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Equation 1 · Actually Deploying an Open-Weight Model in Production

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W0∈Rd×kW_0 \in \mathbb{R}^{d \times k}

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W0W_0

Symbol W_0

W0W_0 is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Rd×k\mathbb{R}^{d \times k}

Symbol R^d × k

RdR^d × k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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multiplication

multiplication

Multiply the quantities on either side.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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What the article says around this equation

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 W0W_0 ∈\in Rd×k\mathbb{R}^{d \times k} , LoRA represents the adapted weight as

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