The positive energy theorem is proven for certain spacetimes with irregular curvature.
problem Proving the positive energy theorem for spacetimes with irregular curvature.
method Weak asymptotically anti-de Sitter initial data sets with distributional curvature under weak dominant energy condition.
result Positive energy theorem established for weakly irregular spacetimes.
Extends denoising and score estimation to energy models via Tweedie's formula.
problem Linking denoising and score estimation for a wider range of distributions.
method Derives a fundamental identity connecting energy score derivatives and scores.
result Establishes a new identity for energy scores analogous to Tweedie's formula.
Paper explores sustainable machine learning with energy harvesting.
problem Energy-efficient distributed machine learning in resource-constrained devices.
method Developed a practical learning framework with theoretical guarantees for distributed learning over energy-harvesting devices.
result Demonstrated significant performance improvement over non-harvesting benchmarks.
Energy distance measures feature heterogeneity in federated learning.
problem Heterogeneity across data sources hinders model aggregation in federated learning.
method Introduced Taylor approximations of energy distance for efficient computation.
result Taylor approximations accurately capture feature discrepancies, improving convergence.
We consider the energy of smooth generalized distributions and also of singular foliations on compact Riemannian manifolds for which the set of their singularities consists of a finite number of isolated points and of pairwise disjoint closed submanifolds. We derive a lower bound for the energy of all q-dimensional a…
EWFM trains continuous flows with only energy evaluations, improving sample quality with fewer computations.
problem Efficiently sampling from complex, high-dimensional Boltzmann distributions using only energy evaluations.
method Energy-Weighted Flow Matching (EWFM) using importance sampling and iterative/annealed training.
result Improved sample quality with up to 3 orders of magnitude fewer energy evaluations compared to existing methods.
This paper analyzes energy and carbon footprints in distributed and federated learning.
problem High energy costs and carbon emissions in centralized AI methods.
method A novel framework quantifying energy and carbon footprints in vanilla and consensus-based FL methods.
result Optimal bounds and operational points for green FL designs and sustainability assessment.
Distributed asynchronous SGD has become widely used for deep learning in large-scale systems, but remains notorious for its instability when increasing the number of workers. In this work, we study the dynamics of distributed asynchronous SGD under the lens of Lagrangian mechanics. Using this description, we introduce …
Reinterprets classifiers as energy-based models for joint distributions.
problem Improving classifier performance and calibration.
method Interprets discriminative classifiers as energy-based models, trains on unlabeled data, and improves model quality.
result Improves calibration, robustness, and out-of-distribution detection.
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.
EBPs model exchangeable data with flexible distributions.
problem Current energy-based models restrict set cardinality and limited distribution forms.
method Introduced Energy-Based Processes (EBPs) that extend energy models to exchangeable data with neural network parameterizations.
result EBPs can express more flexible distributions over sets without cardinality restrictions.
Paper proposes an alternative to MCMC for sampling in energy-based models.
problem Difficulty in generating samples from the current energy function in contrastive approaches.
method Viewing the evolution of the modeling distribution as the evolution of the energy function and samples from this distribution along a time-dependent vector field.
result The proposed method efficiently matches the current distribution in a finite time, unlike MCMC.
We study the global probability distribution of energy consumption per capita around the world using data from the U.S. Energy Information Administration (EIA) for 1980-2010. We find that the Lorenz curves have moved up during this time period, and the Gini coefficient G has decreased from 0.66 in 1980 to 0.55 in 2010,…
BiDVL improves EBLVMs for visual tasks by optimizing two variational distributions.
problem Training EBLVMs is challenging due to intractable distributions.
method Bi-level doubly variational learning with two tractable distributions.
result BiDVL achieves impressive image generation and reconstruction performance.
Energy-efficient sampling for machine learning using magnetic tunnel junctions.
problem Costly and inefficient random sampling in machine learning.
method Energy-efficient algorithm using stochastic magnetic tunnel junctions for uniform Float16 sampling.
result Higher energy efficiency than state-of-the-art algorithms, with a minimum factor of 9721.
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.
