SABON TARIHI WAJEN NINKA TEBURAN LAMBOBI

Ninka matrix biyu — teburan lambobi — yana ɗaya daga cikin ayyuka mafi asali a fannin kwamfuta. Idan aka yi shi ta hanyar makaranta, kuɗin ninka tebura biyu n da n yana girma kamar n³. Algorithm na Volker Strassen na 1969 shi ne na farko da ya yi mafi kyau — “subcubic” (ƙasa da cube), a kalmomin takardar — kuma tun daga lokacin masana lissafi suke auna ci gaba da lamba ɗaya: ma’aunin ω (omega), mafi ƙanƙantar ƙarfin n da ya isa yayin da teburan ke girma.

Strassen ya kawo shi ƙasa da 2.81. Shekaru da dama na aiki, da aka lissafa a cikin takardar, sun tura shi ƙasa zuwa kusan 2.37, da matakai masu ƙara ƙanƙanta. A 2026, Emilien Dupont da abokan aikinsa sun kai 2.371177. Reza Zadeh, na kamfanin Matroid, Inc., yanzu ya tabbatar da ω < 2.37115924.

Wasu zaɓaɓɓun ingantawa a iyakar sama ta ω, daga Strassen a 1969 zuwa wannan takarda. — Table 1, Zadeh (2026), arXiv:2610.10593, CC BY 4.0.

Girke-girke mai saituna 212,820

Waɗannan tarihi ba sa fitowa daga wata dabara mafi wayo don ƙananan tebura. Suna fitowa daga wani abu na algebra da ake kira Coppersmith–Winograd tensor, wanda za a iya yanka shi kuma a sake haɗa shi, a maimaitawa, zuwa ninke-ninken matrix masu zaman kansu da yawa. Yadda ake yanka shi wani babban tarin zaɓuɓɓuka ne ke ƙayyade shi: rarrabuwar yiwuwa (probability distributions), hukuncin entropy da girman matrix da aka ayyana mataki bayan mataki. Duk wani tarin zaɓuɓɓuka mai inganci yana ba da iyaka mai inganci; fasahar ita ce samun mai kyau.

Bisa tsarin Josh Alman da abokan aikinsa da kuma bayanin Dupont da abokan aikinsa, Zadeh ya daidaita lambobi 212,820 a lokaci guda, tare da gyare-gyare uku:

• Sake sikeli bisa muhimmanci. Wasu sassan ginin suna bayyana ne ba kasafai ba, don haka tasirinsu a kan sakamakon ƙarami ne kuma mai ingantawa da ƙyar yake motsa su. An sake sikelin kowace lamba gwargwadon nauyin da sashenta ke ɗauka.
• Maɓallai shida don wuraren cunkoso. Ma’auni na ƙarshe yana dogara ga mafi rauni cikin adadi uku masu gogayya a matakai uku. Wani gyara daban ya yi amfani da maɓallai shida kawai don kiyaye daidaitonsu.
• Fitarwa madaidaiciya. An mayar da girke-girken ƙarshe zuwa ɓangarorin lamba madaidaita masu ƙasa (denominator) na 2⁹⁶.

Hujja ta hanyar dubawa

Iyakar hujja ce da kwamfuta ta taimaka. Wani gajeren shiri, wanda ke amfani da ma’ajiyar daidaitacciya ta Python kawai — babu intanet, babu tsarin AI, babu ƙarin kunshin manhaja — yana sake gina kowace rarrabuwa daga ɓangarorin lambar madaidaita kuma yana kimanta sakamakon da zagayewa mai tabbaci. Yana gano cewa babban adadin tabbatacce ne, da kusan 8.5 cikin biliyan ɗaya, wanda ke tabbatar da iyakar. Marubucin ya jaddada abin da wannan ba ya rufewa: shirin lambar kwamfuta ce da za a iya bincika, ba tsara dukkan ka’idar a cikin mataimakin hujja ba, kuma binciken na gida ne, ba tare da da’awar cewa girke-girken shi ne mafi kyau da zai yiwu ba.

Marubucin ya kuma rubuta cewa kayan aikin AI masu ƙirƙira, waɗanda ba a ambaci sunayensu ba, sun taimaka wajen binciken lambobi, manhajar da rubutun takardar, kuma lambar farko ta dogara ga bayanan lissafi da Eric Naslund ya raba a bainar jama’a. Wata takardar shaidar kwamfuta ta jama’a daban, da aka fitar a ranar 5 ga Oktoba 2026, ta kai 2.371169353; sabuwar ƙimar ta fi ta ƙasa.

Mafi sauri, a ka’ida

Ribar a kan Dupont da abokan aikinsa ita ce 0.00001776 a ma’aunin. Kamar dukkan iyakokin da aka samu ta wannan hanya, tabbacin asymptotic ne: ma’aunin shi kaɗai ba ya faɗi daga wane girman matrix sabon algorithm zai doke waɗanda ake da su a zahiri. Abin da yake canzawa shi ne mafi kyawun amsar da aka sani ga tambayar da ke gudana tun 1969 — da wane sauri, a ka’ida, za a iya ninka teburan lambobi?