Quantization-Aware Unlearning Methods

• The paper presents two leading frameworks, QUAIL and Q-MUL, which introduce innovative loss designs and gradient strategies to overcome quantization challenges in machine unlearning.
• The methods employ techniques like logits-space hinge loss, similar label assignment, and adaptive gradient reweighting to ensure weight updates exceed quantization thresholds.
• Empirical evaluations on language and image tasks demonstrate that these approaches achieve robust forgetting while preserving model performance in low-bit settings.

Quantization-aware unlearning encompasses methodologies designed to robustly remove specific data-derived knowledge from neural networks that employ low-bit quantization for model deployment. As quantization is increasingly used for on-device inference, especially under resource constraints, standard machine unlearning methods tailored for full-precision models are insufficient—quantization can negate unlearning by restoring the “forgotten” knowledge. Two leading quantization-aware unlearning frameworks, QUAIL (“Quantization Aware Unlearning for Mitigating Misinformation in LLMs” (Mishra et al., 21 Jan 2026)) and Q-MUL (“Robust Machine Unlearning for Quantized Neural Networks via Adaptive Gradient Reweighting with Similar Labels” (Tong et al., 18 Mar 2025)), specifically address these challenges through targeted loss design, data preprocessing, and gradient management strategies.

1. Challenges of Machine Unlearning Under Model Quantization

Neural network quantization applies a uniform or non-uniform discretization to model weights and activations, typically reducing precision to 2–8 bits. For a given bit-width $N$, the quantization step size is defined as

$\Delta = \frac{w_{\max} - w_{\min}}{2^N},$

where $w_{\min}$ and $w_{\max}$ specify the range for each quantized tensor. The quantization operator,

$$Q(w) = \Delta \, \mathrm{Round}\left( \frac{w - w_{\min}}{\Delta} \right) + w_{\min},$$

induces bucket collapse: weights differing by less than a quantization threshold $\Delta/2$ quantize to the same value.

Standard machine unlearning proceeds by applying small weight updates (e.g., via gradient ascent on the forget set $D_f$). In quantized models, mean absolute updates ($\approx 2.97 \times 10^{-5}$ for GA+GDR on LLaMA-2-7B) are much smaller than $\Delta/2 \approx 0.134$ for 4-bit weights, resulting in $>99.9\%$ bitwise overlap. Consequently, the quantized unlearned model $Q(\Theta')$ is nearly indistinguishable from the quantized original $Q(\Theta)$, restoring the targeted knowledge and undermining privacy and compliance objectives (Mishra et al., 21 Jan 2026). This issue is pervasive across quantization schemes (RTN, AWQ, GPTQ, LSQ+) and bit-widths: bucket overlap rises to $100\%$ at 4-bit quantization.

2. Frameworks for Quantization-Aware Unlearning

Two principal quantization-aware unlearning approaches have emerged:

• QUAIL introduces a logits-space hinge loss to enforce minimum output separation, inducing weight changes large enough to survive quantization.
• Q-MUL incorporates “Similar Labels” assignment and “Adaptive Gradient Reweighting” to balance update magnitudes and reduce gradient noise.

Comparative Table: Key Methods for Quantization-Aware Unlearning

Framework	Core Technique	Quantization Addressed
QUAIL	Logits-space hinge loss	Output margin $\Delta/2$
Q-MUL	Similar labels + AGR	Balanced updates/labels

QUAIL is specifically designed for LLMs and language/classification tasks; Q-MUL targets low-bit quantized classifiers and mobile networks.

3. QUAIL: Logits-Space Hinge Loss and Algorithmic Structure

QUAIL’s primary innovation is the imposition of a quantization-aware hinge loss:

$$\mathcal{L}_{\mathrm{hinge}}(z', z) = \frac{1}{K} \sum_{k=1}^K \max\left(0, \frac{\Delta_q}{2} - |z'_k - z_k|\right),$$

where $z$ and $z'$ are the output logits of the original and unlearned model respectively, for the same input, and $K$ is the number of output classes. Here, $\Delta_q$ is chosen to match the expected quantization logit step, with margin $=\Delta_q/2$ (empirically $=0.5$). This loss penalizes insufficient logit separation, promoting weight updates exceeding the quantization bucket threshold.

The overall QUAIL objective is

$$\mathcal{L}_{\mathrm{QUAIL}} = \alpha \mathcal{L}_{\mathrm{forget}} + (1-\alpha) \mathcal{L}_{\mathrm{retain}} + \gamma \mathcal{L}_{\mathrm{hinge}},$$

where $\alpha$ and $\gamma$ adjust the tradeoff between forgetting, retention, and quantization robustness.

Algorithmic workflow entails:

• Caching target logits for all forget examples to avoid redundant computation.
• Applying the hinge loss selectively, with gradient sparsity where logit separation is insufficient.
• Updating parameters via:

  θ_un ← θ_un - η·∇[α·L_forget + γ·L_hinge] θ_un ← θ_un - η·∇[(1-α)·L_retain]

  This mechanism ensures weight updates consistently cross quantization bucket thresholds.