This work examines the sensitivity of energy distance to mean differences compared to covariance differences.
problem The sensitivity of energy distance to mean differences compared to covariance differences when distributions are close.
method Analyzes the energy distance in the case where distributions are close, focusing on sensitivity to mean and covariance differences.
result Energy distance is more sensitive to mean differences than covariance differences when distributions are close.
Deep learning depends on tuning layers near critical points.
problem Understanding how deep learning architectures depend on tuning parameters.
method Random energy approach to analyze statistical dependence in deep belief networks.
result Statistical dependence can propagate only if layers are tuned near critical points.
GEBM combines energy function and base distribution for better generative modeling.
problem Improving generative models with better quality samples and performance.
method Alternating training between energy function and base distribution, using MCMC for sampling.
result GEBMs produce higher quality samples and better performance than GANs.
Training energy-based probabilistic models is confronted with apparently intractable sums, whose Monte Carlo estimation requires sampling from the estimated probability distribution in the inner loop of training. This can be approximately achieved by Markov chain Monte Carlo methods, but may still face a formidable obs…
A two-step market clearing method for local energy trading among prosumers and consumers.
problem Integrating distributed energy resources into local energy markets.
method Feeder-based market with Two-StepMarket Clearing (2SMC) mechanism.
result Maximizes market surplus and correct incentives for prosumers and consumers.
BNEM improves Boltzmann sampler efficiency.
problem Generating IID samples from Boltzmann distributions efficiently.
method Bootstrapped Noised Energy Matching (NEM) combined with diffusion-based learning and bootstrapping.
result BNEM achieves state-of-the-art performance with improved robustness.
GEBM improves uncertainty quantification in graph neural networks.
problem Challenges in quantifying epistemic uncertainty in graph neural networks.
method Energy-based model (EBM) that aggregates uncertainty at different structural levels.
result Significantly improves predictive robustness and achieves best separation of in-distribution and out-of-distribution data.
Study the energy distribution of harmonic 1-forms on Riemann surfaces with a short geodesic.
problem Energy distribution of harmonic 1-forms on Riemann surfaces with a short geodesic.
method Analyzes the Jacobian torus of Riemann surfaces with a short geodesic, considering both separating and nonseparating cases.
result Estimates the energy distribution in terms of geometric data of the surface.
Paper trains two models to improve synthesis quality and unsupervised learning.
problem Improving synthesis quality and unsupervised learning.
method Joint training of an energy-based model and a flow-based model using adversarial value function.
result Significant improvement in synthesis quality of the flow model.
A method to automatically learn proposal distributions for energy-based regression models.
problem Manual design and initial estimate of proposal distributions for energy-based regression models.
method Introduces a method to learn an effective proposal distribution automatically, parameterized by a separate network head, and derives a unified training objective to minimize KL divergence and negative log-likelihood.
result Consistently outperforms conventional MDN training on four real-world regression tasks within computer vision.
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as establ…
Energy-based models can generate complex images by combining simpler concepts.
problem Generating natural images that satisfy complex logical combinations of concepts.
method Energy-based models combine probability distributions of simpler concepts to generate compositions.
result Energy-based models can generate images that satisfy conjunctions, disjunctions, and negations of concepts.
A new approach to distill unnormalized EBM for energy-based seq2seq models.
problem Training unnormalized EBM for energy-based seq2seq models is challenging.
method Relating the problem to distributional RL, proposing a general distillation approach.
result General approach applicable to any sequential EBM, illustrated on GAM experiments.
Pileup involves the contamination of the energy distribution arising from the primary collision of interest (leading vertex) by radiation from soft collisions (pileup). We develop a new technique for removing this contamination using machine learning and convolutional neural networks. The network takes as input the ene…
Distributed, controllable energy storage devices offer several benefits to electric power system operation. Three such benefits include reducing peak load, providing standby power, and enhancing power quality. These benefits, however, are only realized during peak load or during an outage, events that are infrequent. T…
In this article we study the role of the Green function for the Laplacian in a compact Riemannian manifold as a tool for obtaining well-distributed points. In particular, we prove that a sequence of minimizers for the Green energy is asymptotically uniformly distributed. We pay special attention to the case of locally …
Study chaotic dynamics in social stratification models leading to thermalization and turbulence.
problem Understanding social stratification dynamics through chaotic nonlinear systems.
method Modeling social network links with oscillators and energies, studying Hamiltonian evolution and nonlinear interactions.
result Chaotic dynamics leads to dynamical thermalization and Kolmogorov-Zakharov turbulence, with implications for wealth inequality.
