scholarly journals An Exhaustive DPLL Algorithm for Model Counting

2018 ◽  
Vol 62 ◽  
pp. 1-32 ◽  
Author(s):  
Umut Oztok ◽  
Adnan Darwiche
Keyword(s):  
Probabilistic Reasoning ◽  
Modular Design ◽  
State Of The Art ◽  
Formal Semantics ◽  
Decision Diagrams ◽  
Sat Solving ◽  
Construction Time ◽  
The Core ◽  
Model Counting ◽  
Proof Of Correctness

State-of-the-art model counters are based on exhaustive DPLL algorithms, and have been successfully used in probabilistic reasoning, one of the key problems in AI. In this article, we present a new exhaustive DPLL algorithm with a formal semantics, a proof of correctness, and a modular design. The modular design is based on the separation of the core model counting algorithm from SAT solving techniques. We also show that the trace of our algorithm belongs to the language of Sentential Decision Diagrams (SDDs), which is a subset of Decision-DNNFs, the trace of existing state-of-the-art model counters. Still, our experimental analysis shows comparable results against state-of-the-art model counters. Furthermore, we obtain the first top-down SDD compiler, and show orders-of-magnitude improvements in SDD construction time against the existing bottom-up SDD compiler.

scholarly journals GANAK: A Scalable Probabilistic Exact Model Counter

2019 ◽  
Author(s):  
Shubham Sharma ◽  
Subhajit Roy ◽  
Mate Soos ◽  
Kuldeep S. Meel
Keyword(s):  
Probabilistic Reasoning ◽  
State Of The Art ◽  
Fundamental Problem ◽  
Approximate Model ◽  
Boolean Formula ◽  
Sat Solvers ◽  
Exact Model ◽  
Universal Hashing ◽  
Model Counting ◽  
Dynamic Decomposition

Given a Boolean formula F, the problem of model counting, also referred to as #SAT, seeks to compute the number of solutions of F. Model counting is a fundamental problem with a wide variety of applications ranging from planning, quantified information flow to probabilistic reasoning and the like. The modern #SAT solvers tend to be either based on static decomposition, dynamic decomposition, or a hybrid of the two. Despite dynamic decomposition based #SAT solvers sharing much of their architecture with SAT solvers, the core design and heuristics of dynamic decomposition-based #SAT solvers has remained constant for over a decade. In this paper, we revisit the architecture of the state-of-the-art dynamic decomposition-based #SAT tool, sharpSAT, and demonstrate that by introducing a new notion of probabilistic component caching and the usage of universal hashing for exact model counting along with the development of several new heuristics can lead to significant performance improvement over state-of-the-art model-counters. In particular, we develop GANAK, a new scalable probabilistic exact model counter that outperforms state-of-the-art exact and approximate model counters sharpSAT and ApproxMC3 respectively, both in terms of PAR-2 score and the number of instances solved. Furthermore, in our experiments, the model count returned by GANAK was equal to the exact model count for all the benchmarks. Finally, we observe that recently proposed preprocessing techniques for model counting benefit exact model counters while hurting the performance of approximate model counters.

scholarly journals ADDMC: Weighted Model Counting with Algebraic Decision Diagrams

2020 ◽  
Vol 34 (02) ◽  
pp. 1468-1476
Author(s):  
Jeffrey Dudek ◽  
Vu Phan ◽  
Moshe Vardi
Keyword(s):  
Dynamic Programming ◽  
Data Structure ◽  
Normal Form ◽  
Standard Model ◽  
State Of The Art ◽  
Conjunctive Normal Form ◽  
Decision Diagrams ◽  
Boolean Formulas ◽  
Model Counting ◽  
Weighted Model

We present an algorithm to compute exact literal-weighted model counts of Boolean formulas in Conjunctive Normal Form. Our algorithm employs dynamic programming and uses Algebraic Decision Diagrams as the main data structure. We implement this technique in ADDMC, a new model counter. We empirically evaluate various heuristics that can be used with ADDMC. We then compare ADDMC to four state-of-the-art weighted model counters (Cachet, c2d, d4, and miniC2D) on 1914 standard model counting benchmarks and show that ADDMC significantly improves the virtual best solver.

scholarly journals BIRD: Engineering an Efficient CNF-XOR SAT Solver and Its Applications to Approximate Model Counting

2019 ◽  
Vol 33 ◽  
pp. 1592-1599 ◽  
Author(s):  
Mate Soos ◽  
Kuldeep S. Meel
Keyword(s):  
Probabilistic Reasoning ◽  
State Of The Art ◽  
Fundamental Problem ◽  
Approximate Model ◽  
Affirmative Answer ◽  
The State ◽  
Boolean Formula ◽  
Wide Range ◽  
Model Counting ◽  
Sat Solver

