arXiv research

New method improves MAP inference for CGMs on path graphs, avoiding approximation and maintaining integrality.

Efficient adjustment sets found for cost-minimized causal estimations.

Gradient flow converges to a minimal convex structure.

Study weak super Ricci flow through neckpinch in metric measure spaces.

A new method for optimal transport using neural ODEs that preserves marginal constraints.

New method improves MMD estimation without convexity assumptions.

New proof of energy functional monotonicity via geodesics in measure space.

This study explains gradient flow dynamics in neural networks for small initialisation.

Curve shortening flow shrinks curves to points under certain conditions.

Gradient descent with geometrically adapted metrics drives $\mathcal{L}^2$ cost to global minimum at uniform rate.

Paper characterizes nc-rank using gradient flow on symmetric space.

Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a no…

Introduces optimization geometrodynamics for dynamic geometric optimization.

We notice that a generic nonsingular gradient field $v = \nabla f$ on a compact 3-fold $X$ with boundary canonically generates a simple spine $K(f, v)$ of $X$. We study the transformations of $K(f, v)$ that are induced by deformations of the data $(f, v)$. We link the Matveev complexity $c(X)$ of $X$ with counting the …

Many applications generate data with an intrinsic network structure such as time series data, image data or social network data. The network Lasso (nLasso) has been proposed recently as a method for joint clustering and optimization of machine learning models for networked data. The nLasso extends the Lasso from sparse…

Paper uses Gaussian processes to solve AC-OPF with renewable uncertainty.

The paper analyzes reg-SGD for convex problems, proving convergence and quantifying the rate of convergence.

Optimal control solves multi-period liability clearing problems.

The main goal of this paper is to present results of existence and non-existence of convex functions on Riemannian manifolds and, in the case of the existence, we associate such functions to the geometry of the manifold. Precisely, we prove that the conservativity of the geodesic flow on a Rieman- nain manifold with in…

Framework learns linear programs from optimal decisions.

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the ba…

Gradient flow in parameters equals linear interpolation in outputs.

This paper presents a novel method to compute the exact Kantorovich-Wasserstein distance between a pair of $d$-dimensional histograms having $n$ bins each. We prove that this problem is equivalent to an uncapacitated minimum cost flow problem on a $(d+1)$-partite graph with $(d+1)n$ nodes and $dn^{\frac{d+1}{d}}$ arcs,…

In this work, we present a method to compute the Kantorovich-Wasserstein distance of order one between a pair of two-dimensional histograms. Recent works in Computer Vision and Machine Learning have shown the benefits of measuring Wasserstein distances of order one between histograms with $n$ bins, by solving a classic…

Develops new synthetic Ricci flow concepts for metric measure spaces.

Optimal bounds on regret and constraint violation in adversarial COCO.

A scalable gradient-based framework for sparse portfolio selection.

We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs which can be solved very efficiently. We prove that the relaxation recovers the glob…

The Hessian of the renormalized volume of geometrically finite hyperbolic $3$-manifolds without rank-$1$ cusps, computed at the hyperbolic metric $g$ with totally geodesic boundary of the convex core, is shown to be a strictly positive bilinear form on the tangent space to Teichmüller space. The metric $g$ is known fro…

Transformers learn linear models in-context without updates.

MPF method improves parameter estimation in probabilistic models.

The economic life of an asset is the optimum length of its usefulness, which is the moment that the asset's expenses are minimum. In this paper, the economic life of physical assets, such as industry machine and equipment, can be interpreted as the moment that the minimum is reached by its equivalent property cost func…

We consider the minimum cost intervention design problem: Given the essential graph of a causal graph and a cost to intervene on a variable, identify the set of interventions with minimum total cost that can learn any causal graph with the given essential graph. We first show that this problem is NP-hard. We then prove…

In this paper we study the curvature flow of a curve in a plane endowed with a minkowskian norm whose unit ball is smooth. We show that many of the properties known in the euclidean case can be extended (with due adaptations) to this new situation. In particular, we show that simple, closed, strictly convex, smooth cur…

Proposes a method to solve deep neural networks' local minimum problem.

The paper constructs upper bounds for cost minimization in shallow neural networks.

Gradient flow in phase retrieval escapes spurious minima with high probability.

Almost all local minima in neural networks are strongly convex.

Develops exact convex optimization formulations for neural networks.

Efficiently finds sparse solutions to max-plus equations for convex regression.

This paper provides formulas for minimum cost super-hedging in a multi-asset binomial market.

Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones. Here we present a qu…

Classifies ancient convex curves in convex domains.

Gradient descent on Hadamard manifolds converges to boundary points, solving optimization problems.

New algorithm tests model calibration in nearly-linear time.

New framework for DNN training guarantees convergence to global minimum.

We study the misclassification error for community detection in general heterogeneous stochastic block models (SBM) with noisy or partial label information. We establish a connection between the misclassification rate and the notion of minimum energy on the local neighborhood of the SBM. We develop an optimally weighte…

A new scheme reduces global search cost by a square root factor.