Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows

• URL: http://arxiv.org/abs/2110.02673v1
• Date: Wed, 6 Oct 2021 11:48:34 GMT
• Title: Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows
• Abstract summary: We propose a continuous normalizing flow for sampling from the high-dimensional probability distributions of Quantum Field Theories in Physics. We test our model on the $phi4$ theory, showing that it systematically outperforms a realNVP baseline in sampling efficiency.
• Score: 3.464871689508835
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a continuous normalizing flow for sampling from the high-dimensional probability distributions of Quantum Field Theories in Physics. In contrast to the deep architectures used so far for this task, our proposal is based on a shallow design and incorporates the symmetries of the problem. We test our model on the $\phi^4$ theory, showing that it systematically outperforms a realNVP baseline in sampling efficiency, with the difference between the two increasing for larger lattices. On the largest lattice we consider, of size $32\times 32$, we improve a key metric, the effective sample size, from 1% to 66% w.r.t. the realNVP baseline.

Related papers

• Entropy Across the Bridge: Conditional-Marginal Discretization for Flow and Schrödinger Samplers [68.9946633641494]
  Flow matching and Schrdinger bridges define probability, yet their inference grids are usually or inherited from one-endpoint diffusion.<n>We derive a conditional-marginal entropy-rate objective for bridge-aware discretization, separating endpoint-conditioned bridge geometry from marginal flow evolution.<n>On EDM/CIFAR-10, the entropic time-discretization gives the best tested five-step FID (186.3 pm 4.0 versus 200.5 pm 2.9 for linear and 238.0 pm 5.3 for cosine)
  arXiv  Detail & Related papers  (2026-05-15T16:11:10Z)
• Theory-optimal Quantization Based on Flatness [31.126049393687143]
  Post-training quantization has emerged as a widely adopted technique for compressing and accelerating the inference of Large Language Models (LLMs)<n>The primary challenges in LLM quantization stem from outliers, which significantly degrade model performance especially at lower bit precision.<n>We propose Bidirectional Diagonal Quantization (BDQ), a novel post-training quantization framework that effectively disperses outlier patterns.
  arXiv  Detail & Related papers  (2026-05-11T10:51:40Z)
• Efficient LLM Reasoning via Variational Posterior Guidance with Efficiency Awareness [2.83639496314338]
  Existing reinforcement learning methods compress reasoning chains by designing elaborate reward functions.<n>We introduce an efficiency-aware evidence lower bound as the theoretical foundation.<n> Experiments on DeepSeek-R1-Distill-Qwen-1.5B and 7B scales demonstrate that VPG-EA improves the comprehensive efficiency metric epsilon cubed by 8.73% and 12.37% over the strongest baselines on each model size.
  arXiv  Detail & Related papers  (2026-05-10T15:18:24Z)
• Tensor network surrogate models for variational quantum computation [0.20391237204597365]
  We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures.<n>For heavy-hexagonal problems with up to three-body interactions, parameters trained on small instances and transferred to systems an order of magnitude larger improve the sampled energy distribution.<n>By extending the training itself with TN simulations on larger system sizes, we avoid local minima and obtain lower-energy samples.
  arXiv  Detail & Related papers  (2026-04-22T04:53:39Z)
• Amortized Inference of Multi-Modal Posteriors using Likelihood-Weighted Normalizing Flows [0.0]
  We present a novel technique for amortized posterior estimation using Normalizing Flows trained with likelihood-weighted importance sampling.<n>We implement the method on multi-modal benchmark tasks in 2D and 3D to check for the efficacy.
  arXiv  Detail & Related papers  (2025-12-04T16:22:53Z)
• Large-scale implementation of quantum subspace expansion with classical shadows [0.5833117322405447]
  We report the first large-scale implementation of quantum subspace expansion (QSE) with informationally complete (IC) measurements.<n>We observe accurate ground state energy recovery and mitigation of local order parameters across system sizes of up to 80 qubits.<n>This represents one of the most significant experimental realizations of classical shadows to date.
  arXiv  Detail & Related papers  (2025-10-29T15:58:37Z)
• Flow-Induced Diagonal Gaussian Processes [7.720921989821054]
  Flow-Induced Diagonal Gaussian Processes (FiD-GP) is a compression framework that incorporates a compact inducing weight matrix.<n>We show how FiD-GP can help to design a single-pass projection for Out-of-Distribution (OoD) detection.
  arXiv  Detail & Related papers  (2025-09-21T16:49:09Z)
• Parallel simulation for sampling under isoperimetry and score-based diffusion models [56.39904484784127]
  As data size grows, reducing the iteration cost becomes an important goal. Inspired by the success of the parallel simulation of the initial value problem in scientific computation, we propose parallel Picard methods for sampling tasks. Our work highlights the potential advantages of simulation methods in scientific computation for dynamics-based sampling and diffusion models.
  arXiv  Detail & Related papers  (2024-12-10T11:50:46Z)
• Bayesian Circular Regression with von Mises Quasi-Processes [57.88921637944379]
