{"id":"https://openalex.org/W7165370013","doi":"https://doi.org/10.48550/arxiv.2606.20381","title":"Rethinking Shrinkage Bias in LLM FP4 Pretraining: Geometric Origin, Systemic Impact, and UFP4 Recipe","display_name":"Rethinking Shrinkage Bias in LLM FP4 Pretraining: Geometric Origin, Systemic Impact, and UFP4 Recipe","publication_year":2026,"publication_date":"2026-06-18","ids":{"openalex":"https://openalex.org/W7165370013","doi":"https://doi.org/10.48550/arxiv.2606.20381"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.20381","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.20381","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2606.20381","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139025316","display_name":"Qian Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Qian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055381638","display_name":"Kunlong Chen","orcid":"https://orcid.org/0000-0002-8828-9595"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Kunlong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139025842","display_name":"Changxin Tian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tian, Changxin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103275577","display_name":"Zhonghui Jiang","orcid":"https://orcid.org/0009-0005-8359-5787"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Zhonghui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139009330","display_name":"Haitao Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Haitao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043761995","display_name":"C Shijia Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Chaofan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076724147","display_name":"Peijie Jiang","orcid":"https://orcid.org/0000-0002-0534-6989"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Peijie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136030426","display_name":"Mingliang Gong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gong, Mingliang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138973732","display_name":"Jia Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Jia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138968082","display_name":"Ziqi Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Ziqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139000305","display_name":"Zhiqiang Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Zhiqiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138965994","display_name":"Jun Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhou, Jun","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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.5845999717712402,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.5845999717712402,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.12860000133514404,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.050599999725818634,"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/rounding","display_name":"Rounding","score":0.8245999813079834},{"id":"https://openalex.org/keywords/recipe","display_name":"Recipe","score":0.815500020980835},{"id":"https://openalex.org/keywords/quantization","display_name":"Quantization (signal processing)","score":0.5641999840736389},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4959999918937683},{"id":"https://openalex.org/keywords/usable","display_name":"USable","score":0.4068000018596649},{"id":"https://openalex.org/keywords/shrinkage","display_name":"Shrinkage","score":0.37689998745918274},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.3646000027656555},{"id":"https://openalex.org/keywords/hadamard-transform","display_name":"Hadamard transform","score":0.29660001397132874}],"concepts":[{"id":"https://openalex.org/C136625980","wikidata":"https://www.wikidata.org/wiki/Q663208","display_name":"Rounding","level":2,"score":0.8245999813079834},{"id":"https://openalex.org/C2778671685","wikidata":"https://www.wikidata.org/wiki/Q219239","display_name":"Recipe","level":2,"score":0.815500020980835},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.5641999840736389},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5440999865531921},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5396000146865845},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4959999918937683},{"id":"https://openalex.org/C2780615836","wikidata":"https://www.wikidata.org/wiki/Q2471869","display_name":"USable","level":2,"score":0.4068000018596649},{"id":"https://openalex.org/C180145272","wikidata":"https://www.wikidata.org/wiki/Q7504144","display_name":"Shrinkage","level":2,"score":0.37689998745918274},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3716999888420105},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.3646000027656555},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30630001425743103},{"id":"https://openalex.org/C60292330","wikidata":"https://www.wikidata.org/wiki/Q1014065","display_name":"Hadamard transform","level":2,"score":0.29660001397132874},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2896000146865845},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.28690001368522644},{"id":"https://openalex.org/C61005703","wikidata":"https://www.wikidata.org/wiki/Q2145211","display_name":"Round-off error","level":2,"score":0.28290000557899475},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.2786000072956085},{"id":"https://openalex.org/C50050167","wikidata":"https://www.wikidata.org/wiki/Q4300498","display_name":"Slumping","level":2,"score":0.2777000069618225},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.26989999413490295},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C201866948","wikidata":"https://www.wikidata.org/wiki/Q228206","display_name":"Random number generation","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C81081738","wikidata":"https://www.wikidata.org/wiki/Q55542","display_name":"Lossless compression","level":3,"score":0.25999999046325684},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.25220000743865967},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.250900000333786}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.20381","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.20381","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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.2606.20381","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.20381","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions","score":0.4198254644870758}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"FP4":[0,15,99],"training":[1,93,133,141,192],"promises":[2],"substantial":[3],"reductions":[4],"in":[5,96],"memory":[6],"and":[7,18,24,78,110,155,175],"computation":[8],"cost":[9],"for":[10,91],"LLM":[11],"pretraining,":[12,159],"yet":[13],"current":[14],"hardware":[16],"paths":[17],"recipes,":[19],"including":[20],"NVIDIA":[21],"Blackwell/Rubin-class":[22],"systems":[23],"AMD":[25],"MI350-series":[26],"GPUs,":[27],"remain":[28],"centered":[29],"on":[30,124],"E2M1":[31,49],"data":[32],"elements.":[33],"In":[34,101],"this":[35,72,107,125],"study,":[36],"we":[37,127],"identify":[38],"a":[39,55,88,130],"fundamental":[40],"limitation":[41],"of":[42,65],"that":[43,71,135,181],"choice:":[44],"non-uniform":[45],"formats":[46],"such":[47],"as":[48,190],"inherently":[50],"suffer":[51],"from":[52,117],"Shrinkage":[53],"Bias,":[54],"systematic":[56],"negative":[57],"rounding":[58,146],"error":[59,109],"caused":[60],"by":[61,81,172],"the":[62,82,92,113],"geometric":[63],"asymmetry":[64],"their":[66],"representable":[67],"bins.":[68],"We":[69],"show":[70],"bias":[73],"accumulates":[74],"multiplicatively":[75],"across":[76],"layers":[77],"is":[79],"amplified":[80],"Random":[83],"Hadamard":[84],"Transform":[85],"(RHT),":[86],"providing":[87],"unified":[89],"explanation":[90],"instability":[94],"observed":[95],"existing":[97],"E2M1-based":[98,169],"recipes.":[100],"contrast,":[102],"uniform":[103,131,187],"grids":[104,189],"(E1M2/INT4)":[105],"bypass":[106],"grid-geometry":[108],"better":[111],"convert":[112],"improved":[114],"bucket":[115],"utilization":[116],"RHT":[118,137],"into":[119],"higher":[120],"quantization":[121],"quality.":[122],"Based":[123],"finding,":[126],"propose":[128],"UFP4,":[129],"4-bit":[132,188],"recipe":[134],"applies":[136],"to":[138,147],"all":[139],"three":[140],"GEMMs":[142],"while":[143],"restricting":[144],"stochastic":[145],"dY":[148],"alone.":[149],"On":[150],"Dense":[151],"1.5B,":[152],"MoE":[153,156],"7.9B,":[154],"124B":[157],"long-run":[158],"UFP4":[160],"consistently":[161],"achieves":[162],"lower":[163],"BF16-relative":[164],"loss":[165],"degradation":[166],"than":[167],"strong":[168],"baselines,":[170],"supported":[171],"scaling-law":[173],"analysis":[174],"ablation":[176],"studies.":[177],"Our":[178],"results":[179],"suggest":[180],"future":[182],"accelerators":[183],"should":[184],"support":[185],"E1M2/INT4-style":[186],"first-class":[191],"primitives":[193],"alongside":[194],"E2M1.":[195]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-06-20T00:00:00"}