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.
Deep neural networks undergo hierarchical free-energy landscape transitions with increasing data size.
problem Understanding the design space and dynamics of deep neural networks.
method Statistical mechanical approach based on replica method.
result Hierarchical free-energy landscape transitions with ultrametricity, leading to simpler configurations in deeper layers.
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.
GMVAE improves clustering in molecular simulations data.
problem Clustering metastable states in multi-basin free-energy landscapes.
method Gaussian mixture variational autoencoder (GMVAE) for dimensionality reduction and clustering.
result Enhanced clustering of metastable states compared to standard VAEs.
In this paper we first analyzed the inductive bias underlying the data scattered across complex free energy landscapes (FEL), and exploited it to train deep neural networks which yield reduced and clustered representation for the FEL. Our parametric method, called Information Distilling of Metastability (IDM), is end-t…
Dimensionality reduction is ubiquitous in analysis of complex dynamics. The conventional dimensionality reduction techniques, however, focus on reproducing the underlying configuration space, rather than the dynamics itself. The constructed low-dimensional space does not provide complete and accurate description of the…
Macromolecular and biomolecular folding landscapes typically contain high free energy barriers that impede efficient sampling of configurational space by standard molecular dynamics simulation. Biased sampling can artificially drive the simulation along pre-specified collective variables (CVs), but success depends crit…
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.
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.
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.
Unified framework for sampling and approximating high-dimensional energy landscapes.
problem Sampling and approximating complex energy landscapes in physical systems with constraints and energy barriers.
method Formulates a minimax optimization problem that jointly adapts surrogate approximation and adaptive sampling.
result Demonstrates effectiveness in biomolecular systems with up to 30 collective variables.
Enhances diffusion-based sampling for molecular systems.
problem Inefficiency and thermodynamic mode miss in diffusion-based samplers for molecular systems.
method Introduces a sequential bias along collective variables (CVs) to encourage exploration and increase temperature in the projected space.
result Improves efficiency, mode discovery, and free energy estimation; first to demonstrate reactive sampling.
We reveal connections between RBMs and Bosons, explaining symmetry breaking in their energy landscapes.
problem Understanding the relationships among different deep generative models and their learning mechanisms.
method Introducing a reciprocal space formulation to RBMs, revealing connections to diffusion processes and Bosons.
result Symmetry breaking in RBM energy landscapes is characterized by singular values and weight matrix eigenvectors.
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.
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.
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.
GDML learns effective CG models from all-atom data.
problem Learning effective coarse-grained force fields efficiently.
method Ensemble learning with stratified sampling and GDML.
result GDML yields smaller free energy error than neural networks.
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.
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.
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.
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 N. 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…
We characterize stationary solutions to McKean-Vlasov equations on the circle.
problem Stationary solutions of McKean-Vlasov equations on the circle.
method Exact equivalence to an infinite-dimensional quadratic system of equations over Fourier coefficients, leading to explicit characterization of stationary states.
result Analytic expressions for the emergence, form, and shape of bifurcations involving multiple Fourier modes, and connections with discontinuous phase transitions.
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 free energy is a key quantity of interest in Ising models, but unfortunately, computing it in general is computationally intractable. Two popular (variational) approximation schemes for estimating the free energy of general Ising models (in particular, even in regimes where correlation decay does not hold) are: (i)…
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.
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.
Gradient flow in a potential energy (or Euclidean action) landscape provides a natural set of paths connecting different saddle points. We apply this method to General Relativity, where gradient flow is Ricci flow, and focus on the example of 4-dimensional Euclidean gravity with boundary S^1 x S^2, representing the can…
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.
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.
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.