Filters








19 Hits in 1.9 sec

Deep Reinforcement Learning for Synthesizing Functions in Higher-Order Logic [article]

Thibault Gauthier
2020 arXiv   pre-print
The paper describes a deep reinforcement learning framework based on self-supervised learning within the proof assistant HOL4.  ...  A close interaction between the machine learning modules and the HOL4 library is achieved by the choice of tree neural networks (TNNs) as machine learning models and the internal use of HOL4 terms to represent  ...  Deep Reinforcement Learning When possible, the deep reinforcement learning approach [41] is preferable to a supervised learning approach for two main reasons. First, an oracle is not required.  ... 
arXiv:1910.11797v3 fatcat:bqtdfbrcxrcc5p6e3tzygogxsy

Learned Provability Likelihood for Tactical Search

Thibault Gauthier
2021 Electronic Proceedings in Theoretical Computer Science  
Experiments over the HOL4 library show an increase in the number of theorems re-proven by TacticToe thanks to this additional guidance.  ...  We adapt the tactical theorem prover TacticToe to factor in these estimations.  ...  In HOList, the prediction effort is concentrated on learning the policy for a few selected tactics and their arguments (theorems) using deep reinforcement learning.  ... 
doi:10.4204/eptcs.342.7 fatcat:xyp7yj4gond3vbw233kaordqoe

HOList: An Environment for Machine Learning of Higher-Order Theorem Proving [article]

Kshitij Bansal, Sarah M. Loos, Markus N. Rabe, Christian Szegedy, and Stewart Wilcox
2019 arXiv   pre-print
We also present a deep reinforcement learning driven automated theorem prover, DeepHOL, with strong initial results on this benchmark.  ...  We present an environment, benchmark, and deep learning driven automated theorem prover for higher-order logic.  ...  TacticToe does not employ deep learning nor reinforcement learning.  ... 
arXiv:1904.03241v3 fatcat:ih4fizuonrbvzk2oyu4pekhftu

Learning to Prove with Tactics [article]

Thibault Gauthier, Cezary Kaliszyk, Josef Urban, Ramana Kumar, Michael Norrish
2018 arXiv   pre-print
We implement a automated tactical prover TacticToe on top of the HOL4 interactive theorem prover. TacticToe learns from human proofs which mathematical technique is suitable in each proof situation.  ...  On a single CPU, with a time limit of 60 seconds, TacticToe proves 66.4 percent of the 7164 theorems in HOL4's standard library, whereas E prover with auto-schedule solves 34.5 percent.  ...  Reinforcement learning All our feature vectors have been learned form human proofs. We now can now also add goal-tactic pairs that appears in the last proof of TacticToe.  ... 
arXiv:1804.00596v1 fatcat:twmo2yoiwrfaxmj2onudf6sw7a

TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learning [article]

Minchao Wu, Michael Norrish, Christian Walder, Amir Dezfouli
2021 arXiv   pre-print
We propose a novel approach to interactive theorem-proving (ITP) using deep reinforcement learning.  ...  We implement the framework in the HOL4 theorem prover.  ...  TacticZero: Learning to Prove Theorems from Scratch with Deep Reinforcement Learning  ... 
arXiv:2102.09756v2 fatcat:hyz573txjjauje2ucfpm2ufw54

Tactic Learning and Proving for the Coq Proof Assistant [article]

Lasse Blaauwbroek, Josef Urban, Herman Geuvers
2020 arXiv   pre-print
In a similar vein as the TacticToe project for HOL4, our system predicts appropriate tactics and finds proofs in the form of tactic scripts.  ...  We present a system that utilizes machine learning for tactic proof search in the Coq Proof Assistant.  ...  In the leanCoP setting, (reinforcement) learning of clausal steps based on the proof state is done in systems such as rlCoP [24, 29] , and (FE)MaLeCoP [22, 38] .  ... 
arXiv:2003.09140v1 fatcat:vozpbh5w4fgrboqnrkju7odxza

Learning to Reason in Large Theories without Imitation [article]

Kshitij Bansal, Christian Szegedy, Markus N. Rabe, Sarah M. Loos, Viktor Toman
2020 arXiv   pre-print
We suggest an exploration mechanism that mixes in additional premises selected by a tf-idf (term frequency-inverse document frequency) based lookup in a deep reinforcement learning scenario.  ...  It approaches the performance of a prover trained by a combination of imitation and reinforcement learning.  ...  Reinforcement learning loop. In the absence of human proofs, we need a mechanism to incrementally improve a proof guidance model, which motivates the reinforcement learning setup we use.  ... 
arXiv:1905.10501v3 fatcat:ft65xynsgbfdxkzlcy4omg7ov4

Learning Equational Theorem Proving [article]

Jelle Piepenbrock, Tom Heskes, Mikoláš Janota, Josef Urban
2021 arXiv   pre-print
We develop Stratified Shortest Solution Imitation Learning (3SIL) to learn equational theorem proving in a deep reinforcement learning (RL) setting.  ...  In the cooperative mode, the final system is combined with the Prover9 system, proving in 2 seconds what standalone Prover9 proves in 60 seconds.  ...  For the Robinson arithmetic normalization task, we use a dataset that was constructed for reinforcement learning experiments in the interactive theorem prover HOL4 [15] .  ... 
arXiv:2102.05547v1 fatcat:gjt2mmtbxvezlehy4za5ll3rs4