Given a Boolean formula φ, the problem of model counting, also referred to as #SAT is to compute the number of solutions of φ. Model counting is a fundamental problem in artificial intelligence with a wide range of applications including probabilistic reasoning, decision making under uncertainty, quantified information flow, and the like. Motivated by the success of SAT solvers, there has been surge of interest in the design of hashing-based techniques for approximate model counting for the past decade. We profiled the state of the art approximate model counter ApproxMC2 and observed that over 99.99% of time is consumed by the underlying SAT solver, CryptoMiniSat. This observation motivated us to ask: Can we design an efficient underlying CNF-XOR SAT solver that can take advantage of the structure of hashing-based algorithms and would this lead to an efficient approximate model counter? The primary contribution of this paper is an affirmative answer to the above question. We present a novel architecture, called BIRD, to handle CNF-XOR formulas arising from hashingbased techniques. The resulting hashing-based approximate model counter, called ApproxMC3, employs the BIRD framework in its underlying SAT solver, CryptoMiniSat. To the best of our knowledge, we conducted the most comprehensive study of evaluation performance of counting algorithms involving 1896 benchmarks with computational effort totaling 86400 computational hours. Our experimental evaluation demonstrates significant runtime performance improvement for ApproxMC3 over ApproxMC2. In particular, we solve 648 benchmarks more than ApproxMC2, the state of the art approximate model counter and for all the formulas where both ApproxMC2 and ApproxMC3 did not timeout and took more than 1 seconds, the mean speedup is 284.40 – more than two orders of magnitude.

scholarly journals Representing Deep Neural Networks Latent Space Geometries with Graphs

Algorithms ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 39
Author(s):  
Carlos Lassance ◽  
Vincent Gripon ◽  
Antonio Ortega
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Deep Learning ◽  
Objective Function ◽  
Learning Process ◽  
Deep Neural Networks ◽  
State Of The Art ◽  
The Core ◽  
Learning Tasks ◽  
Latent Space

Deep Learning (DL) has attracted a lot of attention for its ability to reach state-of-the-art performance in many machine learning tasks. The core principle of DL methods consists of training composite architectures in an end-to-end fashion, where inputs are associated with outputs trained to optimize an objective function. Because of their compositional nature, DL architectures naturally exhibit several intermediate representations of the inputs, which belong to so-called latent spaces. When treated individually, these intermediate representations are most of the time unconstrained during the learning process, as it is unclear which properties should be favored. However, when processing a batch of inputs concurrently, the corresponding set of intermediate representations exhibit relations (what we call a geometry) on which desired properties can be sought. In this work, we show that it is possible to introduce constraints on these latent geometries to address various problems. In more detail, we propose to represent geometries by constructing similarity graphs from the intermediate representations obtained when processing a batch of inputs. By constraining these Latent Geometry Graphs (LGGs), we address the three following problems: (i) reproducing the behavior of a teacher architecture is achieved by mimicking its geometry, (ii) designing efficient embeddings for classification is achieved by targeting specific geometries, and (iii) robustness to deviations on inputs is achieved via enforcing smooth variation of geometry between consecutive latent spaces. Using standard vision benchmarks, we demonstrate the ability of the proposed geometry-based methods in solving the considered problems.

scholarly journals Solving Delete Free Planning with Relaxed Decision Diagram Based Heuristics

2020 ◽  
Vol 67 ◽  
pp. 607-651
Author(s):  
Margarita Paz Castro ◽  
Chiara Piacentini ◽  
Andre Augusto Cire ◽  
J. Christopher Beck
Keyword(s):  
Linear Programming ◽  
Empirical Analysis ◽  
State Of The Art ◽  
The State ◽  
Decision Diagrams ◽  
Binary Decision ◽  
Admissible Heuristics ◽  
The Cost ◽  
Construction Algorithms ◽  
Diagram Representation

We investigate the use of relaxed decision diagrams (DDs) for computing admissible heuristics for the cost-optimal delete-free planning (DFP) problem. Our main contributions are the introduction of two novel DD encodings for a DFP task: a multivalued decision diagram that includes the sequencing aspect of the problem and a binary decision diagram representation of its sequential relaxation. We present construction algorithms for each DD that leverage these different perspectives of the DFP task and provide theoretical and empirical analyses of the associated heuristics. We further show that relaxed DDs can be used beyond heuristic computation to extract delete-free plans, find action landmarks, and identify redundant actions. Our empirical analysis shows that while DD-based heuristics trail the state of the art, even small relaxed DDs are competitive with the linear programming heuristic for the DFP task, thus, revealing novel ways of designing admissible heuristics.

scholarly journals Optimization Learning: Perspective, Method, and Applications

2020 ◽  
Author(s):  
Risheng Liu
Keyword(s):  
Inverse Problems ◽  
Theoretical Analysis ◽  
Iterative Methods ◽  
State Of The Art ◽  
Learning Paradigm ◽  
Rigorous Analysis ◽  
The Core ◽  
Globally Convergent ◽  
Ill Posed ◽  
Art Performance

Numerous tasks at the core of statistics, learning, and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems. Nevertheless, integrating learnable structures into iterations is still a laborious process, which can only be guided by intuitions or empirical insights. Moreover, there is a lack of rigorous analysis of the convergence behaviors of these reimplemented iterations, and thus the significance of such methods is a little bit vague. We move beyond these limits and propose a theoretically guaranteed optimization learning paradigm, a generic and provable paradigm for nonconvex inverse problems, and develop a series of convergent deep models. Our theoretical analysis reveals that the proposed optimization learning paradigm allows us to generate globally convergent trajectories for learning-based iterative methods. Thanks to the superiority of our framework, we achieve state-of-the-art performance on different real applications.