4. Q-MUL: Similar Labels and Adaptive Gradient Reweighting

Q-MUL addresses two distinct limitations in quantized MU:

• Noise amplification from random labels: Assigning random labels to $D_f$ (the “random label” baseline) injects orthogonal gradients with near-zero model probability, often flipping weights by entire quantization steps and resulting in high error and instability. Q-MUL computes a “semantically closest” incorrect label $k_{sl}$ for each forget example by minimizing the absolute difference in softmax outputs:

$$k_{sl} = \arg\min_{k \neq y_i} |p_Q(k|x_i;\theta_q) - p_Q(y_i|x_i;\theta_q)|.$$

The cross-entropy loss is then applied to $(x_i, k_{sl})$ rather than $(x_i, y_i)$.

• Gradient imbalance in discrete training: The quantization process and straight-through estimator (STE) zero many parameter gradients, creating significant gradients magnitude imbalance between forget and retain sets. Adaptive Gradient Reweighting leverages the $\ell_2$ norms of the two sets’ gradients

$$G_f = \mathbb{E}[\|\nabla L_{\mathrm{forget}}\|_2], \quad G_r = \mathbb{E}[\|\nabla L_{\mathrm{retain}}\|_2],$$

to define weighting factors $\alpha_f=G_r/(G_f+G_r), \alpha_r=G_f/(G_f+G_r)$ in the objective. Updates are performed within a quantization-aware training (QAT) loop:

$$\theta_q^{t+1} = \text{Quant}\Big(\theta_q^t - \eta_t \nabla_\theta L_{\mathrm{weighted}}(\theta_q^t)\Big),$$

mitigating the imbalance and maintaining stability across discrete parameter changes.

5. Empirical Evaluation and Metrics

QUAIL and Q-MUL are empirically assessed across challenging benchmarks and quantization settings.

QUAIL: Evaluated primarily on language (MUSE NEWS) and Twitter Misinformation datasets using LLaMA-2-7B as base architecture (4-bit and 8-bit post-training quantization). Key metrics:

• VerMem (M1): average ROUGE-L F1 (lower is better)
• KnowMem$_f$ (M2): ROUGE on QA pairs from forget set (lower is better)
• PrivLeak (M3): AUC gap vs retrain (closer to 0 is better)
• KnowMem$_r$ (M4): QA accuracy on retain set (higher is better)

GA+GDR attains near-perfect forgetting in FP16 but exhibits $24.36$ VerMem degradation at 4-bit; QUAIL limits this degradation to $\sim9$ points and restores privacy metric M3 $\approx 0$, with high retention (M4 $\approx 50$) under 4-bit quantization (Mishra et al., 21 Jan 2026).

Q-MUL: Assessed on image classification datasets (CIFAR-10/100, SVHN, Tiny-ImageNet) using ResNet-18 and MobileNetV2 under LSQ+ QAT, and compared to gold-standard retraining and prior MU baselines. Performance is measured using Forget Accuracy (FA), Retain Accuracy (RA), Test Accuracy (TA), Membership Inference Attack accuracy (MIA), and Average Gap (AG). Q-MUL achieves the lowest AG ($3.11$ compared to RL $9.89$, SalUn $6.05$) and maintains balanced FA/RA/TA versus retraining (Tong et al., 18 Mar 2025). Similar label assignment and AGR step contribute critically to these improvements.

Method	FA	RA	TA	MIA	AG
Retrain	74.76	99.98	72.43	13.36	0.00
RL	68.51	98.91	69.47	85.62	9.89
SalUn	82.22	98.71	67.38	66.78	6.05
Q-MUL	75.71	97.89	67.27	52.11	3.11

6. Limitations and Open Problems

Both frameworks display sensitivity to hyperparameters governing loss tradeoff ($\alpha$, $\gamma$ in QUAIL; learning rate and batch schedules in Q-MUL). For QUAIL, too low a $\gamma$ fails to cross quantization thresholds, while excessive $\gamma$ impairs utility retention. Q-MUL exhibits modest compute overhead ($\approx 1.1\times$ RL) due to gradient norm statistics calculation.

Deployment constraints include focus on uniform post-training quantization (QUAIL) and layering limitations (embeddings and layer-norm not quantized), while Q-MUL has been mainly explored in classification networks. Neither approach currently provides worst-case or certified bounds on adversarial knowledge recovery post-quantization; future work may address theoretical guarantees and broader domain adaptation.

A plausible implication is that direct extension to detection, generative, and language modeling tasks (not yet covered by Q-MUL) could further broaden quantization-aware unlearning applicability, but may require new objective designs sensitive to task structure.

7. Significance and Future Directions

Quantization-aware unlearning establishes a necessary paradigm for enforcing data privacy and compliance (e.g., “right to be forgotten”) in on-device inference regimes. By explicitly characterizing quantization-induced failures of standard unlearning, and introducing loss, label, and gradient management tailored to discrete parameter spaces, frameworks like QUAIL and Q-MUL set state-of-the-art benchmarks for forgetting efficacy and utility retention in quantized networks.

Future directions include extension of quantization-aware methods to mixed-precision settings, systematic study under quantization-aware training (QAT), and development of theoretical security/robustness guarantees for persistent unlearning in quantized models.