01:10:30Z)

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.