arXiv research

CR-FM-NES improves NES for high-dimensional optimization.

Networks are powerful data structures, but are challenging to work with for conventional machine learning methods. Network Embedding (NE) methods attempt to resolve this by learning vector representations for the nodes, for subsequent use in downstream machine learning tasks. Link Prediction (LP) is one such downstream…

NES improves robust optimization with noisy inputs.

We introduce two approaches for combining neural evolution strategy (NES) and proximal policy optimization (PPO): parameter transfer and parameter space noise. Parameter transfer is a PPO agent with parameters transferred from a NES agent. Parameter space noise is to directly add noise to the PPO agent`s parameters. We…

NES optimizes discrete structured VAEs effectively without gradient propagation.

In this paper we propose and analyze a class of $N$-player stochastic games that include finite fuel stochastic games as a special case. We first derive sufficient conditions for the Nash equilibrium (NE) in the form of a verification theorem. The associated Quasi-Variational-Inequalities include an essential game comp…

Save for some special cases, current training methods for Generative Adversarial Networks (GANs) are at best guaranteed to converge to a `local Nash equilibrium` (LNE). Such LNEs, however, can be arbitrarily far from an actual Nash equilibrium (NE), which implies that there are no guarantees on the quality of the found…

Let M be a Riemannian manifold and R its curvature tensor. For a unit vector X tangent to M at a point p, the Jacobi operator is defined by R_X = R(X, .) X$. The manifold M is called pointwise Osserman if, for every point p, the spectrum of the Jacobi operator does not depend of the choice of X, and is called globally …

NE-VAE prevents posterior collapse in VAEs by embedding neighbors in latent space.

This paper presents Natural Evolution Strategies (NES), a recent family of algorithms that constitute a more principled approach to black-box optimization than established evolutionary algorithms. NES maintains a parameterized distribution on the set of solution candidates, and the natural gradient is used to update th…

We show that the second greatest possible dimension of the group of (local) almost isometries of a Finsler metric is $\frac{n^2 -n}{2} +1$ for $n= dim(M)\ne 4$ and $\frac{n^2 -n}{2} +2 =8$ for $n=4$. If a Finsler metric has the group of almost isometries of dimension greater than $\frac{n^2 -n}{2} +1$, then the Finsle…

Transformer adapts to multi-instrumental music generation using NES and Lakh MIDI datasets.

In this study, firstly, Mannheim curves with $κ_1 (s) \ne 0$, $κ_2 (s) \ne 0$ are considered and the conditions are obtained for Mannheim curve to be slant helix. Moreover, the necessary and sufficient conditions are investigated for Mannheim curve to be AW(2), AW(3) and weak AW(2)-types, respectively. Lastly, it is sh…

We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources…

NE-GMM uses ES and GMM to improve uncertainty quantification.

Multi-headed ensembles boost model performance with faster training.

Algorithm learns NE in imperfect information games with imperfect feedback.

Pessimistic Minimax Value Iteration finds efficient NE policies from offline data.

Algorithm finds near-optimal strategy in changing zero-sum games.

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if `similar' means being `more likely to be connected') or c…

Given a generic PL map or a generic smooth fold map $f:N^n\to M^m$, where $m\ge n$ and $2(m+k)\ge 3(n+1)$, we prove that $f$ lifts to a PL or smooth embedding $N\to M\times\mathbb R^k$ if and only if its double point locus $\{(x,y)\in N\times N\mid f(x)=f(y),\,x\ne y\}$ admits an equivariant map to $S^{k-1}$. As a coro…

New methods explain NE embeddings by identifying key variables.

This paper tackles global Nash equilibrium in non-convex multi-player games.

Paper establishes NE existence and efficient algorithms for weakly monotone GMFGs.

We reconsider the training objective of Generative Adversarial Networks (GANs) from the mixed Nash Equilibria (NE) perspective. Inspired by the classical prox methods, we develop a novel algorithmic framework for GANs via an infinite-dimensional two-player game and prove rigorous convergence rates to the mixed NE, reso…

NESS improves neighbor embedding for smooth cell-state transitions in single-cell data.

