How Much Can a LoRA Adapter Memorize? Measuring Adapter Capacity in Bits

Abstract

LoRA adapters are often shared on their own, and the amount of information they can hold about their training data bounds what sharing them can reveal. Following Morris et al. (2026), we measure this amount in bits by training adapters on frozen language models to memorize random token sequences. LoRA adapters store 2 to 3.4 bits per trainable parameter, less than full fine-tuning of the same model. The number of parameters alone does not set this amount: at equal size, adapters on MLP layers store more than adapters on attention layers, and a randomly initialized frozen model supports as much storage as a pretrained one once the scale of its output logits can be trained. We then train the same adapter on a task with supervised fine-tuning (SFT) and with GRPO. At the same accuracy, SFT stores about three times as much information specific to its training examples, and it stores most of the bits of secrets planted in the training data, which GRPO does not store because it rarely samples them.