{"id":"https://openalex.org/W7165484079","doi":"https://doi.org/10.5281/zenodo.20779602","title":"Read Routing Entropy at a Fixed Position: A Cross-Model Study of the Prefix Effect in Mixture-of-Experts Routing","display_name":"Read Routing Entropy at a Fixed Position: A Cross-Model Study of the Prefix Effect in Mixture-of-Experts Routing","publication_year":2026,"publication_date":"2026-06-21","ids":{"openalex":"https://openalex.org/W7165484079","doi":"https://doi.org/10.5281/zenodo.20779602"},"language":"en","primary_location":{"id":"doi:10.5281/zenodo.20779602","doi":"https://doi.org/10.5281/zenodo.20779602","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20779602","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},"volume":null,"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.5281/zenodo.20779602","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138747520","display_name":"Jeffrey W. Shorthill","orcid":"https://orcid.org/0009-0004-3954-2752","observed_orcids":["https://orcid.org/0009-0004-3954-2752"]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shorthill, Jeffrey W.","raw_affiliation_strings":["Independent researcher"],"raw_orcid":"https://orcid.org/0009-0004-3954-2752","affiliations":[{"raw_affiliation_string":"Independent researcher","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5138747520"],"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/T10028","display_name":"Topic Modeling","score":0.6762999892234802,"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"}},"topics":[{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.6762999892234802,"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"}},{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.061799999326467514,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.05590000003576279,"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/mixture-of-experts","display_name":"mixture of experts","score":0.9399999976158142},{"id":"https://openalex.org/keywords/prompt-length","display_name":"prompt length","score":0.652999997138977},{"id":"https://openalex.org/keywords/expert-specialization","display_name":"expert specialization","score":0.5419999957084656},{"id":"https://openalex.org/keywords/deepseek","display_name":"DeepSeek","score":0.6169999837875366},{"id":"https://openalex.org/keywords/qwen3-5","display_name":"Qwen3.5","score":0.9150000214576721},{"id":"https://openalex.org/keywords/large-language-models","display_name":"large language models","score":0.45100000500679016},{"id":"https://openalex.org/keywords/bootstrap-confidence-intervals","display_name":"bootstrap confidence intervals","score":0.37299999594688416},{"id":"https://openalex.org/keywords/model-intercomparison","display_name":"model intercomparison","score":0.5040000081062317}],"concepts":[{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5453000068664551},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5041000247001648},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.4381999969482422},{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.4075999855995178},{"id":"https://openalex.org/C74172769","wikidata":"https://www.wikidata.org/wiki/Q1446839","display_name":"Routing (electronic design automation)","level":2,"score":0.40560001134872437},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.361299991607666},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3517000079154968},{"id":"https://openalex.org/C195780805","wikidata":"https://www.wikidata.org/wiki/Q1535986","display_name":"Metrics","level":5,"score":0.3172999918460846},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31139999628067017},{"id":"https://openalex.org/C28490314","wikidata":"https://www.wikidata.org/wiki/Q189436","display_name":"Speech recognition","level":1,"score":0.2782999873161316},{"id":"https://openalex.org/C204948658","wikidata":"https://www.wikidata.org/wiki/Q1119410","display_name":"Static routing","level":4,"score":0.2718999981880188},{"id":"https://openalex.org/C7573999","wikidata":"https://www.wikidata.org/wiki/Q207580","display_name":"Routing Information Protocol","level":5,"score":0.26080000400543213},{"id":"https://openalex.org/C101721835","wikidata":"https://www.wikidata.org/wiki/Q813908","display_name":"Conditional