Related papers: Optimal spanning tree reconstruction in symbolic r…
Autoregressive language models demonstrate excellent performance in various scenarios. However, the inference efficiency is limited by its one-step-one-word generation mode, which has become a pressing problem recently as the models become…
Given an edge-weighted graph $G=(V,E)$ and a set $E_0\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\ldots,e'_T\in E\setminus E_0$ minimizing $\sum_{t=1}^Tw(X_t)$ where…
We consider the approximation of functions by 2-layer neural networks with a small number of hidden weights based on the squared loss and small datasets. Due to the highly non-convex energy landscape, gradient-based training often suffers…
We survey $k$-best enumeration problems and the algorithms for solving them, including in particular the problems of finding the $k$ shortest paths, $k$ smallest spanning trees, and $k$ best matchings in weighted graphs.
Given an undirected graph $G = (V, E)$ and a weight function $w:E \to \mathbb{R}$, the \textsc{Minimum Dominating Tree} problem asks to find a minimum weight sub-tree of $G$, $T = (U, F)$, such that every $v \in V \setminus U$ is adjacent…
Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem…
We derive tight bounds on the expected weights of several combinatorial optimization problems for random point sets of size $n$ distributed among the leaves of a balanced hierarchically separated tree. We consider {\it monochromatic} and…
A vertex of degree one in a tree is called an end vertex and a vertex of degree at least three is called a branch vertex. For a graph $G$, let $\sigma_2$ be the minimum degree sum of two nonadjacent vertices in $G$. We consider tree…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
Graph Neural Networks (GNNs) have achieved state-of-the-art performance in solving graph classification tasks. However, most GNN architectures aggregate information from all nodes and edges in a graph, regardless of their relevance to the…
We present a novel approach to graph drawing based on reinforcement learning for minimizing the global and the local crossing number, that is, the total number of edge crossings and the maximum number of crossings on any edge, respectively.…
Binary neural networks (BNNs) have been widely adopted to reduce the computational cost and memory storage on edge-computing devices by using one-bit representation for activations and weights. However, as neural networks become…
Generating graph structures is a challenging problem due to the diverse representations and complex dependencies among nodes. In this paper, we introduce Graph Variational Recurrent Neural Network (GraphVRNN), a probabilistic autoregressive…
We propose a novel method for automatic program synthesis. P-Tree Programming represents the program search space through a single probabilistic prototype tree. From this prototype tree we form program instances which we evaluate on a given…
The Prize-Collecting Steiner Tree (PCST) problem is a generalization of the Steiner Tree problem that has applications in network design, content distribution networks, and many more. There are a few centralized approximation algorithms…
Symbolic regression is a machine learning method with the goal to produce interpretable results. Unlike other machine learning methods such as, e.g. random forests or neural networks, which are opaque, symbolic regression aims to model and…
Embeddings of graphs into distributions of trees that preserve distances in expectation are a cornerstone of many optimization algorithms. Unfortunately, online or dynamic algorithms which use these embeddings seem inherently randomized and…
Complex networks theory has commonly been used for modelling and understanding the interactions taking place between the elements composing complex systems. More recently, the use of generative models has gained momentum, as they allow…
The Symbolic Regression (SR) problem, where the goal is to find a regression function that does not have a pre-specified form but is any function that can be composed of a list of operators, is a hard problem in machine learning, both…
[RETRACTED]Data increasingly abounds, but distilling their underlying relationships down to something interpretable remains challenging. One approach is genetic programming, which `symbolically regresses' a data set down into an equation.…