FEMaLeCoP: Fairly Efficient Machine Learning Connection Prover

Kaliszyk, Cezary; Urban, Josef

doi:10.1007/978-3-662-48899-7_7

Cited by 44 publications

(45 citation statements)

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“…They are precalculated to allow fast classification. Furthermore, new training examples can be added to existing classification data efficiently, similarly to [KU15].…”

Section: Generalised Classifiersmentioning

confidence: 99%

“…The hints technique [Ver96] was among the earliest attempts to directly influence proof search by learning from previous proofs. Other systems are E/TSM [Sch00], an extension of E [Sch13] with term space maps, and MaLeCoP [UVŠ11] respectively FEMaLeCoP [KU15], which are versions of leanCoP [Ott08] extended by Naive Bayesian learning. -Learning of strategies: Finding good settings for ATPs automatically has been researched for example in the Blind Strategymaker (BliStr) project [Urb15].…”

Section: Introductionmentioning

confidence: 99%

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Internal Guidance for Satallax

Färber

Brown

2016

Automated Reasoning

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We propose a new internal guidance method for automated theorem provers based on the given-clause algorithm. Our method influences the choice of unprocessed clauses using positive and negative examples from previous proofs. To this end, we present an efficient scheme for Naive Bayesian classification by generalising label occurrences to types with monoid structure. This makes it possible to extend existing fast classifiers, which consider only positive examples, with negative ones. We implement the method in the higher-order logic prover Satallax, where we modify the delay with which propositions are processed. We evaluated our method on a simply-typed higher-order logic version of the Flyspeck project, where it solves 26% more problems than Satallax without internal guidance.

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“…They are precalculated to allow fast classification. Furthermore, new training examples can be added to existing classification data efficiently, similarly to [KU15].…”

Section: Generalised Classifiersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Internal Guidance for Satallax

Färber

Brown

2016

Automated Reasoning

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“…the next tableau extension step [40,20] and first experiments with Monte-Carlo guided proof search [8] and reinforcement learning [21] have been done.…”

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confidence: 99%

ENIGMA-NG: Efficient Neural and Gradient-Boosted Inference Guidance for E

Chvalovský

Jakubův

Suda

et al. 2019

Lecture Notes in Computer Science

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We describe an efficient implementation of clause guidance in saturation-based automated theorem provers extending the ENIGMA approach. Unlike in the first ENIGMA implementation where fast linear classifier is trained and used together with manually engineered features, we have started to experiment with more sophisticated state-of-the-art machine learning methods such as gradient boosted trees and recursive neural networks. In particular the latter approach poses challenges in terms of efficiency of clause evaluation, however, we show that deep integration of the neural evaluation with the ATP data-structures can largely amortize this cost and lead to competitive real-time results. Both methods are evaluated on a large dataset of theorem proving problems and compared with the previous approaches. The resulting methods improve on the manually designed clause guidance, providing the first practically convincing application of gradient-boosted and neural clause guidance in saturation-style automated theorem provers. IntroductionAutomated theorem provers (ATPs) [32] have been developed for decades by manually designing proof calculi and search heuristics. Their power has been growing and they are already very useful, e.g., as parts of large interactive theorem proving (ITP) verification toolchains (hammers) [5]. On the other hand, with small exceptions, ATPs are still significantly weaker than trained mathematicians in finding proofs in most research domains.Recently, machine learning over large formal corpora created from ITP libraries [37,28,19] has started to be used to develop guidance of ATP systems [39,25,2]. This has already produced strong systems for selecting relevant facts for proving new conjectures over large formal libraries [1,4,9]. More recently, machine learning has also started to be used to guide the internal search of the ATP systems. In sophisticated saturation-style provers this has been done by feedback loops for strategy invention [38,16,33] and by using supervised learning [14,26] to select the next given clause [27]. In the simpler connection tableau systems such as leancop [29], supervised learning has been used to choose ⋆ Supported by the ERC Consolidator grant no. 649043 AI4REASON, and by the Czech project AI&Reasoning CZ.02.1.01/0.0/0.0/15 003/0000466 and the European Regional Development Fund.

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“…Learning from many proofs has also recently become a very useful method for automated finding of parameters of ATP strategies [22,9,19,16], and for learning of sequences of tactics in interactive theorem provers (ITPs) [7]. Several experiments with the compact leanCoP [18] system have recently shown that directly using trained machine learner for internal clause selection can significantly prune the search space and solve additional problems [24,11,5]. An obvious next step is to implement efficient learning-based clause selection also inside the strongest superposition-based ATPs.In this work, we introduce ENIGMA -Efficient learNing-based Internal Guidance MAchine for state-of-the-art saturation-based ATPs.…”

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confidence: 99%

ENIGMA: Efficient Learning-Based Inference Guiding Machine

Jakubův

Urban

2017

Lecture Notes in Computer Science

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ENIGMA is a learning-based method for guiding given clause selection in saturationbased theorem provers. Clauses from many proof searches are classified as positive and negative based on their participation in the proofs. An efficient classification model is trained on this data, using fast feature-based characterization of the clauses . The learned model is then tightly linked with the core prover and used as a basis of a new parameterized evaluation heuristic that provides fast ranking of all generated clauses. The approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing a large increase of E's performance. Introduction: Theorem Proving and LearningState-of-the-art resolution/superposition automated theorem provers (ATPs) such as Vampire [15] and E [20] are today's most advanced tools for general reasoning across a variety of mathematical and scientific domains. The stronger the performance of such tools, the more realistic become tasks such as full computer understanding and automated development of complicated mathematical theories, and verification of software, hardware and engineering designs. While performance of ATPs has steadily grown over the past years due to a number of human-designed improvements, it is still on average far behind the performance of trained mathematicians. Their advanced knowledge-based proof finding is an enigma, which is unlikely to be deciphered and programmed completely manually in near future.On large corpora such as Flyspeck, Mizar and Isabelle, the ATP progress has been mainly due to learning how to select the most relevant knowledge, based on many previous proofs [10,12,1,2]. Learning from many proofs has also recently become a very useful method for automated finding of parameters of ATP strategies [22,9,19,16], and for learning of sequences of tactics in interactive theorem provers (ITPs) [7]. Several experiments with the compact leanCoP [18] system have recently shown that directly using trained machine learner for internal clause selection can significantly prune the search space and solve additional problems [24,11,5]. An obvious next step is to implement efficient learning-based clause selection also inside the strongest superposition-based ATPs.In this work, we introduce ENIGMA -Efficient learNing-based Internal Guidance MAchine for state-of-the-art saturation-based ATPs. The method applies fast machine learning algorithms to a large number of proofs, and uses the trained classifier together with simpler heuristics to evaluate the millions of clauses generated during the resolution/superposition proof search. This way, the theorem prover automatically takes into account thousands of previous successes and failures that it has seen in previous problems, similarly to trained humans. Thanks to a carefully chosen efficient learning/evaluation method and its tight integration with the core ATP (in our case the E prover), the penalty for this ubiquitous knowledge-based internal proof guidance is very low. This in turn very significantly improves the per...

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FEMaLeCoP: Fairly Efficient Machine Learning Connection Prover

Cited by 44 publications

References 13 publications

Internal Guidance for Satallax

Internal Guidance for Satallax

ENIGMA-NG: Efficient Neural and Gradient-Boosted Inference Guidance for E

ENIGMA: Efficient Learning-Based Inference Guiding Machine

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