{"id":"https://openalex.org/W7162512523","doi":"https://doi.org/10.48550/arxiv.2605.27078","title":"Two Speeds of Learning: A Representation-Readout Decomposition of Grokking and Double Descent","display_name":"Two Speeds of Learning: A Representation-Readout Decomposition of Grokking and Double Descent","publication_year":2026,"publication_date":"2026-05-26","ids":{"openalex":"https://openalex.org/W7162512523","doi":"https://doi.org/10.48550/arxiv.2605.27078"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.27078","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.27078","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.2605.27078","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026150664","display_name":"Chi-Ning Chou","orcid":"https://orcid.org/0000-0001-9089-2003"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chou, Chi-Ning","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137178555","display_name":"Oscar Uzdelewicz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Uzdelewicz, Oscar","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137189701","display_name":"Neng-Chun Chiu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chiu, Neng-Chun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033186377","display_name":"Yao-Yuan Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Yao-Yuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5016533438","display_name":"SueYeon Chung","orcid":"https://orcid.org/0000-0001-5726-4865"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chung, SueYeon","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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.6942999958992004,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.6942999958992004,"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/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.14339999854564667,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.04809999838471413,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.8163999915122986},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6869000196456909},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.6266000270843506},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.6036999821662903},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5264000296592712},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.49300000071525574},{"id":"https://openalex.org/keywords/mnist-database","display_name":"MNIST database","score":0.4894999861717224},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4239000082015991}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.8163999915122986},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6869000196456909},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.6266000270843506},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.6036999821662903},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5314000248908997},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5264000296592712},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.49300000071525574},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.4894999861717224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45879998803138733},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4528999924659729},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4239000082015991},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C165838908","wikidata":"https://www.wikidata.org/wiki/Q736777","display_name":"Calibration","level":2,"score":0.38190001249313354},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.328000009059906},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3156000077724457},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.30820000171661377},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.2912999987602234},{"id":"https://openalex.org/C206688291","wikidata":"https://www.wikidata.org/wiki/Q7617819","display_name":"Stochastic gradient descent","level":3,"score":0.27459999918937683},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2694000005722046},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.25290000438690186},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.250900000333786}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.27078","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.27078","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.2605.27078","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.27078","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Training":[0],"loss":[1,26,44,49],"and":[2,53,60,67,74,96,111,149,161,192,210,233],"accuracy":[3],"are":[4,57,119],"the":[5,94,100,124,138,154,171,222],"standard":[6],"signals":[7],"used":[8],"to":[9,132,141,170,205],"monitor":[10],"generalization":[11,135,202],"during":[12],"deep":[13],"neural":[14,108],"network":[15],"training.":[16],"Two":[17],"well-documented":[18],"phenomena":[19,70],"complicate":[20],"this":[21,80],"picture:":[22],"in":[23,39,93,99,185],"grokking,":[24],"train":[25,43],"falls":[27],"rapidly":[28],"while":[29,47],"test":[30,48],"performance":[31],"improves":[32],"abruptly":[33],"only":[34],"after":[35],"a":[36,61,144,186,226],"long":[37],"delay;":[38],"epoch-wise":[40,194],"double":[41,195],"descent,":[42],"decreases":[45],"monotonically":[46],"or":[50,200],"error":[51],"rises":[52],"falls.":[54],"Existing":[55],"accounts":[56],"often":[58],"task-specific,":[59],"task-agnostic":[62],"analysis":[63],"framework":[64,175,228],"for":[65,229,237],"diagnosing":[66],"explaining":[68],"these":[69,219],"across":[71,143],"realistic":[72],"tasks":[73,148],"architectures":[75],"is":[76,156,164,203],"missing.":[77],"We":[78],"address":[79],"challenge":[81],"by":[82,214],"analyzing":[83],"two":[84],"competing":[85],"processes":[86,118],"that":[87,116,153],"underlie":[88],"learning":[89,92,163,231],"dynamics:":[90],"representation":[91,162,208],"encoder":[95],"readout":[97,155,211],"calibration":[98],"final":[101],"classifier.":[102],"Using":[103],"tools":[104],"from":[105,182,207],"representational":[106],"geometry,":[107],"tangent":[109],"kernels,":[110],"linear":[112],"probing,":[113],"we":[114,151],"show":[115],"both":[117],"active":[120],"throughout":[121],"training,":[122],"with":[123],"fluctuations":[125],"of":[126,147],"their":[127],"relative":[128],"speed":[129],"giving":[130],"rise":[131],"seemingly":[133],"anomalous":[134],"dynamics.":[136],"Applying":[137],"representation-readout":[139,223],"decomposition":[140,224],"grokking":[142,159,190],"wide":[145],"range":[146],"architectures,":[150],"find":[152],"train-biased":[157],"before":[158],"onset,":[160],"gradual":[165],"but":[166],"not":[167],"absent,":[168],"contrary":[169],"lazy-to-rich":[172],"account.":[173],"The":[174],"further":[176],"provides":[177],"diagnostic":[178],"signatures":[179],"distinguishing":[180],"spurious":[181],"genuine":[183],"generalization:":[184],"previously":[187],"reported":[188],"MNIST":[189],"example":[191],"an":[193],"descent":[196],"example,":[197],"apparent":[198],"delayed":[199],"non-monotone":[201],"shown":[204],"arise":[206],"degradation":[209],"misalignment":[212],"induced":[213],"non-standard":[215],"training":[216],"recipes.":[217],"Together,":[218],"results":[220],"establish":[221],"as":[225],"top-down":[227],"understanding":[230],"dynamics":[232],"revealing":[234],"underlying":[235],"algorithms":[236],"interpretability":[238],"research.":[239]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-28T00:00:00"}
