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.
Symmetric TSP is structurally equivalent to a constrained Group Steiner Tree Problem.
In this work, we introduce Graph Pointer Networks (GPNs) trained using reinforcement learning (RL) for tackling the traveling salesman problem (TSP). GPNs build upon Pointer Networks by introducing a graph embedding layer on the input, which captures relationships between nodes. Furthermore, to approximate solutions to…
This paper presents a framework to tackle combinatorial optimization problems using neural networks and reinforcement learning. We focus on the traveling salesman problem (TSP) and train a recurrent network that, given a set of city coordinates, predicts a distribution over different city permutations. Using negative t…
Two DRL policies collaborate to solve NP-hard routing problems.
This paper introduces a new learning-based approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs. We use deep Graph Convolutional Networks to build efficient TSP graph representations and output tours in a non-autoregressive manner via highly parallelized beam search. Our approach ou…
DeepCO uses deep learning for offline combinatorial optimization in warehouse operations.
Graph Neural Networks (GNN) are a promising technique for bridging differential programming and combinatorial domains. GNNs employ trainable modules which can be assembled in different configurations that reflect the relational structure of each problem instance. In this paper, we show that GNNs can learn to solve, wit…
This research designs a data-driven partition to test independence between continuous variables.
This paper surveys RL for combinatorial optimization, focusing on TSP.
Graph Neural Networks and Guided Local Search improve TSP solutions.
Neural networks struggle with TSP beyond small instances, requiring new approaches.
DPDP combines neural heuristics with DP for vehicle routing problems.
While there are optimal TSP solvers, as well as recent learning-based approaches, the generalization of the TSP to the Multiple Traveling Salesmen Problem is much less studied. Here, we design a neural network solution that treats the salesmen, cities and depot as three different sets of varying cardinalities. We apply…
Deep RL learns 2-opt heuristics to improve TSP solutions.
Deep learning matches classical feature-based AS models for TSP.
This is a survey on the recent theory on minimizing the normalized volume function attached to any klt singularities.
Sym-NCO leverages symmetricities to improve DRL-NCO performance.
Machine learning reduces combinatorial optimization problem dimensions.
In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.
Survey explores interactions between convex and complex geometry.
We survey Mirzakhani's work relating to Riemann surfaces, which spans about 20 papers. We target the discussion at a broad audience of non-experts.
The recently presented idea to learn heuristics for combinatorial optimization problems is promising as it can save costly development. However, to push this idea towards practical implementation, we need better models and better ways of training. We contribute in both directions: we propose a model based on attention …
Hermitian symmetric manifolds are Hermitian manifolds which are homogeneous and such that every point has a symmetry preserving the Hermitian structure. The aim of these notes is to present an introduction to this important class of manifolds, trying to survey the several different perspectives from which Hermitian sym…
Geometric correspondence between spinors and horospheres in hyperbolic space.
Recent developments link Steklov eigenvalues to manifold geometry.
This short note is intended as a "Letter to the Editor" Perspective in order that it serves as a contribution, in view of reaching the physics community caring about rare events and scaling laws and unexpected findings, on a domain of wide interest: sport and money. It is apparent from the data reported and discussed b…
Perhaps surprisingly, it is possible to predict how long an algorithm will take to run on a previously unseen input, using machine learning techniques to build a model of the algorithm's runtime as a function of problem-specific instance features. Such models have important applications to algorithm analysis, portfolio…
We give a quick tour through many of the classical results in the field of minimal submanifolds, starting at the definition. The field of minimal submanifolds remains extremely active and has very recently seen major developments that have solved many longstanding open problems and conjectures; for more on this, see th…
Cell nuclei detection is a challenging research topic because of limitations in cellular image quality and diversity of nuclear morphology, i.e. varying nuclei shapes, sizes, and overlaps between multiple cell nuclei. This has been a topic of enduring interest with promising recent success shown by deep learning method…
New method converts LVAs into linear projections for better understanding of complex models.
Differentiable segmented models for non-stationary data.
We show that the objective function of conventional k-means clustering can be expressed as the Frobenius norm of the difference of a data matrix and a low rank approximation of that data matrix. In short, we show that k-means clustering is a matrix factorization problem. These notes are meant as a reference and intende…
Heegaard Floer theory is a kind of topological quantum field theory, assigning graded groups to closed, connected, oriented 3-manifolds and group homomorphisms to smooth, oriented 4-dimensional cobordisms. Bordered Heegaard Floer homology is an extension of Heegaard Floer homology to 3-manifolds with boundary, with ext…
New method finds optimal training stop point with noisy labeled data.
Equity-Transformer solves NP-hard min-max routing problems efficiently.
This paper is a comment on the survey paper by Biau and Scornet (2016) about random forests. We focus on the problem of quantifying the impact of each ingredient of random forests on their performance. We show that such a quantification is possible for a simple pure forest , leading to conclusions that could apply more…
We introduce the problem of hidden Hamiltonian cycle recovery, where there is an unknown Hamiltonian cycle in an -vertex complete graph that needs to be inferred from noisy edge measurements. The measurements are independent and distributed according to $\calP_n$ for edges in the cycle and $\calQ_n$ otherwise. This …
Explains how knots relate to 4D shapes.
First I will explain my motivation to introduce the -invariants for Riemannian manifolds. I will also recall the notions of ideal immersions and best ways of living. Then I will present a few of the many applications of -invariants to several areas in mathematics. Finally, I will present two optimal inequalities …
This note examines financial distributions to competing teams at the end of the most famous multiple stage professional (male) bicyclist race, TOUR DE FRANCE. A rank-size law (RSL) is calculated for the team financial gains. The RSL is found to be hyperbolic with a surprisingly simple decay exponent (about equal to -1)…
Article explores Thurston's circle packing theorem in 3-manifold geometry.
This is a guided tour through some selected topics in geometric analysis. We have chosen to illustrate many of the basic ideas as they apply to the theory of minimal surfaces. This is, in part, because minimal surfaces is, if not the oldest, then certainly one of the oldest areas of geometric analysis dating back to Eu…
This is a PhD thesis about low dimensional topology, in particular knot thory in 3-manifolds also different from the 3-sphere, topological applications of quantum invariants, and Turaev's shadows. There is an introduction and a survey for these topics. The thesis uses skein theory and focues on the connected sum of cop…
Paper organizes sampling methods for generative modeling.
Proves NP and co-NP status for knot core recognition in solid torus.
In this work, we provide theoretical guarantees for reward decomposition in deterministic MDPs. Reward decomposition is a special case of Hierarchical Reinforcement Learning, that allows one to learn many policies in parallel and combine them into a composite solution. Our approach builds on mapping this problem into a…
In this paper we describe progress made toward the construction of the Witten-Reshetikhin-Turaev theory of knot invariants from the geometric point of view. This is done in the perspective of a joint result of the author with A. Uribe which relates the quantum group and the Weyl quantizations of the moduli space of fla…
Deep learning has been extended to a number of new domains with critical success, though some traditional orienteering problems such as the Travelling Salesman Problem (TSP) and its variants are not commonly solved using such techniques. Deep neural networks (DNNs) are a potentially promising and under-explored solutio…