ENIGMAWatch: ProofWatch Meets ENIGMA

Goertzel, Zarathustra; Jakubův, Jan; Urban, Josef

doi:10.1007/978-3-030-29026-9_21

Cited by 9 publications

(6 citation statements)

References 28 publications

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“…In the former the matching (actually, clause classification) is approximate, weighted and learned, while with hints the clause matching/classification is crisp, logic-rooted and preprogrammed, sometimes running into the NP hardness issues. Our latest comparison [12] done over the Mizar/MPTP corpus in the symbol-based setting showed better performance of ENIGMA over using hints, most likely due to better generalization behavior of ENIGMA based on the statistical (GBDT) learning.…”

Section: B Discussion Of Anonymizationmentioning

confidence: 92%

ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (System Description)

Jakubův

Chvalovský

Olšák

et al. 2020

Lecture Notes in Computer Science

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We describe an implementation of gradient boosting and neural guidance of saturation-style automated theorem provers that does not depend on consistent symbol names across problems. For the gradient-boosting guidance, we manually create abstracted features by considering arity-based encodings of formulas. For the neural guidance, we use symbol-independent graph neural networks (GNNs) and their embedding of the terms and clauses. The two methods are efficiently implemented in the E prover and its ENIGMA learning-guided framework.To provide competitive real-time performance of the GNNs, we have developed a new context-based approach to evaluation of generated clauses in E. Clauses are evaluated jointly in larger batches and with respect to a large number of already selected clauses (context) by the GNN that estimates their collectively most useful subset in several rounds of message passing. This means that approximative inference rounds done by the GNN are efficiently interleaved with precise symbolic inference rounds done inside E. The methods are evaluated on the MPTP large-theory benchmark and shown to achieve comparable realtime performance to state-of-the-art symbol-based methods. The methods also show high complementarity, solving a large number of hard Mizar problems.

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Section: B Discussion Of Anonymizationmentioning

confidence: 92%

ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (System Description)

Jakubův

Chvalovský

Olšák

et al. 2020

Lecture Notes in Computer Science

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“…The selection of the "right" given clause is known to be vital for the success of the proof search. The ENIGMA system [3,7,[10][11][12]14] applies various machine learning methods for given clause selection, learning from a large number of previous successful proof searches. The training data consists of clauses processed during a proof search, labeling the clauses that appear in the discovered proof as positive, and the other (thus unnecessary) processed clauses as negative.…”

Section: Contributionsmentioning

confidence: 99%

“…The first ENIGMA [11] used fast linear classification [4] with hand-crafted clause features based on symbol names, representing clauses by fixed-length numeric vectors. Follow-up versions [3,7,12,14] introduced context-based clause evaluation and fast dimensionality reduction by feature hashing, and employed Gradient Boosting Decision Trees (GBDTs), implemented by the XGBoost and LightGBM systems [2,18]), and Recursive Neural Networks (implemented in PyTorch) as the underlying machine learning methods.…”

Section: Contributionsmentioning

confidence: 99%

Fast and Slow Enigmas and Parental Guidance

Goertzel¹,

Chvalovský²,

Jakubův³

et al. 2021

Preprint

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We describe several additions to the ENIGMA system that guides clause selection in the E automated theorem prover. First, we significantly speed up its neural guidance by adding server-based GPU evaluation. The second addition is motivated by fast weight-based rejection filters that are currently used in systems like E and Prover9. Such systems can be made more intelligent by instead training fast versions of ENIGMA that implement more intelligent pre-filtering. This results in combinations of trainable fast and slow thinking that improves over both the fast-only and slow-only methods. The third addition is based on "judging the children by their parents", i.e., possibly rejecting an inference before it produces a clause. This is motivated by standard evolutionary mechanisms, where there is always a cost to producing all possible offsprings in the current population. This saves time by not evaluating all clauses by more expensive methods and provides a complementary view of the generated clauses. The methods are evaluated on a large benchmark coming from the Mizar Mathematical Library, showing good improvements over the state of the art.

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“…Several learning-guided ATP systems have been developed that interleave proving with supervised learning from proof searches [4,[10][11][12][13]17,19,23,39]. In the saturation-style setting used by ATP systems like E [31] and Vampire [21], direct learning-based selection of the most promising given clauses leads already to large improvements [14], without other changes to the proof search procedure.…”

Section: Introductionmentioning

confidence: 99%

Prolog Technology Reinforcement Learning Prover

Zombori

Urban

Brown

2020

Automated Reasoning

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We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP builds on the leanCoP Prolog implementation and adds learning-guided Monte-Carlo Tree Search as done in the rlCoP system. Other components include a Python interface to plCoP and machine learners, and an external proof checker that verifies the validity of plCoP proofs. The toolkit is evaluated on two benchmarks and we demonstrate its extendability by two additions: (1) guidance is extended to reduction steps and (2) the standard leanCoP calculus is extended with rewrite steps and their learned guidance. We argue that the Prolog setting is suitable for combining statistical and symbolic learning methods. The complete toolkit is publicly released.

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ENIGMAWatch: ProofWatch Meets ENIGMA

Cited by 9 publications

References 28 publications

ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (System Description)

ENIGMA Anonymous: Symbol-Independent Inference Guiding Machine (System Description)

Fast and Slow Enigmas and Parental Guidance

Prolog Technology Reinforcement Learning Prover

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