搜索结果：Finds

We study the problem of selecting a statement that finds common ground across diverse population preferences. Generative AI is uniquely suited for this task because it can access a practically infinite set of statements, but AI systems like the Habermas machine leave the choice of generated statement to a voting rule. What it means for this rule to find common ground, however, is not well-defined. In this work, we propose a formal model for finding common ground in the infinite alternative setting based on the proportional veto core from social choice. To provide guarantees relative to these infinitely many alternatives and a large population, we wish to satisfy a notion of proportional veto core using only query access to the unknown distribution of alternatives and voters. We design an efficient sampling-based algorithm that returns an alternative in the (approximate) proportional veto core with high probability and prove matching lower bounds, which show that no algorithm can do the same using fewer queries. On a synthetic dataset of preferences over text, we confirm the effectiveness of our sampling-based algorithm and compare other social choice methods as well as LLM-based me

In this paper, we propose an approach to finding sets of similar-performing models (in terms of loss/accuracy measurements) with highly different context-aware characteristics. Through experiments on the METABRIC dataset, we show that the proposed method finds multiple models with highly different gene expressions than those found by the control methodology without performance penalties. We argue that the proposed methodology is important whenever one aims to analyze any global characteristic of a model to extract insight into the underlying phenomenon being studied.

We are interested in proving satisfiability of Constrained Horn Clauses (CHCs) over Algebraic Data Types (ADTs). We propose to prove satisfiability by building a tree automaton recognizing the Herbrand model of the CHCs. If such an automaton exists then the model is said to be regular, i.e., the Herbrand model is a regular set of atoms. Kostyukov et al. have shown how to derive an automaton when CVC4 finds a finite model of the CHCs. We propose an alternative way to build the automaton using an encoding into a SAT problem using Clingo, an Answer Set Programming (ASP) tool. We implemented a translation of CHCs with ADTs into an ASP problem. Combined with Clingo, we obtain a semi-complete satisfiability checker: it finds a tree automaton if a regular Herbrand model exists or finds a counter-example if the problem is unsatisfiable.

We study the problem of finding stationary points of non-convex functions when access to the objective is provided only through a comparison oracle that, given two points, outputs which has the larger function value. For a twice differentiable $f\colon\mathbb R^n\to\mathbb R$ with Lipschitz gradient and Hessian, we develop an algorithm that visits an $ε$-stationary point using $\widetilde O(n^2/ε^{1.5})$ queries. Our approach uses a subroutine that estimates the normalized Hessian to accuracy $δ$ using $\widetilde O(n^2\log(1/δ))$ queries. We further study this problem with a quantum comparison oracle model where queries can be made in superpositions, and develop the first quantum algorithm that finds an $ε$-stationary point, which takes $\widetilde O(n/ε^{1.5})$ queries.

In this paper, we plan missions for a fleet of agents in undirected graphs, such as grids, with multiple goals. In contrast to regular multi-agent path-finding, the solver finds and updates the assignment of goals to the agents on its own. In the continuous case for a point agent with motions in the Euclidean plane, the problem can be solved arbitrarily close to optimal. For discrete variants that incur node and edge conflicts, we show that it can be solved in polynomial time, which is unexpected, since traditional vehicle routing on general graphs is NP-hard. We implement a corresponding planner that finds conflict-free optimized routes for the agents. Global assignment strategies greatly reduce the number of conflicts, with the remaining ones resolved by elaborating on the concept of ants-on-the-stick, by solving local assignment problems, by interleaving agent paths, and by kicking agents that have already arrived out of their destinations

We provide a deterministic polynomial-time algorithm that, for a given $k$-uniform hypergraph $H$ with $n$ vertices and edge density $d$, finds a complete $k$-partite subgraph of $H$ with parts of size at least ${c(d, k)(\log n)^{1/(k-1)}}$. This generalizes work by Mubayi and Turán on bipartite graphs. The value we obtain for the part size matches the order of magnitude guaranteed by the non-constructive proof due to Erdős and is tight up to a constant factor.

An n-element set contains an unknown number of excellent elements, and our goal is to identify at least one of these elements. The members of a family of subsets can be asked if they contain at least one excellent element or not. At most one of the answers can be wrong. We find the smallest family that finds one excellent element or claims that there is none.

A fundamental question in parallel computation, posed by Karp, Upfal, and Wigderson (FOCS 1985, JCSS 1988), asks: \emph{given only independence-oracle access to a matroid on $n$ elements, how many rounds are required to find a basis using only polynomially many queries?} This question generalizes, among others, the complexity of finding bases of linear spaces, partition matroids, and spanning forests in graphs. In their work, they established an upper bound of $O(\sqrt{n})$ rounds and a lower bound of $\widetildeΩ(n^{1/3})$ rounds for this problem, and these bounds have remained unimproved since then. In this work, we make the first progress in narrowing this gap by designing a parallel algorithm that finds a basis of an arbitrary matroid in $\tilde{O}(n^{7/15})$ rounds (using polynomially many independence queries per round) with high probability, surpassing the long-standing $O(\sqrt{n})$ barrier. Our approach introduces a novel matroid decomposition technique and other structural insights that not only yield this general result but also lead to a much improved new algorithm for the class of \emph{partition matroids} (which underlies the $\widetildeΩ(n^{1/3})$ lower bound of Karp

We present a new algorithm for identifying superbubbles in HI column density maps of both observed and simulated galaxies that has only a single adjustable parameter. The algorithm includes an automated galaxy-background separation step to focus the analysis on the galactic disk. To test the algorithm, we compare the superbubbles it finds in a simulated galactic disk with the ones it finds in 21cm observations of a similar galactic disk. The sizes and radial distribution of those superbubbles are indeed qualitatively similar. However, superbubbles in the simulated galactic disk have lower central HI column densities. The HI superbubbles in the simulated disk are spatially associated with pockets of hot gas. We conclude that the algorithm is a promising method for systematically identifying and characterizing superbubbles using only HI column density maps that will enable standardized tests of stellar feedback models used in galaxy simulations.

