Machine Learning for First-Order Theorem Proving

Bridge, James P.; Holden, Sean B.; Paulson, Lawrence C.

doi:10.1007/s10817-014-9301-5

Cited by 66 publications

(53 citation statements)

References 25 publications

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“…There are also several examples of ML within the automated reasoning community (see e.g. [39], [32], [8]). A survey on ML for mathematical software was presented at ICMS 2018 [20].…”

Section: Related Work On ML For Mathematical Softwarementioning

confidence: 99%

Improved Cross-Validation for Classifiers that Make Algorithmic Choices to Minimise Runtime Without Compromising Output Correctness

Florescu

England

2020

Lecture Notes in Computer Science

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Our topic is the use of machine learning to improve software by making choices which do not compromise the correctness of the output, but do affect the time taken to produce such output. We are particularly concerned with computer algebra systems (CASs), and in particular, our experiments are for selecting the variable ordering to use when performing a cylindrical algebraic decomposition of n-dimensional real space with respect to the signs of a set of polynomials.In our prior work we explored the different ML models that could be used, and how to identify suitable features of the input polynomials. In the present paper we both repeat our prior experiments on problems which have more variables (and thus exponentially more possible orderings), and examine the metric which our ML classifiers targets. The natural metric is computational runtime, with classifiers trained to pick the ordering which minimises this. However, this leads to the situation were models do not distinguish between any of the non-optimal orderings, whose runtimes may still vary dramatically. In this paper we investigate a modification to the cross-validation algorithms of the classifiers so that they do distinguish these cases, leading to improved results.

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“…There are also several examples of ML within the automated reasoning community (see e.g. [39], [32], [8]). A survey on ML for mathematical software was presented at ICMS 2018 [20].…”

Section: Related Work On ML For Mathematical Softwarementioning

confidence: 99%

Improved Cross-Validation for Classifiers that Make Algorithmic Choices to Minimise Runtime Without Compromising Output Correctness

Florescu

England

2020

Lecture Notes in Computer Science

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“…Table 1 shows the features together with a short description of each. 3 MaLeS uses the same features for first-order problems.…”

Section: The E Featuresmentioning

confidence: 99%

“…Fuchs [5] employed a nearest neighbor algorithm to determine which strategy/ies to run. Bridge's [3] thesis is concerned with machine learning for search heuristic selection in ATPs with a particular focus on problem features and feature selection. In the SAT community, Satzilla [29] very successfully used machine learning to decide when to run which SAT solver.…”

Section: Introductionmentioning

confidence: 99%

MaLeS: A Framework for Automatic Tuning of Automated Theorem Provers

Kühlwein

Urban

2015

J Autom Reasoning

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MaLeS is an automatic tuning framework for automated theorem provers. It provides solutions for both the strategy finding as well as the strategy scheduling problem. This paper describes the tool and the methods used in it, and evaluates its performance on three automated theorem provers: E, LEO-II and Satallax. On a representative subset of the TPTP library a MaLeS-tuned prover solves on average 8.67 % more problems than the prover with its default settings.

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“…We used four different datasets: winequality [12], wilt [13], ml-prove [14], and magic [15]. All of them are classification datasets with real attributes.…”

Section: A Datasetsmentioning

confidence: 99%

“…The order of classes does not have any meaning in this case, thus we used the accuracy of the model instead of the κ statistic. Another reason to use the accuracy instead of κ is that the original paper about the ml-prove dataset [14] also uses accuracy and using the same metric allows us to compare the results more directly.…”

Section: B Evaluation Metricsmentioning

confidence: 99%

Evolving Workflow Graphs Using Typed Genetic Programming

Ken

Pilát

Neruda

2015

2015 IEEE Symposium Series on Computational Intelligence

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When applying machine learning techniques to more complicated datasets, it is often beneficial to use ensembles of simpler models instead of a single, more complicated, model. However, the creation of ensembles is a tedious task which requires a lot of human interaction and experimentation. In this paper, we present a technique for construction of ensembles based on typed genetic programming. The technique describes an ensemble as a directed acyclic graph, which is internally represented as a tree evolved by the genetic programming. The approach is evaluated in a series of experiments on various datasets and compared to the performance of simple models tuned by grid search, as well as to ensembles generated in a systematic manner.

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Machine Learning for First-Order Theorem Proving

Cited by 66 publications

References 25 publications

Improved Cross-Validation for Classifiers that Make Algorithmic Choices to Minimise Runtime Without Compromising Output Correctness

Improved Cross-Validation for Classifiers that Make Algorithmic Choices to Minimise Runtime Without Compromising Output Correctness

MaLeS: A Framework for Automatic Tuning of Automated Theorem Provers

Evolving Workflow Graphs Using Typed Genetic Programming

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