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min-h-screen bg-background text-primary","children":["$","$L16",null,{"title":"LoRA: Low-Rank Adaptation of Large Language Models","pdfUrl":"/journey/papers/lora-low-rank-adaptation-of-large-language-models.pdf","annotations":[{"id":"01M52S8E1BC2E2S5RAVV87PDXW","type":"text","color":"#f2c94c","content":{"text":"which freezes the pre- trained model weights and injects trainable rank decomposition matrices into each layer of the Transformer architecture, greatly reducing the number of trainable pa- rameters for downstream tasks","image":null},"position":{"page":1,"boundingRect":{"page":1,"x":0.23508968609865472,"y":0.40509058599167824,"width":0.5297566366837164,"height":0.056085298196948685},"rects":[{"page":1,"x":0.6154454526345291,"y":0.40509058599167824,"width":0.14940087014784192,"height":0.014563106796116505},{"page":1,"x":0.23508968609865472,"y":0.4195886789181692,"width":0.5297284455577355,"height":0.013522884882108182},{"page":1,"x":0.23508968609865472,"y":0.4335016470180305,"width":0.5297223694121357,"height":0.013522884882108182},{"page":1,"x":0.23508968609865472,"y":0.44661277739251043,"width":0.20388878792390694,"height":0.014563106796116505}]},"comments":[{"id":"01M52S8G92A3574DMCRD9GJ4QV","parentId":null,"isAi":false,"prompt":null,"html":"

Anche se il modello ha miliardi di parametri, per adattarlo a una nuova task potrebbe essere sufficiente muoversi lungo poche direzioni significative nello spazio dei parametri.

","text":"Anche se il modello ha miliardi di parametri, per adattarlo a una nuova task potrebbe essere sufficiente muoversi lungo poche direzioni significative nello spazio dei parametri.","createdAt":"2026-10-16T16:38:26.338Z","updatedAt":"2026-10-16T16:38:26.338Z","replies":[]}],"commentCount":1,"createdAt":"2026-10-16T16:38:24.044Z","updatedAt":"2026-10-16T16:38:24.044Z"},{"id":"01M52SJR70F4AJD0XC2GGSD9S4","type":"text","color":"#57c785","content":{"text":"LoRA performs on-par or better than fine- tuning in model quality on RoBERTa, DeBERTa, GPT-2, and GPT-3, despite hav- ing fewer trainable parameters, a higher training throughput, and, unlike adapters, no additional inference latency.","image":null},"position":{"page":1,"boundingRect":{"page":1,"x":0.23508968609865472,"y":0.47434119278779474,"width":0.5297271317965246,"height":0.056085298196948685},"rects":[{"page":1,"x":0.4902743899768778,"y":0.47434119278779474,"width":0.27452748388452913,"height":0.014563106796116505},{"page":1,"x":0.23508968609865472,"y":0.4888392857142857,"width":0.5297211651310257,"height":0.013522884882108182},{"page":1,"x":0.23508968609865472,"y":0.5026547330097088,"width":0.5297271317965246,"height":0.013522884882108182},{"page":1,"x":0.23508968609865472,"y":0.5158633841886269,"width":0.21038068420683856,"height":0.014563106796116505}]},"comments":[{"id":"01M52SJYDDXSQS1FWWMMDY1BC4","parentId":null,"isAi":false,"prompt":null,"html":"

Con LoRA recuperiamo la filosofia del pre-training generale seguito da una specializzazione per task, già centrale in GPT-1 e BERT. La novità è che, invece di aggiornare tutti i pesi del modello, impariamo piccole modifiche a basso rango da applicare alle trasformazioni interne. In questo modo possiamo mantenere un backbone condiviso e sviluppare adattamenti specifici senza dover conservare o riaddestrare una copia completa del modello.