In an $n \times n$ array filled with symbols, a transversal is a collection of entries with distinct rows, columns and symbols. In this note we show that if no symbol appears more than $βn$ times, the array contains a transversal of size $(1-β/4-o(1))n$. In particular, if the array is filled with $n$ symbols, each appearing $n$ times (an equi-$n$ square), we get transversals of size $(3/4-o(1))n$. Moreover, our proof gives a deterministic algorithm with polynomial running time, that finds these transversals.

In many fields of experimental science, papers that failed to replicate continue to be cited as a result of the poor discoverability of replication studies. As a first step to creating a system that automatically finds replication studies for a given paper, 334 replication studies and 344 replicated studies were collected. Replication studies could be identified in the dataset based on text content at a higher rate than chance (AUROC = 0.886). Additionally, successful replication studies could be distinguished from failed replication studies at a higher rate than chance (AUROC = 0.664).

This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm is based on the SWAP test on trial states generated by a parametrized quantum circuit. The eigenvector is described by a compact set of classical parameters that can be used to reproduce the found approximation to the eigenstate on demand. This variational eigenvector finder can be adapted to solve the generalized eigenvalue problem, to find the eigenvectors of normal matrices and to perform quantum principal component analysis (QPCA) on unknown input mixed states. These algorithms can all be run with low depth quantum circuits, suitable for an efficient implementation on noisy intermediate state quantum computers (NISQC) and, with some restrictions, on linear optical systems. Limitations and potential applications are discussed.

Derandomization is the process of taking a randomized algorithm and turning it into a deterministic algorithm, which has attracted great attention in classical computing. In quantum computing, it is challenging and intriguing to derandomize quantum algorithms, due to the inherent randomness of quantum mechanics. The significance of derandomizing quantum algorithms lies not only in theoretically proving that the success probability can essentially be 1 without sacrificing quantum speedups, but also in experimentally improving the success rate when the algorithm is implemented on a real quantum computer. In this paper, we focus on derandomizing quanmtum algorithms for the triangle sum problem (including the famous triangle finding problem as a special case), which asks to find a triangle in an edge-weighted graph with $n$ vertices, such that its edges sum up to a given weight.We show that when the graph is promised to contain at most one target triangle, there exists a deterministic quantum algorithm that either finds the triangle if it exists or outputs ``no triangle'' if none exists. It makes $O(n^{9/7})$ queries to the edge weight matrix oracle, and thus has the same complexity wi

We present a very simple and intuitive algorithm to find balanced sparse cuts in a graph via shortest-paths. Our algorithm combines a new multiplicative-weights framework for solving unit-weight multi-commodity flows with standard ball growing arguments. Using Dijkstra's algorithm for computing the shortest paths afresh every time gives a very simple algorithm that runs in time $\widetilde{O}(m^2/φ)$ and finds an $\widetilde{O}(φ)$-sparse balanced cut, when the given graph has a $φ$-sparse balanced cut. Combining our algorithm with known deterministic data-structures for answering approximate All Pairs Shortest Paths (APSP) queries under increasing edge weights (decremental setting), we obtain a simple deterministic algorithm that finds $m^{o(1)}φ$-sparse balanced cuts in $m^{1+o(1)}/φ$ time. Our deterministic almost-linear time algorithm matches the state-of-the-art in randomized and deterministic settings up to subpolynomial factors, while being significantly simpler to understand and analyze, especially compared to the only almost-linear time deterministic algorithm, a recent breakthrough by Chuzhoy-Gao-Li-Nanongkai-Peng-Saranurak (FOCS 2020).

The false discovery rate (FDR) measures the share of false positives in a set of statistical tests. I develop simple and intuitive bounds on the FDR in cross-sectional predictability publications. The simplest bound requires just a few lines of math and finds $\text{FDR} \le 25\%$ based on summary statistics in eight out of nine previous studies. A more refined bound finds $\text{FDR} \le 9\%$. The FDR is small because randomly selecting accounting ratios produces statistically significant predictability far more often than would occur if there were no predictability. The bounds also reconcile the disparate FDR estimates in the literature.

Large neural networks can be pruned to a small fraction of their original size, with little loss in accuracy, by following a time-consuming "train, prune, re-train" approach. Frankle & Carbin conjecture that we can avoid this by training "lottery tickets", i.e., special sparse subnetworks found at initialization, that can be trained to high accuracy. However, a subsequent line of work by Frankle et al. and Su et al. presents concrete evidence that current algorithms for finding trainable networks at initialization, fail simple baseline comparisons, e.g., against training random sparse subnetworks. Finding lottery tickets that train to better accuracy compared to simple baselines remains an open problem. In this work, we resolve this open problem by proposing Gem-Miner which finds lottery tickets at initialization that beat current baselines. Gem-Miner finds lottery tickets trainable to accuracy competitive or better than Iterative Magnitude Pruning (IMP), and does so up to $19\times$ faster.