Deep Reinforcement Learning for Synthesizing Functions in Higher-Order Logic

Thibault Gauthier
unpublished
The paper describes a deep reinforcement learning framework based on self-supervised learning within the proof assistant HOL4.  ...  A close interaction between the machine learning modules and the HOL4 library is achieved by the choice of tree neural networks (TNNs) as machine learning models and the internal use of HOL4 terms to represent  ...  Deep Reinforcement Learning When possible, the deep reinforcement learning approach [41] is preferable to a supervised learning approach for two main reasons. First, an oracle is not required.  ... 
doi:10.29007/7jmg fatcat:skbzeodwg5gefo4trnr2hiigja

Learning to Prove Theorems by Learning to Generate Theorems [article]

Mingzhe Wang, Jia Deng
2020 arXiv   pre-print
Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning.  ...  Experiments on real-world tasks demonstrate that synthetic data from our approach improves the theorem prover and advances the state of the art of automated theorem proving in Metamath.  ...  In the case of only human-written theorems but not their proofs, we can no longer perform imitation learning. We instead use reinforcement learning.  ... 
arXiv:2002.07019v2 fatcat:64o5kj6et5c3lpgmjfdbvyk5gu

INT: An Inequality Benchmark for Evaluating Generalization in Theorem Proving [article]

Yuhuai Wu, Albert Qiaochu Jiang, Jimmy Ba, Roger Grosse
2021 arXiv   pre-print
In learning-assisted theorem proving, one of the most critical challenges is to generalize to theorems unlike those seen at training time.  ...  In addition, unlike prior benchmarks for learning-assisted theorem proving, INT provides a lightweight and user-friendly theorem proving environment with fast simulations, conducive to performing learning-based  ...  Deep reinforcement learning in HOL4. CoRR, abs/1910.11797, 2019. URL http://arxiv.org/abs/1910.11797. Thibault Gauthier.  ... 
arXiv:2007.02924v2 fatcat:5dpl46b7jvhkroeteh3iij4igm

Mathematical Reasoning via Self-supervised Skip-tree Training [article]

Markus N. Rabe and Dennis Lee and Kshitij Bansal and Christian Szegedy
2020 arXiv   pre-print
We also analyze the models' ability to formulate new conjectures by measuring how often the predictions are provable and useful in other proofs.  ...  TacticToe: Learning to reason with HOL4 tactics.  ...  Prior work in deep learning for mathematics has focused on learning directly on logical reasoning tasks, such as predicting the proof steps or premises or assignments.  ... 
arXiv:2006.04757v3 fatcat:yrmqpmijjzh6rcnkm3b77k3mwy

Tactic Learning and Proving for the Coq Proof Assistant

Lasse Blaauwbroek, Josef Urban, Herman Geuvers
unpublished
In a similar vein as the TacticToe project for HOL4, our system predicts appropriate tactics and finds proofs in the form of tactic scripts.  ...  We present a system that utilizes machine learning for tactic proof search in the Coq Proof Assistant.  ...  In the leanCoP setting, (reinforcement) learning of clausal steps based on the proof state is done in systems such as rlCoP [24, 29] , and (FE)MaLeCoP [22, 38] .  ... 
doi:10.29007/wg1q fatcat:kihv522yfrf3fjug6gikdpujr4

Graph Representations for Higher-Order Logic and Theorem Proving [article]

Aditya Paliwal, Sarah Loos, Markus Rabe, Kshitij Bansal, Christian Szegedy
2019 arXiv   pre-print
Interactive, higher-order theorem provers allow for the formalization of most mathematical theories and have been shown to pose a significant challenge for deep learning.  ...  In this paper, we consider several graphical representations of higher-order logic and evaluate them against the HOList benchmark for higher-order theorem proving.  ...  This is a major improvement on the baseline models in the HOList paper (32.65%) and even outperforms the reported 38.9% of their best reinforcement learning experiment.  ... 
arXiv:1905.10006v2 fatcat:kokjdqbvpvgvbfl4blxmbrafpe

Graph Representations for Higher-Order Logic and Theorem Proving

Aditya Paliwal, Sarah Loos, Markus Rabe, Kshitij Bansal, Christian Szegedy
2020 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
Interactive, higher-order theorem provers allow for the formalization of most mathematical theories and have been shown to pose a significant challenge for deep learning.  ...  In this paper, we consider several graphical representations of higher-order logic and evaluate them against the HOList benchmark for higher-order theorem proving.  ...  This is a major improvement on the baseline models in the HOList paper (32.65%) and even outperforms the reported 38.9% of their best reinforcement learning experiment.  ... 
doi:10.1609/aaai.v34i03.5689 fatcat:7dwvu7ml4zgmdfzcjofyltc2ga
« Previous Showing results 1 — 15 out of 19 results