FEAT estimates free energy using adaptive transports.
problem Estimating free energy across scientific domains.
method Uses learned transports and stochastic interpolants.
result Provides consistent, minimum-variance estimators.
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48 results for “free-energy”
Convergent Message-Passing Algorithms for Inference over General Graphs with Convex Free Energiescs.LG
Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixedpoints of the belief propagation (BP) algorithm correspond to the local minima of the free energy. However BP fails to converge in many cases o…
mAIS improves free energy evaluation efficiency.
problem Computational infeasibility of exact free energy evaluation.
method mAIS, a marginalized version of AIS.
result mAIS is more efficient under certain conditions.
Learned Mappings for Targeted Free Energy Perturbation between Peptide Conformationscond-mat.stat-mech
Deep neural networks improve free energy calculations for peptide conformations.
problem Challenges in developing suitable mappings for free energy perturbation.
method Adapted machine learning approach to train deep neural networks for mapping between Boltzmann distributions.
result Accurate free energy differences calculated between thermodynamic states with spring centers separated by 1 Å and sometimes 2 Å.
Estimating Gibbs free energies via isobaric-isothermal flowsphysics.comp-ph
New model estimates Gibbs free energies using machine learning and isobaric-isothermal flows.
problem Estimating Gibbs free energies for complex systems.
method Normalizing flows trained to sample isobaric-isothermal ensemble.
result Excellent agreement with established baselines for water phases.
Coupling between Phase Separation and Geometry on a Closed Elastic Curve: Free Energy Minimization and Dynamicscond-mat.soft
Study of phase separation and geometry on a closed elastic curve, including dynamics and free energy minimization.
problem Free energy and dynamics of a closed elastic filament coupled to a scalar concentration field.
method Analytical and numerical simulations of coupled Willmore flow and Cahn--Hilliard gradient flow on differential geometry.
result Qualitative changes in free energy landscape due to closure constraint, leading to metastable and stable multi-domain morphologies.
Active inference minimizes expected free energy for optimal behavior.
problem Understanding and optimizing behavior in complex systems.
method Combines Bayesian decision theory, optimal Bayesian design, and the free energy principle.
result Active inference emerges as a unified framework for information-seeking, utility maximization, and goal-directed behavior.
We use matricial free energy to regularize autoencoders, producing Gaussian-like codes.
problem Generating Gaussian-like codes for autoencoders.
method Define a differentiable loss function based on singular values of the code matrix, minimizing matricial free energy.
result Minimizing matricial free energy results in Gaussian-like codes that generalize.
Paper analyzes the free energy of CNNs with skip connections in Bayesian learning.
problem Dependency of CNNs with skip connections on the number of parameters.
method Examines the Bayesian free energy of CNNs with and without skip connections.
result The upper bound of free energy of Bayesian CNN with skip connections does not depend on overparametrization.
Targeted free energy estimation via learned mappingsphysics.comp-ph
New method uses neural networks to improve free energy estimation.
problem Estimating free energy differences using FEP is limited by insufficient overlap between distributions.
method Developed a neural network to parameterize a high-dimensional mapping in configuration space.
result Demonstrated substantial variance reduction in free energy estimates.
New result on critical points of Bethe free energy under deformation retracts.
problem Characterizing critical points of Bethe free energy for complex graphs.
method Analyzing homotopy types and deformation retracts of factor graphs.
result Critical points of Bethe free energy are invariant under deformation retracts.
Study on existence of ground states for free energy on hyperbolic space.
problem Existence of ground states for a free energy functional on hyperbolic space.
method Derived HLS-type inequalities on Cartan-Hadamard manifolds to prove existence.
result Established conditions for the existence of ground states on hyperbolic space.
We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Beth…
Study free energy in spherical spin glasses, proving universality dichotomy.
problem Analyzing free energy in spherical spin glass models with different tail exponents.
method Introduced a tail-adapted normalization and used universality dichotomy.
result Sharp universality dichotomy for free energy across different tail exponents.
Paper improves zero-shot protein stability prediction by clarifying free-energy foundations.
problem Improving zero-shot protein stability prediction using inverse folding models.
method Clarifying the free-energy foundations of inverse folding models and proposing better estimates of relative stability.
result Significant gains in zero-shot performance can be achieved with simple methods.
