Equation 1 · Part 3 · Actually Deploying an Open-Weight Model in Production

multiplication

W_0 \in \mathbb{R}^{d \times k}

multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

Full expressionmultiplicationArticle meaning

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

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Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

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Sources cited in the article section

[7] Llama Cookbook: LLM Fine-Tuning Overview ↗
[5] LoRA: Low-Rank Adaptation of Large Language Models ↗
[6] QLoRA: Efficient Finetuning of Quantized LLMs ↗

These citations provide research context; check each source for the exact claim it supports.