Generative Adversarial Networks (GAN) have become one of the most successful frameworks for unsupervised generative modeling. As GANs are difficult to train much research has focused on this. However, very little of this research has directly exploited game-theoretic techniques. We introduce Generative Adversarial Netw…

We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave saddle-point problem in the policy space. Specifically, we show that despite its nonconve…

Let $M$ be a closed, connected, orientable topological four-manifold with $H_1(M)$ nontrivial and free abelian, $b_2(M)\ne 0, 2$, and $χ(M)\ne 0$. We show that if $G$ is a finite group of 2-rank $\le 1$ which admits a homologically trivial, locally linear, effective action on $M$, then $G$ must be cyclic. With addition…

If $(M,g)$ is a compact Riemannian manifold of dimension $n\ge 2$ we give necessary and sufficient conditions for improved $L^p(M)$-norms of eigenfunctions for all $2<p\ne p_c=\tfrac{2(n+1)}{n-1}$, the critical exponent. Since improved $L^{p_c}(M)$ bounds imply improvement all other exponents, these conditions are nece…

If p/q > 18, p is odd, and $p/q \ne 37/2$, (p,q)-Dehn surgery for the (-2,3,7)-pretzel knot produces a 3-manifold without Reebless foliation.

Study on Carathéodory metric discrepancies on Teichmüller spaces.

This is the second paper of two in a series under the same title ([CRX]); both study the quantitative volume space form rigidity conjecture: a closed $n$-manifold of Ricci curvature at least $(n-1)H$, $H=\pm 1$ or $0$ is diffeomorphic to a $H$-space form if for every ball of definite size on $M$, the lifting ball on th…

A special Kähler-Ricci potential on a Kähler manifold is any nonconstant $C^\infty$ function $τ$ such that $J(\nablaτ)$ is a Killing vector field and, at every point with $dτ\ne 0$, all nonzero tangent vectors orthogonal to $\nablaτ$ and $J(\nablaτ)$ are eigenvectors of both $\nabla dτ$ and the Ricci tensor. For instan…

Computing Nash equilibrium (NE) of multi-player games has witnessed renewed interest due to recent advances in generative adversarial networks. However, computing equilibrium efficiently is challenging. To this end, we introduce the Gradient-based Nikaido-Isoda (GNI) function which serves: (i) as a merit function, vani…

Simple algorithms identify best items or full rankings from choice-based feedback.

New assumptions and algorithm solve offline two-player zero-sum Markov games.

Tractable model explains market dynamics using Langevin and SUSY QM.

EPINE enhances network embedding by improving adjacency matrix-based high-order proximity.

Study examines pricing strategies in competitive supply chains with discrete prices.

Study mapping class groups of specific 3D shapes.

We prove that if $G$ is a non-uniform lattice in a rank-one semi-simple Lie group $\ne Isom(\H^2_\R)$ then $G$ is quasi-isometrically co-Hopf. This means that every quasi-isometric embedding $G\to G$ is coarsely onto and thus is a quasi-isometry.

The paper proves non-existence results for λ-biharmonic submersions from curved manifolds.

Machine learning detects new minerals at Mars rover landing sites.

An algebraic curvature tensor is called Osserman if the eigenvalues of the associated Jacobi operator are constant on the unit sphere. A Riemannian manifold is called conformally Osserman if its Weyl conformal curvature tensor at every point is Osserman. We prove that a conformally Osserman manifold of dimension $n \ne…

In this paper we de ne conditional random elds in reproducing kernel Hilbert spaces and show connections to Gaussian Process classi cation. More speci cally, we prove decomposition results for undirected graphical models and we give constructions for kernels. Finally we present e cient means of solving the optimization…

We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and $M\ne SO_0(2,2)/SO(2)\tm SO(2).$ Let E be any vector bundle over M, Then any E-valued $L^2$ harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps fro…

Consider the wreath product $H\wr G$, where $H\ne 1$ is finite and $G$ is finitely generated. We show that the Assouad-Nagata dimension $\dim_{AN}(H\wr G)$ of $H\wr G$ depends on the growth of $G$ as follows: If the growth of $G$ is not bounded by a linear function, then $\dim_{AN}(H\wr G)=\infty$, otherwise $\dim_{AN}…