Interpretable sparse fine-tuning with TopKLoRA enables faithful circuit discovery

Fine-tuning on datasets of unknown origin can create a backdoor in the trained model when the data includes poisoned examples. Difficult to localise and remove, backdoors can persist through safety training. While parameter-efficient fine-tuning methods capture the full parameter changes introduced during training, they are not easily interpretable. We present the full method of TopKLoRA, extending the preliminary proposal of Masiak et al. (2025), an interpretable-by-design LoRA variant in which only the $k$ largest adapter latents are active at each token. Unlike SAEs, TopKLoRA is trained purely on downstream loss, where optimisation pressure incentivises learning functionally causal latents. We demonstrate this sparse LoRA adapter in a sleeper-agent backdoor case study where we create model organisms by fine-tuning gemma-2-2b, Qwen2.5-1.5B, and Qwen2.5-7B on a poisoned instruction-following dataset. For each organism, we identify and ablate a circuit that is both necessary and sufficient to implement the backdoor. Furthermore, our new fine-tuning method produces sparse circuits that are up to an order of magnitude smaller than a dense LoRA baseline, allowing surgical ablation of the malicious capability without sacrificing instruction-following performance. Finally, we propose a technique to construct model organisms with localised circuits using TopKLoRA latents and gradient-routing, which we use to validate the findings of our circuit search algorithm. We consider these findings as a step toward interpretable-by-design architectures that provide faithful units of analysis without compromising model performance. We share our code: https://github.com/interpretable-finetuning/TopKLoRA.