{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/premise-selection-with-neural-networks-and","title":"Premise selection with neural networks and distributed representation of features","arxiv_id":"1807.10268","date":"2018-07-26","proceeding":null,"authors":["Andrzej Stanisław Kucik","Konstantin Korovin"],"abstract":"We present the problem of selecting relevant premises for a proof of a given\nstatement. When stated as a binary classification task for pairs (conjecture,\naxiom), it can be efficiently solved using artificial neural networks. The key\ndifference between our advance to solve this problem and previous approaches is\nthe use of just functional signatures of premises. To further improve the\nperformance of the model, we use dimensionality reduction technique, to replace\nlong and sparse signature vectors with their compact and dense embedded\nversions. These are obtained by firstly defining the concept of a context for\neach functor symbol, and then training a simple neural network to predict the\ndistribution of other functor symbols in the context of this functor. After\ntraining the network, the output of its hidden layer is used to construct a\nlower dimensional embedding of a functional signature (for each premise) with a\ndistributed representation of features. This allows us to use 512-dimensional\nembeddings for conjecture-axiom pairs, containing enough information about the\noriginal statements to reach the accuracy of 76.45% in premise selection task,\nonly with simple two-layer densely connected neural networks.","url_abs":"http://arxiv.org/abs/1807.10268v1","url_pdf":"http://arxiv.org/pdf/1807.10268v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"premise-selection-with-neural-networks-and","repo_url":"https://gitlab.com/korovin/iprover","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"binary-classification","task_name":"Binary Classification"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.10268","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}