Unified framework for planning under uncertainty using variational inference.
problem Planning under uncertainty with separate objectives for exploration and exploitation.
method Variational inference on a generative model augmented with priors.
result EFE-based planning emerges as variational inference, enabling scalable, resource-aware policies.
This paper generalizes neural transport learning for free energy estimation in arbitrary state spaces.
problem Efficient estimation of free energy in various state spaces.
method Generalized neural transport learning approach for arbitrary state spaces.
result Validation of the proposed method's effectiveness and efficiency in diverse settings.
Unified analysis of mean-field and convex hierarchies for estimating Ising model free energy.
problem Estimating the free energy of Ising models in various regimes.
method Unified analysis using mean-field approximation and convex hierarchies, proving tight bounds and optimality.
result Unified tight bounds for both mean-field and convex hierarchies, showing they are within of the free energy.
The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant) of a closed 3-manifold with gauge group U(N) for arbitrary . We prove that the free energy of an arbitrary closed 3-manifold is uniformly Gevrey-1. As a …
The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be axiomatically derived. Here we apply the free energy principle to general decision trees tha…
Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms correspond to extrema of the Bethe and Kikuchi free energy. However, belief propagation does not always converge, which explains the need for approach…
Physics-constrained Bayesian inference of state functions in classical density-functional theorycond-mat.stat-mech
Bayesian inference learns free energy landscapes from experimental data.
problem Characterize the free energy landscape of classical many-body systems from experimental data.
method Combines non-parametric Bayesian inference with physically-motivated constraints to automate the construction of approximate free energy functionals.
result Inference algorithms yield a probability distribution over free energy functionals, leading to highly accurate analytic expressions.
Study shows TAP free energy minimization provides better posterior inference in high-dimensional linear models.
problem Deviation from true posterior mean and underestimation of posterior uncertainty in variational inference.
method Minimization of TAP free energy in a high-dimensional asymptotic framework, showing geometric and statistical properties.
result Local minimizer of TAP free energy provides consistent estimate of posterior marginals and correctly calibrated posterior inference.
We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. As an extension of Welling and Teh (2001), we define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals and derive an …
Bayesian free energy remains bounded for deep ReLU networks in overparametrized cases.
problem Understanding the generalization performance of deep ReLU neural networks.
method Analyzes Bayesian free energy in overparametrized deep ReLU neural networks.
result Bayesian free energy is bounded even in overparametrized deep ReLU networks.
New method learns collective variables using autoencoders for molecular simulations.
problem Learning low-dimensional slow degrees of freedom (collective variables) for molecular simulations.
method Iterative method involving CV learning with autoencoders and reweighting scheme.
result Achieves convergence of learned collective variables.
The Bethe free energy approximation is reliable when convex on a submanifold, the 'Bethe box'.
problem Accuracy of the Bethe free energy approximation in probabilistic inference.
method Analysis of convexity and verification conditions based on the Bethe Hessian matrix.
result The Bethe approximation is mostly accurate if it is convex on a submanifold, the 'Bethe box'.
CRBMs improve financial regime detection with PCD and free energy analysis.
problem Detecting systemic risk regimes in financial time series.
method Extended RBM to CRBM with autoregressive conditioning and PCD. Decomposed free energy into magnitude and correlation components.
result CRBM's free energy metric distinguishes between magnitude shocks and market regimes.
Adaptive approximations improve variational inference for complex models.
problem Efficiently approximate marginal distributions and partition functions in complex probabilistic models.
method Two classes of adaptive approximations that include Bethe, tree-reweighted, and convex free energies.
result Proposed approximations automatically adapt to a given model and outperform existing methods.
Enhanced diffusion sampling improves rare event sampling in biomolecular simulations.
problem Efficiently sampling rare transition events in biomolecular systems.
method Quantitative steering protocols to generate biased ensembles and exact reweighting.
result Fast, accurate, and scalable estimation of equilibrium properties.
Enhanced diffusion sampling tackles rare event sampling in biomolecular simulations.
problem Efficiently sampling rare transition events in biomolecular simulations.
method Quantitative steering protocols to generate biased ensembles, followed by exact reweighting.
result Fast, accurate, and scalable estimation of equilibrium properties for folding free energies.
New algorithm nearly achieves ground state free energy of SK model.
problem Determining the ground state free energy of the SK model.
method Controlled Loosening-up (CLuP) algorithm applied to SK models.
result Achieves ground state free energy of ~0.76 for n in the thousands.
