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Only B and A are trained; $W_0$ never moves during fine-tuning [ 5 ] . The effect on trainable parameter count for that one matrix is to fall from dk to r(d + k) , which is small whenever the chosen rank r is small relative to d and k — and because BA can be merged back into $W_0$ after training, LoRA adds no extra inference latency once deployed. Hu and colleagues report, for their comparison against full fine-tuning of GPT-3 175B, up to a 10,000-fold reduction in trainable parameters and a threefold reduction in GPU memory requirement, with quality on par with or better than full fine-tuning on the benchmarks they tested [ 5 ] . Those figures are the paper’s own reported comparison for a…

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