scholarly journals Asymmetric Distribution Measure for Few-shot Learning

2020 ◽  
Author(s):  
Wenbin Li ◽  
Lei Wang ◽  
Jing Huo ◽  
Yinghuan Shi ◽  
Yang Gao ◽  
...  
Keyword(s):  
State Of The Art ◽  
Asymmetric Distribution ◽  
Query Image ◽  
Local Descriptor ◽  
Innovative Design ◽  
Feature Representations ◽  
The Core ◽  
Measure Function ◽  
Asymmetric Relation ◽  
Core Idea

The core idea of metric-based few-shot image classification is to directly measure the relations between query images and support classes to learn transferable feature embeddings. Previous work mainly focuses on image-level feature representations, which actually cannot effectively estimate a class's distribution due to the scarcity of samples. Some recent work shows that local descriptor based representations can achieve richer representations than image-level based representations. However, such works are still based on a less effective instance-level metric, especially a symmetric metric, to measure the relation between a query image and a support class. Given the natural asymmetric relation between a query image and a support class, we argue that an asymmetric measure is more suitable for metric-based few-shot learning. To that end, we propose a novel Asymmetric Distribution Measure (ADM) network for few-shot learning by calculating a joint local and global asymmetric measure between two multivariate local distributions of a query and a class. Moreover, a task-aware Contrastive Measure Strategy (CMS) is proposed to further enhance the measure function. On popular miniImageNet and tieredImageNet, ADM can achieve the state-of-the-art results, validating our innovative design of asymmetric distribution measures for few-shot learning. The source code can be downloaded from https://github.com/WenbinLee/ADM.git.

scholarly journals Al Thumama Stadium: Local and Global Architectural Reach

2019 ◽  
Author(s):  
Hani Awni Hawamdeh
Keyword(s):  
State Of The Art ◽  
Vital Role ◽  
Local Identity ◽  
World Cup ◽  
The Core ◽  
Long Run ◽  
The World ◽  
Unique Experience ◽  
Core Mission

The world cup stadia have been a constant concern for the hosting countries. Many of them have become a burden on the economies of their countries, only to become white elephants after the tournaments end. Therefore, the core mission of the Supreme Committee for Delivery & Legacy in Qatar was to ensure that the World Cup Stadiums are built with a legacy and to remain functional in the long run, not just as facilities, but as cultural icons. Such efforts have promoted the exercise of stadia building in Qatar as a positive and unique experience. As a firm, we, at Arab Engineering Bureau, are honored to be part of the effort all through the making of Al Thumama Stadium, which will be discussed in this paper. Instead of a white elephant, Al Thumama Stadium is arguably a symbol of the local identity that will become part of the World Cup legacy, whilst being a state-of-the-art facility that plays a vital role in development of its surrounding neighborhood.

scholarly journals Dolius: A Distributed Parallel SAT Solving Framework

10.29007/hvqt ◽  
2018 ◽  
Author(s):  
Gilles Audemard ◽  
Benoît Hoessen ◽  
Saïd Jabbour ◽  
Cédric Piette
Keyword(s):  
Shared Memory ◽  
State Of The Art ◽  
Divide And Conquer ◽  
Sat Solving ◽  
Sat Solvers ◽  
Sat Solver

Over the years, parallel SAT solving becomes more and more important. However, most of state-of-the-art parallel SAT solvers are portfolio-based ones. They aim at running several times the same solver with different parameters. In this paper, we propose a tool called Dolius, mainly based on the divide and conquer paradigm. In contrast to most current parallel efficient engines, Dolius does not need shared memory, can be distributed, and scales well when a large number of computing units is available. Furthermore, our tool contains an API allowing to plug any SAT solver in a simple way.

scholarly journals Trust in multi-agent systems

2004 ◽  
Vol 19 (1) ◽  
pp. 1-25 ◽  
Author(s):  
SARVAPALI D. RAMCHURN ◽  
DONG HUYNH ◽  
NICHOLAS R. JENNINGS
Keyword(s):  
Large Scale ◽  
State Of The Art ◽  
Comprehensive Treatment ◽  
Multi Agent Systems ◽  
Agent Based ◽  
Agent Systems ◽  
The Core ◽  
Open Distributed Systems ◽  
Multi Agent

Trust is a fundamental concern in large-scale open distributed systems. It lies at the core of all interactions between the entities that have to operate in such uncertain and constantly changing environments. Given this complexity, these components, and the ensuing system, are increasingly being conceptualised, designed, and built using agent-based techniques and, to this end, this paper examines the specific role of trust in multi-agent systems. In particular, we survey the state of the art and provide an account of the main directions along which research efforts are being focused. In so doing, we critically evaluate the relative strengths and weaknesses of the main models that have been proposed and show how, fundamentally, they all seek to minimise the uncertainty in interactions. Finally, we outline the areas that require further research in order to develop a comprehensive treatment of trust in complex computational settings.

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