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 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.
CLuP achieves near optimal ground state energies for positive and negative Hopfield models.
problem Finding near optimal ground state energies for positive and negative Hopfield models.
method Controlled Loosening-up (CLuP) algorithm with fully lifted random duality theory (fl RDT).
result Achieves ground state free energies of 1.77 and 0.33 for positive and negative Hopfield models respectively. Study on existence of ground states on curved spaces with conditions on potential growth.
problem Existence of ground states for aggregation-diffusion models on Cartan-Hadamard manifolds.
method Investigation of a free energy functional on Cartan-Hadamard manifolds, considering entropy and interaction energies.
result Necessary and sufficient conditions for existence of ground states are found, depending on the growth of the attractive potential.
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.
Study on ground states of semilinear elliptic equations with various potential wells.
problem Characterizing ground states of semilinear elliptic equations with arbitrary potential wells.
method Analyzing solutions in convex domains and manifolds with non-negative Ricci curvature, using Morse theory and min-max methods.
result Ground states are mountain-pass type with Morse index 1 in convex domains and manifolds with non-negative Ricci curvature.
The paper identifies magnetic ground states and their role in determining the conformal class of a surface.
problem Understanding the magnetic ground states and their relation to the conformal class of a surface.
method Analyzing the magnetic Laplacian and its eigenvalues on a Riemannian surface.
result The ground state spectrum uniquely determines the volume and conformal class of the metric.
New method uses adiabatic principles to improve ground-state preparation in quantum computing.
problem Challenges in variational training of complex energy landscapes.
method Iterative Hamiltonian deformation complemented with adiabatic principles.
result Consistent convergence to target ground state through sequence of intermediate problems.
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.
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.
Study finds conditions for global minimizers on curved manifolds with fast diffusion and nonlocal interactions.
problem Existence of global minimizers for a free energy functional on negatively curved manifolds.
method Investigation of Carlson-Levin type inequalities for Cartan-Hadamard manifolds.
result Establishes necessary and sufficient conditions for the existence of global energy minimizers.
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…
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.
Statistical learning theory connects to spin glass models via Rademacher complexity and replica theory.
problem Bounding generalization gap in statistical learning theory.
method Linking Rademacher complexity in statistical learning to synthetic models in statistical physics.
result Rademacher complexity is closely related to ground state energy in spin glass models.
Study of Dirac equation with non-local nonlinearity on spheres.
problem Conformally invariant Dirac equation with non-local nonlinearity.
method Investigation of compactness, bubbling, and energy quantization of energy functional; characterization of ground state solutions; proof of Aubin-type inequality and Brezis-Nirenberg type result.
result Existence of solutions to the conformal Einstein-Dirac problem in dimension 4.
Quantum annealing improves VB inference, avoiding local minima.
problem Variational Bayes inference stuck in local minima.
method Quantum annealing approach to VB inference.
result Quantum annealing variational Bayes (QAVB) outperforms classical VB.
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 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.
The excited states of polyatomic systems are rather complex, and often exhibit meta-stable dynamical behaviors. Static analysis of reaction pathway often fails to sufficiently characterize excited state motions due to their highly non-equilibrium nature. Here, we proposed a time series guided clustering algorithm to ge…
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…
We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN) to model molecular properties from datasets of quantum calculations. Inspired by a many-body expansion, HIP-NN decomposes properties, such as energy, as a sum over hierarchical terms. These terms are generated from a neural network--a composit…
Study small perturbations on low energy Laplace eigenfunctions.
problem Understanding small changes in low energy Laplace eigenfunctions.
method Investigates nodal geometry and topology, focusing on low frequency regimes and small perturbations.
result Highlight interesting aspects of spectral theory and nodal phenomena tied to ground state/low energy eigenfunctions.
In this paper, we prove the existence of the free boundary minimal hypersurface of least area in compact manifolds with boundary. Such hypersurface can be viewed as the ground state of the volume spectrum introduced by Gromov. Moreover, we characterize the orientation and Morse index of them.
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.
BOBYQA optimizes deep networks with fewer queries than other methods.
problem Generating adversarial examples with fewer queries than non-model-based methods.
method Model-based derivative-free optimisation algorithm (BOBYQA).
result BOBYQA achieves state-of-the-art results with fewer queries than other methods.