Controller seeks informative system observations to predict nonlinear dynamics.
problem Predicting nonlinear dynamics with uncertain parameters.
method Expected free energy minimization for balancing goal state and informative observations.
result Controller improves performance in uncertain parameter scenarios.
New algorithms learn latent variable models without tuning, outperforming existing methods.
problem Learning latent variable models without manual tuning.
method Two particle-based algorithms using free energy minimization and coin betting.
result Learning algorithms are entirely tuning-free and competitive with existing methods.
Paper connects free-energy and low-degree hardness in high-dimensional statistics.
problem High-dimensional statistical inference problems are computationally hard.
method Defines a free-energy criterion and connects it to low-degree hardness.
result Establishes connection between free-energy and low-degree hardness for Gaussian models.
A neural network model minimizes region-based free energy for faster inference in MRFs.
problem Efficient inference in complex Markov random fields (MRFs).
method Region-based Energy Neural Network (RENN) that directly minimizes region-based free energy.
result RENN outperforms other methods in marginal distribution estimation, partition function estimation, and MRF learning.
Free Energy Mixercs.CL
FEM improves attention mechanisms by applying value-driven log-linear tilts.
problem Standard attention mechanisms read via convex average, limiting channel-wise selection.
method Free Energy Mixer (FEM) applies a value-driven, per-channel log-linear tilt to a fast prior over indices.
result FEM outperforms strong baselines on NLP, vision, and time-series tasks.
Novel ML model predicts solvation free energies from atom interactions.
problem Predicting solvation free energies from atomistic interactions.
method Two encoding functions extract atomic feature vectors, interactions calculated by inner product.
result Outstanding performance and transferability on 6,493 experimental measurements.
Enhances predictive models against misspecification and outliers.
problem Suboptimal generalization under misspecification and outliers.
method Combines PAC ensemble bounds with a generalized logarithm score function.
result Produces predictive distributions resistant to both misspecification and outliers.
Proposes a new method for learning MRFs without sampling.
problem Learning deep undirected graphical models (MRFs) efficiently.
method Optimizes a saddle-point objective derived from the Bethe free energy approximation, using trained inference networks to amortize the optimization.
result The method compares favorably with loopy belief propagation and achieves better held-out log likelihood.
We present a joint message passing approach that combines belief propagation and the mean field approximation. Our analysis is based on the region-based free energy approximation method proposed by Yedidia et al. We show that the message passing fixed-point equations obtained with this combination correspond to station…
This paper introduces a new approach to active inference using constrained Bethe Free Energy.
problem Tackling the limitations of existing epistemic behavior models in active inference.
method Introducing a constrained Bethe Free Energy (CBFE) perspective to optimize epistemic behavior in generative models.
result CBFE optimization leads to more robust and flexible epistemic behavior compared to existing methods.
Surprisal-Rényi Free Energystat.ML
SRFE clarifies KL divergences without unifying learning frameworks.
problem Inductive biases of KL divergences and their limitations.
method Introducing SRFE, a log-moment-based functional of the likelihood ratio.
result SRFE recovers KL divergences as limits and reveals a mean-variance tradeoff.
Normalizing flows for atomic solidsphysics.comp-ph
Normalizing flows model atomic solids without needing ground-truth samples.
problem Modeling atomic solids without ground-truth samples.
method Normalizing flows to transform a base distribution into the target solid.
result Excellent agreement between model estimates and literature values for Helmholtz free energy.
FEPS models agents to learn and act in complex environments without deep neural networks.
problem Modeling complex adaptive systems and understanding self-organizing behavior.
method Introducing Free Energy Projective Simulation (FEPS) within the constraints of the free energy principle and active inference.
result FEPS agents resolve ambiguity and infer optimal policies in partially observable environments.
Deep learning enhances active inference for dynamic state spaces.
problem Limited applicability of active inference to continuous state spaces.
method Use of deep learning to approximate probability distributions for active inference.
result Active inference can be applied to continuous state spaces.
One-dimensional crystals have convex shapes under certain conditions.
problem Determining if one-dimensional crystals have convex shapes.
method Analyzing the free energy under mass constraints and convexity assumptions.
result In one dimension, crystals have convex shapes under given conditions.
New method learns discrete graph diffusion via free-energy gradient flows.
problem Challenges in translating continuous diffusion models to discrete spaces.
method Proposes a novel computational approach using a specific metric on the simplex.
result Recover the underlying functional for various graph classes.