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.
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.
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.
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…
Agents learn and control complex mechanical systems through shared memories.
problem Controlling multi-joint dynamical systems.
method Coupled autoregressive active inference agents using Bayesian filtering and minimizing expected free energy.
result Demonstrated learning and control of a double mass-spring-damper system.
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.
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.
The study explores how agents learn and adapt preferences in dynamic environments.
problem Adaptive behavior and preference learning in reinforcement learning tasks.
method The approach involves self-supervised learning of preferences, distinguishing between environmental and intrinsic observations, and evaluating with model-free and model-based reinforcement learning.
result The methodology successfully minimizes surprisal and expected free energy in dynamic environments.
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.
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…
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.
Active inference is a process theory of the brain that states that all living organisms infer actions in order to minimize their (expected) free energy. However, current experiments are limited to predefined, often discrete, state spaces. In this paper we use recent advances in deep learning to learn the state space an…
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.
New algorithm minimizes FE objectives for synthetic AIF agents.
problem Minimizing Free Energy for synthetic active inference agents.
method Variational message passing on Constrained FFGs.
result Message passing algorithms induce epistemic behavior in AIF agents.
Geometric Brownian motion (GBM) is a key model for representing self-reproducing entities. Self-reproduction may be considered the definition of life [5], and the dynamics it induces are of interest to those concerned with living systems from biology to economics. Trajectories of GBM are distributed according to the we…
We study the parameter estimation problem in mixture models with observational nonidentifiability: the full model (also containing hidden variables) is identifiable, but the marginal (observed) model is not. Hence global maxima of the marginal likelihood are (infinitely) degenerate and predictions of the marginal likel…
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.
New framework improves EM algorithm convergence under log-Sobolev inequality.
problem Improving convergence of the EM algorithm.
method Extending gradient flow techniques to EM algorithm, using free energy representation.
result Exponential convergence of EM algorithm under log-Sobolev inequality.
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.
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.
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.
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.
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.
This paper introduces the Metric-Free Natural Gradient (MFNG) algorithm for training Boltzmann Machines. Similar in spirit to the Hessian-Free method of Martens [8], our algorithm belongs to the family of truncated Newton methods and exploits an efficient matrix-vector product to avoid explicitely storing the natural g…
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.
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.
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 finds surfaces in spherical caps that maximize modified energy.
problem Geometry of surfaces with free boundaries and capillary conditions.
method Monotonicity formulae and energy maximization analysis.
result Capillary minimal surfaces maximize a modified energy in their conformal orbit.
Paper proposes energy objective for training normalizing flows without determinants.
problem Challenges in training normalizing flows due to Jacobian determinants.
method Introduces energy objective based on proper scoring rules, determinant-free.
result Energy objective supports novel model families and competitive performance.
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.
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.
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.
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…
Vector approximate message passing (VAMP) is a computationally simple approach to the recovery of a signal x from noisy linear measurements y=Ax+w. Like the AMP proposed by Donoho, Maleki, and Montanari in 2009, VAMP is characterized by a rigorous state evolution (SE) that holds …
Straight lines are a basin of attraction for the elastic flow at least to level 1.9615π.
problem Understanding the basin of attraction for the free boundary free elastic flow.
method Steepest descent gradient flow for elastic energy, numerical evidence.
result Straight lines have a basin of attraction at least to level 1.9615π.
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.
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.
Free energy perturbation (FEP) was proposed by Zwanzig more than six decades ago as a method to estimate free energy differences, and has since inspired a huge body of related methods that use it as an integral building block. Being an importance sampling based estimator, however, FEP suffers from a severe limitation: …
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 …
This work develops machine learning for micromagnetic energy minimization.
problem Minimizing Gibbs free energy in full 3D micromagnetic simulations.
method Advanced machine learning techniques, including Physics-Informed Neural Networks (PINNs) and Extreme Learning Machines (ELMs), with reformulated bounds and optimization schemes.
result Competitive performance of machine learning methods compared to traditional numerical approaches.
Proposes an energy-based sliced Wasserstein distance for improved probability measure comparison.
problem Inefficiencies and limitations in existing sliced Wasserstein distance approaches.
method Introduces an energy-based slicing distribution for better performance and stability.
result Demonstrates superior performance of the EBSW distance in various applications.
Bayesian calibration for BCP self-assembly models using image data and measure transport.
problem Calibrating models of BCP self-assembly from image data with aleatory uncertainty.
method Likelihood-free inference via measure transport and summary statistics.
result Expected information gains can be computed efficiently for model calibration.
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)…