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LoRA (Low-Rank Adaptation)

Visual diagram · (in preparation) · Math · Worked example · 3 difficulty levels.

TL;DR. A parameter-efficient fine-tuning method injecting small trainable matrices into frozen pre-trained layers.

Technical Definition

A parameter-efficient fine-tuning method injecting small trainable matrices into frozen pre-trained layers.

How it works

LoRA freezes W and adds ΔW = BA where B and A are small matrices. With rank r=8 and d=4096, this adds 65K parameters instead of 16.7M. LoRA enables fine-tuning large models on consumer GPUs with zero additional inference latency.

Mathematical Notation

W' = W + BA    where B ∈ ℝ^{d×r}, A ∈ ℝ^{r×d}

Low-rank matrices B and A have far fewer parameters than the full weight matrix — a 256x reduction with r=8.

Related Concepts

  • Transformer — An architecture that uses self-attention to process sequences in parallel, powering modern language models like GPT and BERT.
  • Large Language Model (LLM) — A massive neural network trained on vast text corpora to understand and generate human language with remarkable fluency.
  • Fine-Tuning — Adapting a pre-trained model to a specific task by continuing training on a smaller, task-specific dataset.

Further Reading

  • LoRA Paper