Hamiltonian Score Matching and Generative Flows

• URL: http://arxiv.org/abs/2410.20470v1
• Date: Sun, 27 Oct 2024 15:17:52 GMT
• Title: Hamiltonian Score Matching and Generative Flows
• Authors: Peter Holderrieth, Yilun Xu, Tommi Jaakkola,
• Abstract summary: We introduce Hamiltonian velocity predictors (HVPs) as a tool for score matching and generative models. We present two innovations constructed with HVPs: Hamiltonian Score Matching (HSM), which estimates score functions by augmenting data via Hamiltonian trajectories, and Hamiltonian Generative Flows (HGFs), a novel generative model that encompasses diffusion models and flow matching as HGFs with zero force fields.
• Score: 9.566017873326725
• License:
• Abstract: Classical Hamiltonian mechanics has been widely used in machine learning in the form of Hamiltonian Monte Carlo for applications with predetermined force fields. In this work, we explore the potential of deliberately designing force fields for Hamiltonian ODEs, introducing Hamiltonian velocity predictors (HVPs) as a tool for score matching and generative models. We present two innovations constructed with HVPs: Hamiltonian Score Matching (HSM), which estimates score functions by augmenting data via Hamiltonian trajectories, and Hamiltonian Generative Flows (HGFs), a novel generative model that encompasses diffusion models and flow matching as HGFs with zero force fields. We showcase the extended design space of force fields by introducing Oscillation HGFs, a generative model inspired by harmonic oscillators. Our experiments validate our theoretical insights about HSM as a novel score matching metric and demonstrate that HGFs rival leading generative modeling techniques.

Related papers

• Latent Space Energy-based Neural ODEs [73.01344439786524]
  This paper introduces a novel family of deep dynamical models designed to represent continuous-time sequence data. We train the model using maximum likelihood estimation with Markov chain Monte Carlo. Experiments on oscillating systems, videos and real-world state sequences (MuJoCo) illustrate that ODEs with the learnable energy-based prior outperform existing counterparts.
  arXiv  Detail & Related papers  (2024-09-05T18:14:22Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Infusing Self-Consistency into Density Functional Theory Hamiltonian Prediction via Deep Equilibrium Models [30.746062388701187]
  We introduce a unified neural network architecture, the Deep Equilibrium Density Functional Theory Hamiltonian (DEQH) model. DEQH model inherently captures the self-consistency nature of Hamiltonian. We propose a versatile framework that combines DEQ with off-the-shelf machine learning models for predicting Hamiltonians.
  arXiv  Detail & Related papers  (2024-06-06T07:05:58Z)
• Wasserstein proximal operators describe score-based generative models and resolve memorization [12.321631823103894]
  We first formulate SGMs in terms of the Wasserstein proximal operator (WPO) We show that WPO describes the inductive bias of diffusion and score-based models. We present an interpretable kernel-based model for the score function which dramatically improves the performance of SGMs.
  arXiv  Detail & Related papers  (2024-02-09T03:33:13Z)
• Separable Hamiltonian Neural Networks [1.8674308456443722]
  Hamiltonian neural networks (HNNs) are state-of-the-art models that regress the vector field of a dynamical system. We propose separable HNNs that embed additive separability within HNNs using observational, learning, and inductive biases.
  arXiv  Detail & Related papers  (2023-09-03T03:54:43Z)
• Mapping Molecular Hamiltonians into Hamiltonians of Modular cQED Processors [50.893896302254944]
  We introduce a general method to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson complex and the spin-boson model of charge transfer.
  arXiv  Detail & Related papers  (2023-06-10T04:52:58Z)
• Real-time simulations of transmon systems with time-dependent Hamiltonian models [0.0]
  We study aspects of Hamiltonian models which can affect the time evolution of transmon systems. We denote the corresponding computer models as non-ideal gate-based quantum computer (NIGQC) models.
  arXiv  Detail & Related papers  (2023-04-21T14:58:49Z)
• Learning Neural Hamiltonian Dynamics: A Methodological Overview [109.40968389896639]
  Hamiltonian dynamics endows neural networks with accurate long-term prediction, interpretability, and data-efficient learning. We systematically survey recently proposed Hamiltonian neural network models, with a special emphasis on methodologies.
  arXiv  Detail & Related papers  (2022-02-28T22:54:39Z)
• SyMetric: Measuring the Quality of Learnt Hamiltonian Dynamics Inferred from Vision [73.26414295633846]
  A recently proposed class of models attempts to learn latent dynamics from high-dimensional observations. Existing methods rely on image reconstruction quality, which does not always reflect the quality of the learnt latent dynamics. We develop a set of new measures, including a binary indicator of whether the underlying Hamiltonian dynamics have been faithfully captured.
  arXiv  Detail & Related papers  (2021-11-10T23:26:58Z)
• Machine Learning S-Wave Scattering Phase Shifts Bypassing the Radial Schr\"odinger Equation [77.34726150561087]
  We present a proof of concept machine learning model resting on a convolutional neural network capable to yield accurate scattering s-wave phase shifts. We discuss how the Hamiltonian can serve as a guiding principle in the construction of a physically-motivated descriptor.
  arXiv  Detail & Related papers  (2021-06-25T17:25:38Z)
• Entanglement Dynamics of Random GUE Hamiltonians [0.0]
  We study dynamics of entanglement assuming that the overall time-evolution is governed by non-integrable Hamiltonians. We derive universal average time evolution of the reduced density matrix and the purity. We find general expressions for exponential $n$-point correlation functions in the gas of GUE eigenvalues.
  arXiv  Detail & Related papers  (2020-01-01T05:00:00Z)

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.