Equation 2 · Part 5 · Actually Deploying an Open-Weight Model in Production

Symbol A

W = W_0 + \Delta W = W_0 + BA, \qquad B \in \mathbb{R}^{d \times r},\ A \in \mathbb{R}^{r \times k},\ r \ll \min(d, k)

A

What this part means

trained.

Its job in the formula

A appears in the objective or constraint used by the optimization on the right.

Full expressionSymbol AArticle meaning

Where the article explains it

Only B and A are trained; $W_0$ never moves during fine-tuning [ 5 ] .

The passage around this formula

Low-Rank Adaptation, LoRA, takes a different approach: it freezes the pretrained weight matrix entirely and represents the update as the product of two much smaller matrices. For a frozen weight matrix $W_0$ $\in$ $\mathbb{R}^{d \times k}$ , LoRA represents the adapted weight as $W = W_0 + \Delta W = W_0 + BA, \qquad B \in \mathbb{R}^{d \times r},\ A \in \mathbb{R}^{r \times k},\ r \ll \min(d, k)$ . Only B and A are trained; $W_0$ never…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

[5] LoRA: Low-Rank Adaptation of Large Language Models ↗

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