A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study introduces weak elastic energy for curves on Riemannian surfaces.
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 -regular graphs we show that bounds for the Willmore energy imply area and diameter bounds. We then consider the -lower s…
We consider a relaxed notion of energy of non-parametric codimension one surfaces that takes account of area, mean curvature, and Gauss curvature. It is given by the best value obtained by approximation with inscribed polyhedral surfaces. The BV and measure properties of functions with finite relaxed energy are studied…
The paper studies harmonic maps to the circle with complex singular sets.
This work relaxes energy constraints in self-attention layers for a more general analysis.
In this paper we address the problem of finding the most probable state of a discrete Markov random field (MRF), also known as the MRF energy minimization problem. The task is known to be NP-hard in general and its practical importance motivates numerous approximate algorithms. We propose a submodular relaxation approa…
For any n>1 we give an explicit example of an n-axially symmetric Cartesian current in B^3 x S^2 with non-trivial vertical part and non-constant graph part minimizing the relaxed Dirichlet energy among the n-axially symmetric Cartesian currents with the same boundary. This stands in sharp contrast with a results of Har…
A new method relaxes molecules without needing non-equilibrium data.
Defines weak normals for irregular curves in high-dimensional spaces.
MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence…
ShotgunCSP predicts crystal structures using machine learning, achieving high accuracy with minimal computation.
The paper studies how adding a 'Gauge Mass' term breaks gauge symmetry in Yang-Mills-Higgs systems and analyzes the resulting behavior.
The paper studies ideal flows of closed curves, classifying critical points and proving flow behavior.
Recently, supervised hashing methods have attracted much attention since they can optimize retrieval speed and storage cost while preserving semantic information. Because hashing codes learning is NP-hard, many methods resort to some form of relaxation technique. But the performance of these methods can easily deterior…
New approach relaxes inductive biases of physics-inspired NNs for better performance.
We present a new proximal bundle method for Maximum-A-Posteriori (MAP) inference in structured energy minimization problems. The method optimizes a Lagrangean relaxation of the original energy minimization problem using a multi plane block-coordinate Frank-Wolfe method that takes advantage of the specific structure of …
In this paper, we consider the classical variational problem in the Galilean space. we develop the Euler-Lagrange equations for a elastic line on an oriented surface in the Galilean 3-dimensional space . Using the varia- tion method, we will try to give some characterization for the solution curve (the elastic lin…
New elastic energy for irregular curves defined through polygonal approximations.
A new optimization algorithm improves convergence in unconstrained problems.
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)…
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified and a novel rearrangement algorithm is proposed, which we show is strictly decreas…
Training neural networks involves finding minima of a high-dimensional non-convex loss function. Knowledge of the structure of this energy landscape is sparse. Relaxing from linear interpolations, we construct continuous paths between minima of recent neural network architectures on CIFAR10 and CIFAR100. Surprisingly, …
Machine learning models accurately predict molecular magnetic anisotropy tensors.
Study on existence of ground states on curved spaces with conditions on potential growth.
Two non-local asymptotic invariants of magnetic fields for the ideal magnetohydrodynamics are introduced. The velocity of variation of the invariants for a non-ideal magnetohydrodynamics with a small magnetic dissipation is estimated. By means of the invariants the spectra of electromagnetic fields are investigated. A …
New metric measure space theory for Lipschitz constants.
TeaNet uses GCNs to model complex atomic interactions inspired by electronic relaxation.
Structured prediction energy networks (SPENs; Belanger & McCallum 2016) use neural network architectures to define energy functions that can capture arbitrary dependencies among parts of structured outputs. Prior work used gradient descent for inference, relaxing the structured output to a set of continuous variables a…
We study on which compact Sasakian 3-manifolds the Reeb field, which is a Beltrami field with eigenvalue 2, is an energy minimizer in its adjoint orbit under the action of volume preserving diffeomorphisms. This minimization property for Beltrami fields is relevant because of its connections with the phenomenon of magn…
Stability of Morse index for Yang-Mills connections in 4D.
Derives equilibrium law for Plateau borders in wet soap films and foams.
The Bethe free energy approximation is reliable when convex on a submanifold, the 'Bethe box'.
CBO interprets as SGD, leading to global convergence for nonconvex functions.
The paper analyzes profitable bidding strategies for BESS in day-ahead and intraday markets.
New model improves transfer learning and semi-supervised learning.
The current trend of pushing CNNs deeper with convolutions has created a pressing demand to achieve higher compression gains on CNNs where convolutions dominate the computation and parameter amount (e.g., GoogLeNet, ResNet and Wide ResNet). Further, the high energy consumption of convolutions limits its deployment on m…
New bounds on trajectory safety in training models with Langevin Dynamics.
Recently, digital music libraries have been developed and can be plainly accessed. Latest research showed that current organization and retrieval of music tracks based on album information are inefficient. Moreover, they demonstrated that people use emotion tags for music tracks in order to search and retrieve them. In…
ASBS improves sampling from Boltzmann distributions without importance weighting.
Prior work on neural network verification has focused on specifications that are linear functions of the output of the network, e.g., invariance of the classifier output under adversarial perturbations of the input. In this paper, we extend verification algorithms to be able to certify richer properties of neural netwo…
We describe a new technique for computing lower-bounds on the minimum energy configuration of a planar Markov Random Field (MRF). Our method successively adds large numbers of constraints and enforces consistency over binary projections of the original problem state space. These constraints are represented in terms of …
We develop an efficient sampling method by simulating Langevin dynamics with an artificial force rather than a natural force by using the gradient of the potential energy. The standard technique for sampling following the predetermined distribution such as the Gibbs-Boltzmann one is performed under the detailed balance…
U-turn chains improve sampling from complex distributions.
Submodular extensions of an energy function can be used to efficiently compute approximate marginals via variational inference. The accuracy of the marginals depends crucially on the quality of the submodular extension. To identify the best possible extension, we show an equivalence between the submodular extensions of…
Stability of hypersurface immersions in Riemannian manifolds proved for perturbations.
Neural networks are based on a simplified model of the brain. In this project, we wanted to relax the simplifying assumptions of a traditional neural network by making a model that more closely emulates the low level interactions of neurons. Like in an RNN, our model has a state that persists between time steps, so tha…
We propose two variants of the Smith-Wilson method for practical application in the insurance industry. Our first variant relaxes the Smith-Wilson energy and can be used to incorporate less reliable market data with a certain weight rather than disregarding it completely. This is particularly useful for deriving yield …
New method improves neural network verification by considering multivariate input space of ReLU neurons.