arXiv research

Paper proposes new loss functions for training energy networks.

Characterizes complex Hessian equations for bounded energy functions.

For a fixed smooth map $u_0$ between two Riemann surfaces $Σ$ and $S$ with non-zero degree, we consider the energy function on Teichmüller space $\mc{T}$ of $Σ$ that assigns to a complex structure $t\in \mc{T}$ on $Σ$ the energy of the harmonic map $u_t:Σ_t:=(Σ,t) \to S$ homotopic to $u_0$. We prove that the energy fun…

This note discusses the higher K-energy functionals which were defined by Bando and Mabuchi, and integrate higher Futaki invariants. Two new formulas for the higher K-energy functionals are given, and the second K-energy is shown to be related to Donaldson's Lagrangian applied to metrics on the tangent bundle.

According to Pixton, there are Morse-Smale diffeomorphisms of the 3-sphere which have no energy function, that is a Lyapunov function whose critical points are all periodic points of the diffeomorphism. We introduce the concept of quasi-energy function for a Morse-Smale diffeomorphism as a Lyapunov function with the le…

Derive Dirichlet scalar curvature energy functional variation formula

We study the energy functional on the set of Lagrangian tori in $\mathbb{C}P^2$ . We prove that the value of the energy functional on a certain family of Hamiltonian minimal Lagrangian tori in $\mathbb{C}P^2$ is strictly larger than energy of the Clifford torus.

We introduce the "Energy-based Generative Adversarial Network" model (EBGAN) which views the discriminator as an energy function that attributes low energies to the regions near the data manifold and higher energies to other regions. Similar to the probabilistic GANs, a generator is seen as being trained to produce con…

New method trains deep neural networks for non-interacting kinetic-energy functionals in DFT.

Improved diffusion models using energy distillation and sequential Monte Carlo.

Traditional centralized energy systems have the disadvantages of difficult management and insufficient incentives. Blockchain is an emerging technology, which can be utilized in energy systems to enhance their management and control. Integrating token economy and blockchain technology, token economic systems in energy …

Study proves uniform ellipticity implies uniform polyconvexity for anisotropic energy functionals.

Unified perspective on Hopfield networks with attention module.

Geodesics found in a metric space of m-subharmonic functions.

Energy Transformer integrates attention, energy models, and associative memory.

Characterizes CR manifolds as critical points of an energy functional.

In this paper, energy function is used to investigate the eigen-solutions of $-Δu+ Vu=λu$ on the Riemannian manifolds. We give a new way to prove the positivity of the initial energy of energy function, which leads to a simple way to obtain the growth of eigen-solutions.

Synthetic approach to pluripotential theory measures finite energy.

Morse theory connects low energy submanifolds in 3-sphere.

The paper calculates the second variation of energy functions for families of canonically polarized manifolds.

In this paper we study the energy function associated to fourth order equations of critical growth on smooth compact conformally flat manifolds of dimension greater or equal than 5.

Energy functional for Legendrian knots in Heisenberg group, invariant under PU(2,1).

The paper analyses the extrema of p-energy functional on a Finsler space with constant curvature.

Proves weight polytope matches with energy vectors in toric varieties.

In this sequel to arXiv:1510.03817, we apply our abstract Lojasiewicz-Simon gradient inequality to prove Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces which impose minimal regularity requirements on pairs of connections and sections. The Lojasiewicz-Simon gradient …

Gradient Ricci solitons can be extended to non-gradient Ricci solitons using energy function.

We develop the calculus for hypersurface variations based on variation of the hypersurface defining function. This is used to show that the functional gradient of a new Willmore-like, conformal hypersurface energy agrees exactly with the obstruction to smoothly solving the singular Yamabe problem for conformally compac…

Study sesqui-harmonic map flow from Riemannian surfaces

We extend short-time existence and stability of the Dirichlet energy flow as proven in a previous paper by the authors to a broader class of energy functionals. Furthermore, we derive some monotonely decreasing quantities for the Dirichlet energy flow and investigate an equation of soliton type. In particular, we show …

Strict plurisubharmonicity proven for Teichmüller energy on Hitchin representations.

The paper studies critical points of horizontal energy functional in Riemannian foliations.

Structured Prediction Energy Networks (SPENs) are a simple, yet expressive family of structured prediction models (Belanger and McCallum, 2016). An energy function over candidate structured outputs is given by a deep network, and predictions are formed by gradient-based optimization. This paper presents end-to-end lear…

Improves energy efficiency of neuromorphic hardware by optimizing memory organization and encoding schemes.

Probabilistic models can be defined by an energy function, where the probability of each state is proportional to the exponential of the state's negative energy. This paper considers a generalization of energy-based models in which the probability of a state is proportional to an arbitrary positive, strictly decreasing…

The paper improves energy decay estimates for Dir-stationary Q-valued functions and applies them to Liouville-type theorems and continuity.

For a bounded smooth domain in the plane and smooth boundary data we consider the minimisation of the Willmore functional for graphs subject to Dirichlet or Navier boundary conditions. For $H^2$-regular graphs we show that bounds for the Willmore energy imply area and diameter bounds. We then consider the $L^1$-lower s…

A new loss function ED simplifies training energy-based models without scores.

The paper examines conditions for the equator map to be minimizing or unstable for higher order energy functionals.

EBM predicts protein conformations at atomic scale using crystallized data.

New energy functional bounds Ricci flows on ancient spaces.

We apply our abstract gradient inequalities developed by the authors in arXiv:1510.03817 to prove Lojasiewicz--Simon gradient inequalities for the harmonic map energy function using Sobolev spaces which impose minimal regularity requirements on maps between closed, Riemannian manifolds. Our Lojasiewicz--Simon gradient …

The study extends calibrated geometry to smooth maps and finds energy bounds.

We introduce certain energy functionals to the complex Monge-Ampere equation over a bounded domain with inhomogeneous boundary condition, and use these functionals to show the convergence of the solution to the parabolic Monge-Ampere equation.

Let X be a smooth, linearly normal n dimensional complex projective variety. Assume that the projective dual of X has codimension one with defining polynomial D(X). In this paper the log of the norm of D(X) is expressed as the restriction to the Bergman metrics of an energy functional on X. We show how, for smooth plan…

A new method trains discrete EBMs without sampling.

Lowered regularity assumption for a phase-dependent Helfrich energy equation.

Minimal submanifolds are found as energy concentration sets in variational problems.

Extends K-energy to complexified Kähler classes for scalar curvature study.