The Role of Entropy in Guiding a Connection Prover
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21730%2F21%3A00354436" target="_blank" >RIV/68407700:21730/21:00354436 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-030-86059-2_13" target="_blank" >https://doi.org/10.1007/978-3-030-86059-2_13</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-86059-2_13" target="_blank" >10.1007/978-3-030-86059-2_13</a>
Alternative languages
Result language
angličtina
Original language name
The Role of Entropy in Guiding a Connection Prover
Original language description
In this work we study how to learn good algorithms for selecting reasoning steps in theorem proving. We explore this in the connection tableau calculus implemented by leanCoP where the partial tableau provides a clean and compact notion of a state to which a limited number of inferences can be applied. We start by incorporating a state-of-the-art learning algorithm — a graph neural network (GNN) – into the plCoP theorem prover. Then we use it to observe the system’s behavior in a reinforcement learning setting, i.e., when learning inference guidance from successful Monte-Carlo tree searches on many problems. Despite its better pattern matching capability, the GNN initially performs worse than a simpler previously used learning algorithm. We observe that the simpler algorithm is less confident, i.e., its recommendations have higher entropy. This leads us to explore how the entropy of the inference selection implemented via the neural network influences the proof search. This is related to research in human decision-making under uncertainty, and in particular the probability matching theory. Our main result shows that a proper entropy regularization, i.e., training the GNN not to be overconfident, greatly improves plCoP ’s performance on a large mathematical corpus.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
<a href="/en/project/EF15_003%2F0000466" target="_blank" >EF15_003/0000466: Artificial Intelligence and Reasoning</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Automated Reasoning with Analytic Tableaux and Related Methods
ISBN
978-3-030-86058-5
ISSN
0302-9743
e-ISSN
1611-3349
Number of pages
18
Pages from-to
218-235
Publisher name
Springer
Place of publication
Cham
Event location
Birmingham
Event date
Sep 6, 2021
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000711656700013