Study compares multivariate scoring rules for distribution forecasts.
problem Evaluating the discrimination ability of multivariate scoring rules.
method Simulation study comparing energy and variogram scores using historical data.
result Variogram score with p=0.5 outperforms other scores.
Energy Matching unifies flow matching and energy-based models for generative modeling.
problem Inability of flow-based models to integrate partial observations and priors.
method Energy Matching framework that integrates flow matching and energy-based models.
result Substantially outperforms existing EBMs on CIFAR-10 and ImageNet generation.
New method improves sampling from noisy energy models.
problem Training and sampling challenges in Energy-Based Models.
method Pseudo-Gibbs sampling with moment matching.
result Effective sampling from clean model using noisy DSM-trained model.
Energy-based diffusion models improve molecular sampling and simulation.
problem Inconsistency between diffusion model scores and equilibrium distributions.
method Fokker-Planck regularization to enforce consistency.
result Improved consistency and efficient sampling of biomolecular systems.
NNs accurately predict energy eigenvalues and other physical phenomena in 1D quantum mechanics.
problem Understanding how neural networks interpret physics.
method Training NNs to predict energy eigenvalues from potentials and testing their ability to generalize.
result NNs can predict physical phenomena not learned during training, indicating a new way of understanding physics.
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.
Paper designs energy-based controllers and observers for complex systems.
problem Controlling and observing infinite-dimensional systems with in-domain actuation.
method Uses Stokes-Dirac structures and jet-bundle structures to derive controllers and observers.
result Control schemes derived in both frameworks are equivalent.
In this paper, we attack the anomaly detection problem by directly modeling the data distribution with deep architectures. We propose deep structured energy based models (DSEBMs), where the energy function is the output of a deterministic deep neural network with structure. We develop novel model architectures to integ…
We show that balls, circles and 2-spheres can be identified by generalized Riesz energy among compact submanifolds of the Euclidean space that are either closed or with codimension 0, where the Riesz energy is defined as the double integral of some power of the distance between pairs of points. As a consequence, we obt…
Volatility is a key measure of risk in financial analysis. The high volatility of one financial asset today could affect the volatility of another asset tomorrow. These lagged effects among volatilities - which we call volatility spillovers - are studied using the Vector AutoRegressive (VAR) model. We account for the p…
Paper extends port-Hamiltonian model to include internal energy for compressible and incompressible flow.
problem Modeling fluid flow dynamics with internal energy and constraints.
method Derived port-Hamiltonian model using interconnection maps and added internal energy and constraint forces.
result Model accurately represents both compressible and incompressible fluid flow.
ASBS improves sampling from Boltzmann distributions without importance weighting.
problem Sampling from Boltzmann distributions with known energies but unknown samples.
method Adjoint Schrödinger Bridge Sampler using kinetic-optimal transportation.
result ASBS achieves scalable and efficient sampling without importance weighting.
In this paper, we analyze energy-harvesting adaptive diffusion networks for a distributed estimation problem. In order to wisely manage the available energy resources, we propose a scheme where a censoring algorithm is jointly applied over the diffusion strategy. An energy-aware variation of a diffusion algorithm is us…
Study quantizes energy distribution in inhomogeneous phase transitions.
problem Quantifying energy distribution in inhomogeneous Allen-Cahn phase transitions.
method Analysis of varifolds and convergence of integer rectifiable varifolds.
result Equidistribution of energy between Dirichlet and Potential energy in phase field limit.
The implementation of optimal power flow (OPF) methods to perform voltage and power flow regulation in electric networks is generally believed to require extensive communication. We consider distribution systems with multiple controllable Distributed Energy Resources (DERs) and present a data-driven approach to learn c…