4,402 research outputs found
The Potential of Restarts for ProbSAT
This work analyses the potential of restarts for probSAT, a quite successful
algorithm for k-SAT, by estimating its runtime distributions on random 3-SAT
instances that are close to the phase transition. We estimate an optimal
restart time from empirical data, reaching a potential speedup factor of 1.39.
Calculating restart times from fitted probability distributions reduces this
factor to a maximum of 1.30. A spin-off result is that the Weibull distribution
approximates the runtime distribution for over 93% of the used instances well.
A machine learning pipeline is presented to compute a restart time for a
fixed-cutoff strategy to exploit this potential. The main components of the
pipeline are a random forest for determining the distribution type and a neural
network for the distribution's parameters. ProbSAT performs statistically
significantly better than Luby's restart strategy and the policy without
restarts when using the presented approach. The structure is particularly
advantageous on hard problems.Comment: Eurocast 201
Genetic Algorithm for Restricted Maximum k-Satisfiability in the Hopfield Network
The restricted Maximum k-Satisfiability MAX- kSAT is an enhanced Boolean satisfiability counterpart that has attracted numerous amount of research. Genetic algorithm has been the prominent optimization heuristic algorithm to solve constraint optimization problem. The core motivation of this paper is to introduce Hopfield network incorporated with genetic algorithm in solving MAX-kSAT problem. Genetic algorithm will be integrated with Hopfield network as a single network. The proposed method will be compared with the conventional Hopfield network. The results demonstrate that Hopfield network with genetic algorithm outperforms conventional Hopfield networks. Furthermore, the outcome had provided a solid evidence of the robustness of our proposed algorithms to be used in other satisfiability problem
Compositional Vector Space Models for Knowledge Base Completion
Knowledge base (KB) completion adds new facts to a KB by making inferences
from existing facts, for example by inferring with high likelihood
nationality(X,Y) from bornIn(X,Y). Most previous methods infer simple one-hop
relational synonyms like this, or use as evidence a multi-hop relational path
treated as an atomic feature, like bornIn(X,Z) -> containedIn(Z,Y). This paper
presents an approach that reasons about conjunctions of multi-hop relations
non-atomically, composing the implications of a path using a recursive neural
network (RNN) that takes as inputs vector embeddings of the binary relation in
the path. Not only does this allow us to generalize to paths unseen at training
time, but also, with a single high-capacity RNN, to predict new relation types
not seen when the compositional model was trained (zero-shot learning). We
assemble a new dataset of over 52M relational triples, and show that our method
improves over a traditional classifier by 11%, and a method leveraging
pre-trained embeddings by 7%.Comment: The 53rd Annual Meeting of the Association for Computational
Linguistics and The 7th International Joint Conference of the Asian
Federation of Natural Language Processing, 201
Maximum 2-satisfiability in radial basis function neural network
Maximum k-Satisfiability (MAX-kSAT) is the logic to determine the maximum number of satisfied clauses. Correctly, this logic plays a prominent role in numerous applications as a combinatorial optimization logic. MAX2SAT is a case of MAX-kSAT and is written in Conjunctive Normal Form (CNF) with two variables in each clause. This paper presents a new paradigm in using MAX2SAT by implementing in Radial Basis Function Neural Network (RBFNN). Hence, we restrict the analysis to MAX2SAT clauses. We utilize Dev C++ as the platform of training and testing our proposed algorithm. In this study, the effectiveness of RBFNN-MAX2SAT can be estimated by evaluating the proposed models with testing data sets. The results obtained are analysed using the ratio of satisfied clause (RSC), the root means square error (RMSE), and CPU time. The simulated results suggest that the proposed algorithm is effective in doing MAX2SAT logic programming by analysing the performance by obtaining lower Root Mean Square Error, high ratio of satisfied clauses and lesser CPU time
Maximum Weight Matching via Max-Product Belief Propagation
Max-product "belief propagation" is an iterative, local, message-passing
algorithm for finding the maximum a posteriori (MAP) assignment of a discrete
probability distribution specified by a graphical model. Despite the
spectacular success of the algorithm in many application areas such as
iterative decoding, computer vision and combinatorial optimization which
involve graphs with many cycles, theoretical results about both correctness and
convergence of the algorithm are known in few cases (Weiss-Freeman Wainwright,
Yeddidia-Weiss-Freeman, Richardson-Urbanke}.
In this paper we consider the problem of finding the Maximum Weight Matching
(MWM) in a weighted complete bipartite graph. We define a probability
distribution on the bipartite graph whose MAP assignment corresponds to the
MWM. We use the max-product algorithm for finding the MAP of this distribution
or equivalently, the MWM on the bipartite graph. Even though the underlying
bipartite graph has many short cycles, we find that surprisingly, the
max-product algorithm always converges to the correct MAP assignment as long as
the MAP assignment is unique. We provide a bound on the number of iterations
required by the algorithm and evaluate the computational cost of the algorithm.
We find that for a graph of size , the computational cost of the algorithm
scales as , which is the same as the computational cost of the best
known algorithm. Finally, we establish the precise relation between the
max-product algorithm and the celebrated {\em auction} algorithm proposed by
Bertsekas. This suggests possible connections between dual algorithm and
max-product algorithm for discrete optimization problems.Comment: In the proceedings of the 2005 IEEE International Symposium on
Information Theor
Extracting Rules from Neural Networks with Partial Interpretations
We investigate the problem of extracting rules, expressed in Horn logic, from
neural network models. Our work is based on the exact learning model, in which
a learner interacts with a teacher (the neural network model) via queries in
order to learn an abstract target concept, which in our case is a set of Horn
rules. We consider partial interpretations to formulate the queries. These can
be understood as a representation of the world where part of the knowledge
regarding the truthiness of propositions is unknown. We employ Angluin s
algorithm for learning Horn rules via queries and evaluate our strategy
empirically
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