entropy","level":3,"score":0.2572999894618988},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.25290000438690186}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.5281/zenodo.20779602","doi":"https://doi.org/10.5281/zenodo.20779602","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20779602","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.20779603","doi":"https://doi.org/10.5281/zenodo.20779603","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20779603","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.22089025","doi":"https://doi.org/10.5281/zenodo.22089025","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22089025","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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"},{"id":"doi:10.5281/zenodo.22151499","doi":"https://doi.org/10.5281/zenodo.22151499","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.22151499","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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:10.5281/zenodo.20779602","doi":"https://doi.org/10.5281/zenodo.20779602","is_oa":true,"landing_page_url":"https://doi.org/10.5281/zenodo.20779602","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"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":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Routing":[0,256],"entropy":[1,21,64,116,235],"is":[2,110,117,131,143,236,259,270,291],"increasingly":[3],"used":[4],"as":[5,195,272,301,322],"a":[6,111,154,171,196,212,231,237,260,273,279],"signal":[7],"for":[8,42,91,98],"adaptive":[9],"compute,":[10],"safety":[11],"telemetry,":[12],"and":[13,72,75,97,123,130,177,210,276,304,332,338],"expert":[14],"specialization.":[15],"Across":[16],"recent":[17],"uses":[18],"of":[19,50,128,223],"routing":[20,25,63,115,201,234],"that":[22,182,229],"we":[23],"surveyed,":[24],"statistics":[26],"are":[27,226,299],"typically":[28],"pooled":[29],"across":[30],"token":[31,43,193],"positions":[32,129],"or":[33,45,214],"reduced":[34],"to":[35,54,145,160,315],"sequence-level":[36],"measures":[37],"without":[38],"an":[39,218,250],"explicit":[40],"control":[41],"position":[44,87,194,206],"prompt":[46,161,173],"length.":[47],"The":[48,104],"magnitude":[49],"the":[51,83,108,120,125,141,146,164,167,178,186,204,208,264,267,288,296,310,318,329],"positional":[52,105],"contribution":[53],"these":[55],"measurements":[56],"therefore":[57,152],"remains":[58],"unknown.":[59],"We":[60,190],"measured":[61],"per-token":[62],"in":[65,107,158,199,233,239,254],"four":[66],"mixture-of-experts":[67],"runs,":[68],"Qwen3.5-35B-A3B,":[69],"Qwen3.5-397B-A17B,":[70],"DeepSeek-V3-0324":[71,326],"DeepSeek":[73,323],"R1":[74],"compared":[76],"position-averaged":[77],"readouts":[78,81],"against":[79],"fixed-position":[80,179,213],"on":[82,94,102,163,263,278],"same":[84,165,265],"prompts.":[85],"Full":[86],"curves":[88],"were":[89],"retained":[90],"five":[92],"prompts":[93,222],"one":[95],"model":[96],"301":[99,286],"raw-text":[100,281],"windows":[101],"another.":[103],"term":[106],"router":[109],"prefix":[112,157,274],"effect.":[113],"Per-token":[114],"depressed":[118],"over":[119,217],"chat":[121],"template":[122,140],"roughly":[124],"opening":[126],"tens":[127],"flat":[132],"after":[133],"that.":[134],"On":[135],"raw":[136],"text":[137],"with":[138,293],"no":[139],"depression":[142],"confined":[144],"first":[147],"token.":[148],"An":[149],"all-token":[150,168,219],"average":[151,169,220],"dilutes":[153],"fixed":[155],"low-entropy":[156],"proportion":[159],"length;":[162],"captures,":[166],"orders":[170],"graded":[172],"suite":[174],"by":[175],"length,":[176],"readout":[180,205,216],"removes":[181],"order":[183],"and,":[184],"at":[185],"extremes,":[187],"reverses":[188],"it.":[189],"recommend":[191],"treating":[192],"default":[197],"covariate":[198],"any":[200],"statistic,":[202],"reporting":[203],"alongside":[207],"value,":[209],"preferring":[211],"position-matched":[215],"when":[221],"different":[224],"lengths":[225],"compared.":[227],"Under":[228],"control,":[230],"difference":[232,238],"routing.":[240],"Version":[241],"2.0":[242],"(2026-08-28)":[243],"supersedes":[244],"version":[245,316],"1.1":[246],"(\"Sequence":[247],"Position":[248],"Explains":[249],"Apparent":[251],"Complexity":[252],"Gradient":[253],"Mixture-of-Experts":[255],"Entropy\").":[257],"It":[258],"new":[261],"paper":[262],"runs:":[266],"opening-depression":[268],"finding":[269],"stated":[271],"effect":[275],"tested":[277],"full-precision":[280],"run":[282],"(Run":[283],"4,":[284],"Qwen3.5-35B-A3B-Base,":[285],"windows);":[287],"two-readout":[289],"disagreement":[290],"reported":[292,306,320],"bootstrap":[294],"intervals;":[295],"chat-template":[297],"markers":[298],"documented":[300],"literal":[302],"text;":[303],"every":[305],"value":[307],"regenerates":[308],"from":[309],"public":[311],"data":[312],"bundle.":[313],"Correction":[314],"1.1:":[317],"checkpoint":[319],"there":[321],"V3.1":[324],"was":[325],"(Unsloth":[327],"UD-Q2_K_XL);":[328],"capture":[330],"command":[331],"archive":[333],"record":[334],"load":[335],"DeepSeek-V3-0324.":[336],"Data":[337],"code:":[339],"https://huggingface.co/datasets/ec75hash/routing-entropy-token-position":[340]},"counts_by_year":[],"updated_date":"2026-10-08T09:06:37.294493","created_date":"2026-06-22T00:00:00"}