","text":"Con LoRA recuperiamo la filosofia del pre-training generale seguito da una specializzazione per task, già centrale in GPT-1 e BERT. La novità è che, invece di aggiornare tutti i pesi del modello, impariamo piccole modifiche a basso rango da applicare alle trasformazioni interne. In questo modo possiamo mantenere un backbone condiviso e sviluppare adattamenti specifici senza dover conservare o riaddestrare una copia completa del modello.","createdAt":"2026-10-16T16:44:08.493Z","updatedAt":"2026-10-16T16:44:08.493Z","replies":[]}],"commentCount":1,"createdAt":"2026-10-16T16:44:02.144Z","updatedAt":"2026-10-16T16:44:02.144Z"},{"id":"01M52SQSMDKY0J065ERF1TF19A","type":"text","color":"#57c785","content":{"text":"pre-trained model can be shared and used to build many small LoRA modules for dif- ferent tasks","image":null},"position":{"page":2,"boundingRect":{"page":2,"x":0.23508968609865472,"y":0.31472130721220526,"width":0.5882311081137892,"height":0.02847607489597781},"rects":[{"page":2,"x":0.23986159525644618,"y":0.31472130721220526,"width":0.5834591989559977,"height":0.014563106796116505},{"page":2,"x":0.23508968609865472,"y":0.32863427531206657,"width":0.07704054486056615,"height":0.014563106796116505}]},"comments":[{"id":"01M52SS09MDEKYCQ83T50BKVHS","parentId":null,"isAi":false,"prompt":null,"html":"

Un Grande lavoro di generalizzazione poi può essere seguito da tanti piccola LoRA per andare a specializzare i modelli in determinati ambienti o renderli personalizzabili.

","text":"Un Grande lavoro di generalizzazione poi può essere seguito da tanti piccola LoRA per andare a specializzare i modelli in determinati ambienti o renderli personalizzabili.","createdAt":"2026-10-16T16:47:27.029Z","updatedAt":"2026-10-16T16:47:54.045Z","replies":[]}],"commentCount":1,"createdAt":"2026-10-16T16:46:47.437Z","updatedAt":"2026-10-16T16:46:47.437Z"},{"id":"01M52ST2HMF18WMYHDJF8RWHCP","type":"text","color":"#57c785","content":{"text":"LoRA makes training more efficient and lowers the hardware barrier to entry by up to 3 times when using adaptive optimizers since we do not need to calculate the gradients or maintain the optimizer states for most parameters","image":null},"position":{"page":2,"boundingRect":{"page":2,"x":0.23059238040393779,"y":0.3789658460471567,"width":0.5928124397859446,"height":0.04229152219140083},"rects":[{"page":2,"x":0.23059238040393779,"y":0.3789658460471567,"width":0.5927349005044843,"height":0.014563106796116505},{"page":2,"x":0.23508968609865472,"y":0.3934747746185853,"width":0.5883151340912276,"height":0.013522884882108182},{"page":2,"x":0.23508968609865472,"y":0.40669426144244103,"width":0.32826042688480944,"height":0.014563106796116505}]},"comments":[{"id":"01M52STV0AP6TMR03YG7K46R58","parentId":null,"isAi":false,"prompt":null,"html":"

Con il full fine-tuning dobbiamo mantenere per tutti i parametri allenabili:

pesi;
gradienti;
stati dell'ottimizzatore;
eventuali copie dei pesi a precisione maggiore.

Con LoRA, invece, i pesi originali rimangono congelati.

Quindi gradienti e stati di Adam vengono mantenuti soltanto per le matrici A e B.

