Quantinue: Quantization for Unlearning operator

Machine unlearning aims to make a trained model behave like a model retrained without designated forget data, and the resulting model is typically quantized for efficient deployment. Low-bit quantization, however, can undo unlearning by discarding parameter changes introduced during unlearning and recovering knowledge that was previously forgotten. Existing methods address this by making the unlearning stage more robust to quantization, but they still treat unlearning and quantization as two separate steps. We instead replace the two stages, unlearning and quantization, with quantization itself the unlearning operator. Quantization maps continuous weights to discrete codes while seeking to retain the original model behavior. We guide this mapping not only to retain the original model behavior on the retain data, but also to induce forgetting behavior on the forget data, directly constructing an unlearned low-bit model without a preceding continuous-space unlearning update. Activation statistics from forget and retain calibration data define an element-wise score that determines where and how strongly the assigned code deviates from the reconstruction-driven code. The resulting process separates ordinary quantization error from code-displacement error and compensates them separately, reducing compensation along forget-sensitive directions for the code displacement error. Both code assignment and error compensation use only forward calibration statistics, without gradient computation or fine-tuning. On the MUSE and TOFU benchmarks, our method achieves the lowest aggregate distance to the retrained reference among the compared methods in 4 bit precision. These results suggest that quantization, previously a threat to unlearning, can instead serve as an effective means of achieving it.