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.
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.
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.
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.
Poisson variational autoencoders introduce a metabolic cost term that penalizes high baseline activity.
problem Energy constraints in computation.
method Poisson variational autoencoders with a Kullback-Leibler divergence term proportional to firing rates.
result Poisson variational autoencoders introduce a metabolic cost term that penalizes high baseline activity.
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.
PVI improves SIVI by directly optimizing ELBO without parametric assumptions.
problem Intractable variational densities in SIVI methods.
method Particle Variational Inference (PVI) using empirical measures to approximate optimal mixing distributions.
result PVI directly optimizes the ELBO and performs favorably compared to other SIVI methods.
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.
EnVAE uses energy score for likelihood-free VAEs, improving image reconstructions.
problem Likelihood misspecification in VAEs leads to blurry reconstructions and poor data fidelity.
method Deterministic decoder, energy score as reconstruction loss, fast variant for efficiency.
result EnVAE achieves superior reconstruction and generation quality compared to likelihood-based baselines.
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.
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.
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…
Optimal flat ribbons can be created from nonplanar curves with minimal energy.
problem Finding the optimal shape of flat ribbons from nonplanar curves.
method Direct method of the calculus of variations.
result Optimal flat ribbons can be created with minimal bending energy, but they may have isolated planar points.
The Duffing oscillator's parameters are identified online using variational message passing.
problem Estimating parameters of a nonlinear Duffing oscillator in real-time.
method Variational message passing on a factor graph of the Duffing oscillator's generative model.
result The online inference procedure performs as well as offline methods.
We show that k-means (Lloyd's algorithm) is obtained as a special case when truncated variational EM approximations are applied to Gaussian Mixture Models (GMM) with isotropic Gaussians. In contrast to the standard way to relate k-means and GMMs, the provided derivation shows that it is not required to consider Gau…
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.
This paper presents studies on a deterministic annealing algorithm based on quantum annealing for variational Bayes (QAVB) inference, which can be seen as an extension of the simulated annealing for variational Bayes (SAVB) inference. QAVB is as easy as SAVB to implement. Experiments revealed QAVB finds a better local …
From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov-Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension 8, using variational arguments, we also obtain solutions which are global minimizers of the correspondi…
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…
This review reports some theoretical results on the Geometry of membranes. The governing equations to describe equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are derived from the variation of free energies of these structures. Some analytic solutions to these e…
We study some analytical and geometric properties of a two-dimensional nonlinear sigma model with gravitino which comes from supersymmetric string theory. When the action is critical w.r.t. variations of the various fields including the gravitino, there is a symmetric, traceless and divergence-free energy-momentum tens…
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.
New algorithm trains latent diffusion models using interacting particles.
problem Training latent diffusion models efficiently and accurately.
method Reformulate training as minimizing a free energy functional, then approximate with interacting particles.
result The new algorithm outperforms previous methods in experiments.
In this paper, we derive the first and the second variation of the energy functional for a pseudo-Finsler metric using the family of affine connections associated to the Chern connection. This opens the possibility to accomplish computations with coordinate-free methods. Using the second variation formula, we introduce…
After a brief introduction to several variational problems in the study of shapes of thin thickness structures, we deal with variational problems on 2-dimensional surface in 3-dimensional Euclidian space by using exterior differential forms. The morphological problems of lipid bilayers and stabilities of cell membranes…
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)…
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.
EDG generates Boltzmann samples from latent variables efficiently.
problem Sampling from complex energy functions in high dimensions.
method Combines variational autoencoders and diffusion models; uses a decoder and diffusion-based encoder.
result EDG outperforms existing methods in various sampling tasks.
The paper solves a thermodynamics problem about crystal shape.
problem Understanding if minimizing free energy with convex potential and mass constraint generates a convex crystal.
method Utilized a stability theorem, convexity, and a new maximum principle approach to prove a three-dimensional convexity theorem.
result Completely settled the Almgren problem in R3 under generic conditions. Mathematical framework for field theories on Finsler spacetimes.
problem Developing a consistent calculus for field theories on Finsler spacetimes.
method Constructing configuration bundles and applying coordinate-free calculus of variations.
result Averaged energy-momentum conservation law for Finsler field theories.
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.
AIF improves physical AI agents' performance in dynamic environments.
problem Physical AI agents are less capable than biological agents in open-ended real-world environments.
method Developed from probability theory, Bayesian machine learning, variational inference, and Active Inference (AIF), grounded in the Free Energy Principle.
result AIF minimizes variational free energy and is well-suited to physical constraints.
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.
We present a variational renormalization group (RG) approach using a deep generative model based on normalizing flows. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with reduced mutual information. Conversely, the neural net directly maps independent Gauss…
We propose a method for solving statistical mechanics problems defined on sparse graphs. It extracts a small Feedback Vertex Set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense interactions with an effective energy on every configuration of the FVS, then learn…
The study examines stationary surfaces with boundaries and their properties.
problem Investigating stationary surfaces with boundaries and their critical points.
method A generalized bending energy functional is considered, and the first variation is computed. Boundary-value problems are examined, and a characterization of free-boundary surfaces is given.
result Characterization of free-boundary surfaces with rotational symmetry for scaling-invariant functionals.
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.
We propose a general framework for solving statistical mechanics of systems with finite size. The approach extends the celebrated variational mean-field approaches using autoregressive neural networks, which support direct sampling and exact calculation of normalized probability of configurations. It computes variation…
Derive Dirichlet scalar curvature energy functional variation formula
problem Dirichlet scalar curvature energy functional
method First variation formula
result Introduce Dirichlet-Einstein metrics
Proposes a new method to estimate Bayesian neural network depth.
problem Estimating the depth of Bayesian neural networks.
method Uses a discrete truncated normal distribution to learn depth mean and variance, inferring posterior distributions by minimizing variational free energy.
result Improves test accuracy and reduces posterior depth variance on the spiral dataset.
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.
Neural network models transform physical systems into latent Gaussian distributions.
problem Simplifying and solving classical Hamiltonian systems.
method Symplectic neural networks for canonical transformations.
result Captures nonlinear collective modes in latent space.
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 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.
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.
New method shortens and straightens curves, proving convergence and well-posedness.
problem Shortening and straightening of curves.
method Conceptual shift in curve shortening to tangent aligning, variational study of geometric flows.
result Proves convergence to a straight line and global well-posedness for various geometric flows.