","text":"Con il full fine-tuning dobbiamo mantenere per tutti i parametri allenabili:\n\npesi;\n\ngradienti;\n\nstati dell'ottimizzatore;\n\neventuali copie dei pesi a precisione maggiore.\n\nCon LoRA, invece, i pesi originali rimangono congelati.\n\nQuindi gradienti e stati di Adam vengono mantenuti soltanto per le matrici A e B.","createdAt":"2026-10-16T16:48:27.146Z","updatedAt":"2026-10-16T16:48:27.146Z","replies":[]}],"commentCount":1,"createdAt":"2026-10-16T16:48:02.100Z","updatedAt":"2026-10-16T16:48:02.100Z"},{"id":"01M52V0HYFVH0G4XWM4KCZX3W7","type":"area","color":"#57c785","content":{"text":null,"image":"$17"},"position":{"page":10,"boundingRect":{"page":10,"x":0.678065442825112,"y":0.33042757454923716,"width":0.14484655269058297,"height":0.06484320821775312},"rects":[]},"comments":[{"id":"01M52V0MJVRB8DMZZQN9CAEY1H","parentId":null,"isAi":false,"prompt":null,"html":"

A parità di parametri allenabili, può essere più efficace applicare LoRA a più matrici del Transformer con rank basso, piuttosto che concentrarsi su una sola matrice con rank elevato.

","text":"A parità di parametri allenabili, può essere più efficace applicare LoRA a più matrici del Transformer con rank basso, piuttosto che concentrarsi su una sola matrice con rank elevato.","createdAt":"2026-10-16T17:09:05.755Z","updatedAt":"2026-10-16T17:09:05.755Z","replies":[]}],"commentCount":1,"createdAt":"2026-10-16T17:09:03.055Z","updatedAt":"2026-10-16T17:09:03.055Z"},{"id":"01M52V42TNBGFYQSGKJC0HV18E","type":"text","color":"#f2c94c","content":{"text":"Table 6 shows that, surprisingly, LoRA already performs competitively with a very small r (more so for {Wq , Wv } than just Wq ). This suggests the update matrix ∆W could have a very small “intrinsic rank”.6","image":null},"position":{"page":10,"boundingRect":{"page":10,"x":0.1764994394618834,"y":0.8056627080443828,"width":0.6470657143357623,"height":0.04319088072122053},"rects":[{"page":10,"x":0.1764994394618834,"y":0.8056627080443828,"width":0.6470657143357623,"height":0.014563106796116505},{"page":10,"x":0.1764994394618834,"y":0.8209626386962552,"width":0.6469834947799888,"height":0.012482662968099861},{"page":10,"x":0.24559977578475337,"y":0.8258711858529819,"width":0.0063340807174887895,"height":0.008321775312066574},{"page":10,"x":0.1764994394618834,"y":0.8342363037447988,"width":0.11153294858376542,"height":0.012482662968099861},{"page":10,"x":0.1764994394618834,"y":0.8363709257975035,"width":0.10522094179161995,"height":0.012482662968099861}]},"comments":[{"id":"01M52V447NGN64Z02TWG4E4F26","parentId":null,"isAi":false,"prompt":null,"html":"

Anche se una matrice del Transformer contiene milioni di parametri, la modifica necessaria per adattarla a una task potrebbe essere rappresentabile attraverso poche direzioni indipendenti.

","text":"Anche se una matrice del Transformer contiene milioni di parametri, la modifica necessaria per adattarla a una task potrebbe essere rappresentabile attraverso poche direzioni indipendenti.","createdAt":"2026-10-16T17:11:00.085Z","updatedAt":"2026-10-16T17:11:00.085Z","replies":[]}],"commentCount":1,"createdAt":"2026-10-16T17:10:58.645Z","updatedAt":"2026-10-16T17:10:58.645Z"}],"backHref":"/en/journey","labels":{"back":"Back to The Journey","notes":"Notes & annotations","analysis":"Analysis","openAnalysis":"Open analysis","closeAnalysis":"Close analysis","resizeAnalysis":"Resize","page":"Page","loadError":"This PDF could not be loaded. Check that the exported paper is available.","source":"Source"},"analysis":"$L18","year":2021,"sourceUrl":"https://arxiv.org/pdf/2106.09685"}]}]

Work10 works

Projects8 projects

The Journey10 papers

About23 years

Work10 works

Projects8 projects

The Journey10 papers

About23 years

Work10 works

Projects8 projects

The Journey10 papers

About23 years