  In this work we explore a family of expressive and interpretable distributions over circle-valued random functions. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Gibbs sampling. We present experiments applying this model to the prediction of wind directions and the percentage of the running gait cycle as a function of joint angles.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Quasi-Bayes meets Vines [2.3124143670964448]
  We propose a different way to extend Quasi-Bayesian prediction to high dimensions through the use of Sklar's theorem. We show that our proposed Quasi-Bayesian Vine (QB-Vine) is a fully non-parametric density estimator with emphan analytical form.
  arXiv  Detail & Related papers  (2024-06-18T16:31:02Z)
• Posterior and variational inference for deep neural networks with heavy-tailed weights [0.0]
  We consider deep neural networks in a Bayesian framework with a prior distribution sampling the network weights at random. We show that the corresponding posterior distribution achieves near-optimal minimax contraction rates. We also provide variational Bayes counterparts of the results, that show that mean-field variational approximations still benefit from near-optimal theoretical support.
  arXiv  Detail & Related papers  (2024-06-05T15:24:20Z)
• Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation [39.20075231137991]
  We address the computation of the cumulative distribution function (CDF) of the spectral measure of the Hamiltonian. We introduce a signal processing technique for identifying the inflection point of the CDF. We conduct numerical experiments on a 26-qubit fully-connected Heisenberg model using a truncated density-matrix renormalization group (DMRG) initial state of low bond dimension.
  arXiv  Detail & Related papers  (2024-05-06T18:00:03Z)
• Maximum Weight Entropy [6.821961232645206]
  This paper deals with uncertainty quantification and out-of-distribution detection in deep learning using Bayesian and ensemble methods. Considering neural networks, a practical optimization is derived to build such a distribution, defined as a trade-off between the average empirical risk and the weight distribution entropy.
  arXiv  Detail & Related papers  (2023-09-27T14:46:10Z)
• Normalizing flows for lattice gauge theory in arbitrary space-time dimension [135.04925500053622]
  Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We discuss masked autoregressive with tractable and unbiased Jacobian determinants, a key ingredient for scalable and exact flow-based sampling algorithms. For concreteness, results from a proof-of-principle application to SU(3) gauge theory in four space-time dimensions are reported.
  arXiv  Detail & Related papers  (2023-05-03T19:54:04Z)
• Solving Oscillation Problem in Post-Training Quantization Through a Theoretical Perspective [74.48124653728422]
  Post-training quantization (PTQ) is widely regarded as one of the most efficient compression methods practically. We argue that an overlooked problem of oscillation is in the PTQ methods.
  arXiv  Detail & Related papers  (2023-03-21T14:52:52Z)
• Optimal Scaling for Locally Balanced Proposals in Discrete Spaces [65.14092237705476]
  We show that efficiency of Metropolis-Hastings (M-H) algorithms in discrete spaces can be characterized by an acceptance rate that is independent of the target distribution. Knowledge of the optimal acceptance rate allows one to automatically tune the neighborhood size of a proposal distribution in a discrete space, directly analogous to step-size control in continuous spaces.
  arXiv  Detail & Related papers  (2022-09-16T22:09:53Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Sensing Cox Processes via Posterior Sampling and Positive Bases [56.82162768921196]
  We study adaptive sensing of point processes, a widely used model from spatial statistics. We model the intensity function as a sample from a truncated Gaussian process, represented in a specially constructed positive basis. Our adaptive sensing algorithms use Langevin dynamics and are based on posterior sampling (textscCox-Thompson) and top-two posterior sampling (textscTop2) principles.
  arXiv  Detail & Related papers  (2021-10-21T14:47:06Z)
• Simulating Large PEPs Tensor Networks on Small Quantum Devices [0.0]
  We map low-bond-dimension PEPs tensor networks to quantum circuits. We employ this approach to calculate the values of a long-range loop observable in the topological Wen plaquette model. Our results serve as a proof-of-concept for simulating large two-dimensional quantum systems on small quantum devices.
  arXiv  Detail & Related papers  (2021-10-01T16:19:06Z)
• The edge of chaos: quantum field theory and deep neural networks [0.0]
  We explicitly construct the quantum field theory corresponding to a general class of deep neural networks. We compute the loop corrections to the correlation function in a perturbative expansion in the ratio of depth $T$ to width $N$. Our analysis provides a first-principles approach to the rapidly emerging NN-QFT correspondence, and opens several interesting avenues to the study of criticality in deep neural networks.
  arXiv  Detail & Related papers  (2021-09-27T18:00:00Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• On Deep Instrumental Variables Estimate [21.003925102068298]
  "Deep Instrumental Variable (IV)" is a framework based on deep neural networks to address endogeneity. We consider a two-stage estimator using deep neural networks in the linear instrumental variables model. We show that the second-stage estimator achieves the semiparametric efficiency bound.
  arXiv  Detail & Related papers  (2020-04-30T17:03:00Z)

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.