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.
Enhanced VMC methods improve neural wavefunction training.
problem Efficiently training neural wavefunctions in VMC to converge to energy minimum.
method Rayleigh-Gauss-Newton (RGN) optimization and parallel tempering sampling.
result RGN method achieves superlinear convergence with reduced computational cost.
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.
FAST selects coresets more efficiently by matching distributions in the frequency domain.
problem Efficiently selecting representative subsets of large datasets for deep learning.
method FAST uses spectral graph theory and CFD to match distributions, addressing limitations of existing methods.
result FAST significantly outperforms state-of-the-art coreset selection methods in accuracy and energy efficiency.
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.
Bayesian optimization helps learn optimal controls for nuclear fusion reactions.
problem Learning optimal controls for nuclear fusion reactions to prolong plasma stability.
method Theoretical Bayesian optimization algorithm to recommend state-action pairs.
result More efficient use of simulator for learning optimal controls.
The paper proposes a thermodynamic potential to guide training of generative models, breaking ergodicity to improve functionality.
problem Improving generative model functionality while limiting access to underrepresented patterns.
method Constructing a thermodynamic potential that guides training, leading to multiple minima in the free energy.
result Training a generative model breaks ergodicity, preventing escape into the high-temperature phase.
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.
Study of unoriented SL(4) foams in 3-manifolds.
problem Understanding unoriented SL(4) foams in 3-manifolds.
method Combinatorial evaluation and state space study of unoriented SL(4) foams.
result State space of any web is free of rank given by the number of its 4-colorings over a localized ground ring.
Formula derived for G2-manifolds, showing moduli spaces are incomplete.
problem Incompleteness of moduli spaces for G2-manifolds. method Derived a formula for the energy of paths in moduli spaces, provided conditions for finite energy and length.
result Compact G2-manifolds produced by the generalised Kummer construction have incomplete moduli spaces. 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…
We generalize our previous results (Theorem 1 and Corollary 2 in arXiv:1412.4114) and Theorem 1 in arXiv:1502.00668) on the existence of an L2-energy gap for Yang-Mills connections over closed four-dimensional manifolds and energies near the ground state (occupied by flat, anti-self-dual, or self-dual connections) t…
The paper estimates key metrics for linear models with Markov or hidden Markov sources.
problem Estimating free energy, mutual information, and MMSE for linear models with specific signal priors.
method Replica analysis in statistical physics, focusing on Markov and hidden Markov sources.
result The linear model with Markov or hidden Markov sources can be simplified into decoupled AWGN channels.
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.
This article considers the quasi-local conserved quantities with respect to a reference spacetime with a cosmological constant. We follow the approach developed by the authors in [25,26,7] and define the quasi-local energy as differences of surface Hamiltonians. The ground state for the gravitational energy is taken to…
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.
Paper optimizes UAV navigation for IoT data freshness and energy efficiency.
problem Improving data freshness and connectivity for IoT devices with UAVs.
method Deep reinforcement learning model with experience replay for energy-efficient UAV trajectory optimization.
result The proposed approach is 3.6% and 3.13% more energy efficient than greedy and baseline methods.
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.
New method uses quantum computing to process classical data efficiently.
problem Inefficient quantum machine learning due to data loading and trainability issues.
method Linear Hamiltonian-based machine learning with ground state problems for k-local Hamiltonians.
result Demonstrated the effectiveness and scalability of the method on up to 50 qubits.
This study proposes hidden state curiosity to enhance RL models' resilience against noise.
problem Curiosity traps in RL models distract agents from discovering novel experiences.
method Proposed hidden state curiosity based on the Free Energy Principle to reward agents for KL divergence between predictive priors and posteriors.
result Agents with hidden state curiosity are more resilient against curiosity traps compared to those with prediction error curiosity.
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.
Many spectral unmixing methods rely on the non-negative decomposition of spectral data onto a dictionary of spectral templates. In particular, state-of-the-art music transcription systems decompose the spectrogram of the input signal onto a dictionary of representative note spectra. The typical measures of fit used to …