Free Energy Minimization: A Unified Framework for Modelling, Inference, Learning,and Optimization

• URL: http://arxiv.org/abs/2011.14963v1
• Date: Wed, 25 Nov 2020 11:29:03 GMT
• Title: Free Energy Minimization: A Unified Framework for Modelling, Inference, Learning,and Optimization
• Authors: Sharu Theresa Jose, Osvaldo Simeone
• Abstract summary: Free energy minimization is first introduced, here and historically, as a thermodynamic principle. The mentioned applications to modelling, inference, learning, and optimization are covered starting from basic principles.
• Score: 42.275148861039895
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The goal of these lecture notes is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modelling, generalized Bayesian inference, learning with latent variables, statistical learning analysis of generalization,and local optimization. Free energy minimization is first introduced, here and historically, as a thermodynamic principle. Then, it is described mathematically in the context of Fenchel duality. Finally, the mentioned applications to modelling, inference, learning, and optimization are covered starting from basic principles.

Related papers

• On the Entropy Dynamics in Reinforcement Fine-Tuning of Large Language Models [54.61810451777578]
  Entropy serves as a critical metric for measuring the diversity of outputs generated by large language models.<n>Recent studies increasingly focus on monitoring and adjusting entropy to better balance exploration and exploitation in reinforcement fine-tuning.
  arXiv  Detail & Related papers  (2026-02-03T11:14:58Z)
• Thermodynamically Optimal Regularization under Information-Geometric Constraints [0.6345523830122167]
  Modern machine learning relies on a collection of empirically successful but theoretically heterogeneous regularization techniques.<n>We propose a unifying theoretical framework connecting thermodynamic optimality, information geometry, and regularization.
  arXiv  Detail & Related papers  (2026-01-24T06:26:18Z)
• PhysRVG: Physics-Aware Unified Reinforcement Learning for Video Generative Models [100.65199317765608]
  Physical principles are fundamental to realistic visual simulation, but remain a significant oversight in transformer-based video generation.<n>We introduce a physics-aware reinforcement learning paradigm for video generation models that enforces physical collision rules directly in high-dimensional spaces.<n>We extend this paradigm to a unified framework, termed Mimicry-Discovery Cycle (MDcycle), which allows substantial fine-tuning.
  arXiv  Detail & Related papers  (2026-01-16T08:40:10Z)
• FEAT: Free energy Estimators with Adaptive Transport [61.85373609950878]
  We present Free energy Estimators with Adaptive Transport (FEAT), a novel framework for free energy estimation. FEAT leverages learned transports implemented via interpolants, alongside variational upper and lower bounds on free energy differences. Experimental validation on toy examples, molecular simulations, and quantum field theory demonstrates improvements over existing learning-based methods.
  arXiv  Detail & Related papers  (2025-04-15T15:16:18Z)
• Feasible Learning [78.6167929413604]
  We introduce Feasible Learning (FL), a sample-centric learning paradigm where models are trained by solving a feasibility problem that bounds the loss for each training sample. Our empirical analysis, spanning image classification, age regression, and preference optimization in large language models, demonstrates that models trained via FL can learn from data while displaying improved tail behavior compared to ERM, with only a marginal impact on average performance.
  arXiv  Detail & Related papers  (2025-01-24T20:39:38Z)
• Quantum thermodynamics of the spin-boson model using the principle of minimal dissipation [41.94295877935867]
  We investigate the influence of the environment on quantities such as work, heat and entropy production. The results reveal significant differences to the weak-coupling forms of work, heat and entropy production.
  arXiv  Detail & Related papers  (2024-04-18T12:11:18Z)
• Towards Constituting Mathematical Structures for Learning to Optimize [101.80359461134087]
  A technique that utilizes machine learning to learn an optimization algorithm automatically from data has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. We propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems.
  arXiv  Detail & Related papers  (2023-05-29T19:37:28Z)
• The Principle of Uncertain Maximum Entropy [0.0]
  We present a new principle we call uncertain maximum entropy that generalizes the classic principle and provides interpretable solutions. We introduce a convex approximation and expectation-maximization based algorithm for finding solutions to our new principle.
  arXiv  Detail & Related papers  (2023-05-17T00:45:41Z)
• When to Update Your Model: Constrained Model-based Reinforcement Learning [50.74369835934703]
  We propose a novel and general theoretical scheme for a non-decreasing performance guarantee of model-based RL (MBRL) Our follow-up derived bounds reveal the relationship between model shifts and performance improvement. A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns.
  arXiv  Detail & Related papers  (2022-10-15T17:57:43Z)
• IRL with Partial Observations using the Principle of Uncertain Maximum Entropy [8.296684637620553]
  We introduce the principle of uncertain maximum entropy and present an expectation-maximization based solution. We experimentally demonstrate the improved robustness to noisy data offered by our technique in a maximum causal entropy inverse reinforcement learning domain.
  arXiv  Detail & Related papers  (2022-08-15T03:22:46Z)
• Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse [5.096726017663865]
  Deep generative models allow for the direct estimation of the free energy at a given point in parameter space. In this contribution, we will review this novel machine-learning-based estimation method.
  arXiv  Detail & Related papers  (2021-11-22T15:59:08Z)
• Finite Sample Analysis of Minimax Offline Reinforcement Learning: Completeness, Fast Rates and First-Order Efficiency [83.02999769628593]
  We offer a theoretical characterization of off-policy evaluation (OPE) in reinforcement learning. We show that the minimax approach enables us to achieve a fast rate of convergence for weights and quality functions. We present the first finite-sample result with first-order efficiency in non-tabular environments.
  arXiv  Detail & Related papers  (2021-02-05T03:20:39Z)
• From particle swarm optimization to consensus based optimization: stochastic modeling and mean-field limit [0.0]
  We consider a continuous description based on differential equations of the PSO process for solving global optimization problems. We derive in the large particle limit the corresponding mean-field approximation based on Vlasov-Fokker-Planck-type equations. We compute the related macroscopic hydrodynamic equations that clarify the link with the recently introduced consensus based optimization methods.
  arXiv  Detail & Related papers  (2020-12-10T11:58:19Z)
• Targeted free energy estimation via learned mappings [66.20146549150475]
  Free energy perturbation (FEP) was proposed by Zwanzig more than six decades ago as a method to estimate free energy differences. FEP suffers from a severe limitation: the requirement of sufficient overlap between distributions. One strategy to mitigate this problem, called Targeted Free Energy Perturbation, uses a high-dimensional mapping in configuration space to increase overlap.
  arXiv  Detail & Related papers  (2020-02-12T11:10:00Z)
• A Near-Optimal Gradient Flow for Learning Neural Energy-Based Models [93.24030378630175]
  We propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs) We derive a second-order Wasserstein gradient flow of the global relative entropy from Fokker-Planck equation. Compared with existing schemes, Wasserstein gradient flow is a smoother and near-optimal numerical scheme to approximate real data densities.
  arXiv  Detail & Related papers  (2019-10-31T02:26:20Z)

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.