arXiv research

Classifies SL(n) covariant matrix-valued valuations on Lp-spaces.

Study on convex capillary hypersurfaces with Lp curvature in half-space.

This is a short survey of Riemannian geometric applications of Lp-cohomology of thick spaces, p not equal to 2.

In this paper, we give a new sharp generalization bound of lp-MKL which is a generalized framework of multiple kernel learning (MKL) and imposes lp-mixed-norm regularization instead of l1-mixed-norm regularization. We utilize localization techniques to obtain the sharp learning rate. The bound is characterized by the d…

The abstract discusses p-harmonic forms and their geometric properties, proving new theorems about Lp-cohomology.

The loop space LP_1 of the Riemann sphere is an infinite dimensional complex manifold consisting of maps (loops) from S^1 to P_1 in some fixed C^k or Sobolev W^{k,p} space. In this paper we compute the Dolbeault cohomology groups H^{0,1}(LP_1).

Sharp Lp affine isoperimetric inequalities are established for the entire class of Lp projection bodies and the entire class of Lp centroid bodies. These new inequalities strengthen the Lp Petty projection and the Lp Busemann--Petty centroid inequality.

Proves existence and uniqueness of solutions to the Lp Gaussian Minkowski problem.

We prove that the first reduced cohomology with values in a mixing Lp-representation, p larger than 1, vanishes for a class of amenable groups including connected amenable Lie groups. In particular this solves for this class of amenable groups a conjecture of Gromov saying that every finitely generated amenable group h…

FLAIR measures LP competitiveness in AMMs, improving LP performance evaluations.

JIT liquidity providers can sometimes reduce overall market liquidity by crowding out passive LPs.

Study on LP-Sasakian manifolds with generalized η-Ricci solitons.

We show that the log-likelihood of several probabilistic graphical models is Lipschitz continuous with respect to the lp-norm of the parameters. We discuss several implications of Lipschitz parametrization. We present an upper bound of the Kullback-Leibler divergence that allows understanding methods that penalize the …

LP algorithm optimizes neural networks with architectural constraints.

The object of the present paper is to study locally $φ$-symmetric LP-Sasakian manifolds admitting semi-symmetric metric connection and obtain a necessary and sufficient condition for a locally $φ$-symmetric LP-Sasakian manifold with respect to semi-symmetric metric connection to be locally $φ$-symmetric LP-Sasakian man…

Study on liquidity providers' performance in decentralized exchanges.

We assume data independently sampled from a mixture distribution on the unit ball of the D-dimensional Euclidean space with K+1 components: the first component is a uniform distribution on that ball representing outliers and the other K components are uniform distributions along K d-dimensional linear subspaces restric…

Label assignment problems with large state spaces are important tasks especially in computer vision. Often the pairwise interaction (or smoothness prior) between labels assigned at adjacent nodes (or pixels) can be described as a function of the label difference. Exact inference in such labeling tasks is still difficul…

In this work we introduce a category of discrete Lagrange--Poincare systems LP_d and study some of its properties. In particular, we show that the discrete mechanical systems and the discrete mechanical systems obtained by the Lagrangian reduction of symmetric discrete mechanical systems are objects in LP_d. We introdu…

Study analyzes factors affecting profits in crypto liquidity provision.

New LP method recovers MAP solution from noisy stable instances.

New algorithm reduces online decision-making regret with efficient LP re-solving and parallel first-order method.

Study growth of LP wealth in G3Ms affected by trading fees and arbitrage.

Optimizes liquidity withdrawal timing for AMM LPs to balance fees and impermanent loss.

High-fee pools attract more liquidity but execute less volume; low-fee pools have more stable LPs.

New method prunes large causal bounds LPs for scalable inference.

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their correspondi…

We use a new combinatorial technique to prove the optimal interior partial regularity result for Lp-vectorfields with integer fluxes minimizing the Lp-energy. More precisely, we prove that the minimal vectorfields are Hölder outside a set which is locally finite inside the domain. The results continue the program start…

Existence and uniqueness of the solution to the discrete Lp Minkowski problem for $\mathfrak{p}$-capacity are proved when $p \geq 1$ and $1<\mathfrak{p}<n$. For general Lp Minkowski problem for $\mathfrak{p}$-capacity, existence and uniqueness of the solution are given when $p \geq 1$ and $1<\mathfrak{p}\le 2$. These r…

LP-SparseMAP relaxes SparseMAP for more complex structures.

We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even). Distance-based methods are popular in machine learning. In large-scale applications, sto…

AMM finds optimal contract for LPs to maximize order flow.

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…

AI enhances refinery optimization by detecting data errors and improving decision-making.

Optimal fees for G3Ms align LP value with market accuracy.

We compute the $L^p$-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds.

New formula identifies and quantifies costs for automated market makers.

New offline RL algorithm with optimal sample complexity using LP and error bounds.

Modeling DEX liquidity with heterogeneous LPs and MEV bots.

This paper improves conformal prediction for robust interval estimation under distribution shifts.

Optimal fees protect passive LPs in AMMs under varying market conditions.

Paper optimizes liquidity provision in decentralized finance markets.

LP-FT improves personalized model training in FL by balancing generalization and personalization.

Paper calculates greeks for DeFi LPs and introduces Impermanent Gain.

Maximum a posteriori (MAP) inference is a fundamental computational paradigm for statistical inference. In the setting of graphical models, MAP inference entails solving a combinatorial optimization problem to find the most likely configuration of the discrete-valued model. Linear programming (LP) relaxations in the Sh…

Graph neural networks improve solving linear optimization problems.

Link prediction (LP) algorithms propose to each node a ranked list of nodes that are currently non-neighbors, as the most likely candidates for future linkage. Owing to increasing concerns about privacy, users (nodes) may prefer to keep some of their connections protected or private. Motivated by this observation, our …

Optimizes arm selection with side information in Gaussian bandits.