{"id":"https://openalex.org/W7166081733","doi":"https://doi.org/10.48550/arxiv.2606.26454","title":"Data-driven Machine Learning Cannot Reach Symbolic-level Logical Reasoning -- The Limit of the Scaling Law","display_name":"Data-driven Machine Learning Cannot Reach Symbolic-level Logical Reasoning -- The Limit of the Scaling Law","publication_year":2026,"publication_date":"2026-06-24","ids":{"openalex":"https://openalex.org/W7166081733","doi":"https://doi.org/10.48550/arxiv.2606.26454"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.26454","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.26454","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2606.26454","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139434951","display_name":"Tiansi Dong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dong, Tiansi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036018012","display_name":"Mateja Jamnik","orcid":"https://orcid.org/0000-0003-2772-2532"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jamnik, Mateja","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139423701","display_name":"Pietro Li\u00f2","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li\u00f2, Pietro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.37459999322891235,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11948","display_name":"Machine Learning in Materials Science","score":0.37459999322891235,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.09920000284910202,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11273","display_name":"Advanced Graph Neural Networks","score":0.0908999964594841,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/syllogism","display_name":"Syllogism","score":0.8550999760627747},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4993000030517578},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.48829999566078186},{"id":"https://openalex.org/keywords/logical-reasoning","display_name":"Logical reasoning","score":0.48080000281333923},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.3952000141143799},{"id":"https://openalex.org/keywords/conjunction","display_name":"Conjunction (astronomy)","score":0.34610000252723694},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.3188000023365021}],"concepts":[{"id":"https://openalex.org/C131598440","wikidata":"https://www.wikidata.org/wiki/Q107342","display_name":"Syllogism","level":2,"score":0.8550999760627747},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6927000284194946},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5842999815940857},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4993000030517578},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.490200012922287},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.48829999566078186},{"id":"https://openalex.org/C43971567","wikidata":"https://www.wikidata.org/wiki/Q3142865","display_name":"Logical reasoning","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.3952000141143799},{"id":"https://openalex.org/C59656382","wikidata":"https://www.wikidata.org/wiki/Q191536","display_name":"Conjunction (astronomy)","level":2,"score":0.34610000252723694},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.3188000023365021},{"id":"https://openalex.org/C97364631","wikidata":"https://www.wikidata.org/wiki/Q484284","display_name":"Deductive reasoning","level":2,"score":0.3102000057697296},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3068000078201294},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.30169999599456787},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C134752490","wikidata":"https://www.wikidata.org/wiki/Q374182","display_name":"Logical consequence","level":2,"score":0.28139999508857727},{"id":"https://openalex.org/C21847791","wikidata":"https://www.wikidata.org/wiki/Q191081","display_name":"Logical conjunction","level":2,"score":0.2728999853134155},{"id":"https://openalex.org/C71008984","wikidata":"https://www.wikidata.org/wiki/Q2890076","display_name":"Rigour","level":2,"score":0.2574000060558319}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.26454","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.26454","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2606.26454","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.26454","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"score":0.5621213912963867,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"By":[0],"promoting":[1],"vectors":[2],"to":[3,107,118,128],"spheres":[4],"and":[5,50,70,160,169],"enabling":[6],"explicit":[7],"model":[8],"construction,":[9],"neural":[10,58],"networks":[11],"can":[12],"perform":[13],"symbolic-level":[14,152],"syllogistic":[15,86,155],"reasoning":[16,156,159],"without":[17],"training":[18,36,123,170],"data.":[19],"We":[20],"identify":[21],"two":[22,62],"fundamental":[23],"limitations":[24],"that":[25,166],"prevent":[26],"conventional":[27,64],"data-driven":[28],"machine":[29],"learning":[30,93],"systems":[31],"from":[32],"achieving":[33],"this":[34,77],"capability:":[35],"data":[37,113,168],"generated":[38],"by":[39],"the":[40,92,100,122],"combination":[41],"table":[42],"cannot":[43,102,141,173],"distinguish":[44],"all":[45],"24":[46],"valid":[47],"syllogism":[48,135],"types,":[49],"end-to-end":[51],"premise-to-conclusion":[52],"mapping":[53],"creates":[54],"contradictory":[55],"targets":[56],"within":[57],"components.":[59],"Experiments":[60],"with":[61,89,130],"representative":[63],"systems,":[65],"GPT-5":[66,80],"using":[67,73],"linguistic":[68],"inputs":[69,140],"Euler":[71,115],"Net":[72],"visual":[74],"inputs,":[75],"support":[76],"analysis.":[78],"ChatGPT":[79],"may":[81],"reach":[82],"100%":[83,98,146],"accuracy":[84,106,117,127,148],"in":[85],"reasoning,":[87],"but":[88],"hallucinations.":[90],"Because":[91],"process":[94],"terminates":[95],"upon":[96],"reaching":[97],"accuracy,":[99],"system":[101],"progress":[103],"beyond":[104],"empirical":[105],"symbolic":[108,175],"level":[109,176],"reasoning.":[110,153,178],"Random":[111],"test":[112,147],"reduced":[114],"Net's":[116],"56%.":[119],"Repeatedly":[120],"expanding":[121],"set":[124],"increased":[125],"its":[126],"97%,":[129],"perfect":[131],"performance":[132],"on":[133],"8":[134],"types.":[136],"However,":[137],"because":[138],"unintended":[139],"be":[142],"exhaustively":[143],"covered,":[144],"even":[145],"does":[149],"not":[150],"imply":[151],"Since":[154],"underpins":[157],"logical":[158,177],"human":[161],"rationality,":[162],"these":[163],"results":[164],"suggest":[165],"increasing":[167],"time":[171],"alone":[172],"ensure":[174]},"counts_by_year":[],"updated_date":"2026-07-22T05:54:00.624950","created_date":"2026-06-27T00:00:00"}
